Point Location. Preprocess a planar, polygonal subdivision for point location queries. p = (18, 11)


 Felicia Richard
 2 years ago
 Views:
Transcription
1 Point Location Prerocess a lanar, olygonal subdivision for oint location ueries. = (18, 11) Inut is a subdivision S of comlexity n, say, number of edges. uild a data structure on S so that for a uery oint = (x, y), we can find the face containing fast. Imortant metrics: sace and uery comlexity.
2 The Slab Method Draw a vertical line through each vertex. This decomoses the lane into slabs. In each slab, the vertical order of line segments remains constant. s5 D D s4 C C s3 s s1 Partition into slabs Slab 1 If we know which slab = (x, y) lies, we can erform a binary search, using the sorted order of segments.
3 The Slab Method To find which slab contains, we erform a binary search on x, among slab boundaries. second binary search in the slab determines the face containing. s5 D D s4 C C s3 s s1 Partition into slabs Slab 1 Thus, the search comlexity is O(log n). ut the sace comlexity is Θ(n ).
4 Otimal Schemes There are other schemes (kdtree, uadtrees) that can erform oint location reasonably well, they lack theoretical guarantees. Most have very bad worstcase erformance. inding an otimal scheme was challenging. Several schemes were develoed in 70 s that did either O(log n) uery, but with O(n log n) sace, or O(log n) uery with O(n) sace. Today, we will discuss an elegant and simle method that achieved otimality, O(log n) time and O(n) sace [D. Kirkatrick 83]. Kirkatrick s scheme however involves large constant factors, which make it less attractive in ractice. Later we will discuss a more ractical, randomized otimal scheme.
5 Kirkatrick s lgorithm Start with the assumtion that lanar subdivision is a triangulation. If not, triangulate each face, and label each triangular face with the same label as the original containing face. If the outer face is not a triangle, comute the convex hull, and triangulate the ockets between the subdivision and CH. Now ut a large triangle abc around the subdivision, and triangulate the sace between the two. a b c
6 Modifying Subdivision y Euler e formula, the final size of this triangulated subdivision is still O(n). This transformation from S to triangulation can be erformed in O(n log n) time. a b c If we can find the triangle containing, we will know the original subdivision face containing.
7 Hierarchical Method Kirkatrick s method is hierarchical: roduce a seuence of increasingly coarser triangulations, so that the last one has O(1) size. Seuence of triangulations T 0, T 1,..., T k, with following roerties: 1. T 0 is the initial triangulation, and T k is just the outer triangle abc.. k is O(log n). 3. Each triangle in T i+1 overlas O(1) triangles of T i. Let us first discuss how to construct this seuence of triangulations.
8 uilding the Seuence Main idea is to delete some vertices of T i. Their deletion creates holes, which we retriangulate. u v Vertex deletion and re triangulation We want to go from O(n) size subdivision T 0 to O(1) size subdivision T k in O(log n) stes. Thus, we need to delete a constant fraction of vertices from T i. critical condition is to ensure each new triangle in T i+1 overlas with O(1) triangles of T i.
9 Indeendent Sets Suose we want to go from T i to T i+1, by deleting some oints. Kirkatrick s choice of oints to be deleted had the following two roerties: [Constant Degree] Each deletion candidate has O(1) degree in grah T i. If has degree d, then deleting leaves a hole that can be filled with d triangles. When we retriangulate the hole, each new triangle can overla at most d original triangles in T i. u v Vertex deletion and re triangulation
10 Indeendent Sets [Indeendent Sets] No two deletion candidates are adjacent. This makes retriangulation easier; each hole handled indeendently. u v Vertex deletion and re triangulation
11 I.S. Lemma Lemma: Every lanar grah on n vertices contains an indeendent vertex set of size n/18 in which each vertex has degree at most 8. The set can be found in O(n) time. We rove this later. Let s use this now to build the triangle hierarchy, and show how to erform oint location. Start with T 0. Select an ind set S 0 of size n/18, with max degree 8. Never ick a, b, c, the outer triangle s vertices. Remove the vertices of S 0, and retriangulate the holes. Label the new triangulation T 1. It has at most 17 18n vertices. Recursively build the hierarchy, until T k is reduced to abc. The number of vertices dros by 17/18 each time, so the deth of hierarchy is k = log 18/17 n 1 log n
12 Illustration n k o y z T m j l i c d b e h 0 1 a f g T x v w r u s t T 3 H J I T E C G D T4 (not shown) K T 4 H I J T 3 C D E G T r s t u v w x y z T 1 a b c d e f g h i j k l m n o T 0
13 The Data Structure Modeled as a DG: the root corresonds to single triangle T k. The nodes at next level are triangles of T k 1. Each node for a triangle in T i+1 has ointers to all triangles of T i that it overlas. To locate a oint, start at the root. If outside T k, we are done (exterior face). Otherwise, set t = T k, as the triangle at current level containing. T n k o m j h g l i a c d f 0 1 b e T y z x v w u t r s T 3 H J I T G E D C T4 (not shown) K T 4 H I J T 3 C D E G T r s t u v w x y z T 1 a b c d e f g h i j k l m n o T 0
14 The Search H J I E G D C x y w v u r s z t n m k j l i a c d b e o h g f K H I J C D E G r s t u v w x y z a b c d e f g h i j k l m n o Check each triangle of T k 1 that overlas with t at most 6 such triangles. Udate t, and descend the structure until we reach T 0. Outut t.
15 nalysis H J I G E D C y z x v w u t r s n o m k j h g l i a c d f b e K H I J C D E G r s t u v w x y z a b c d e f g h i j k l m n o Search time is O(log n) there are O(log n) levels, and it takes O(1) time to move from level i to level i 1. Sace comlexity reuires summing u the sizes of all the triangulations. Since each triangulation is a lanar grah, it is sufficient to count the number of vertices. The total number of vertices in all triangulations is n ( 1 + (17/18) + (17/18) + (17/18) 3 + ) 18n. Kirkatrick structure has O(n) sace and O(log n) uery time.
16 inding I.S. We describe an algorithm for finding the indeendent set with desired roerties. Mark all nodes of degree 9. While there is an unmarked node, do 1. Choose an unmarked node v.. dd v to IS. 3. Mark v and all its neighbors. lgorithm can be imlemented in O(n) time kee unmarked vertices in list, and reresenting T so that neighbors can be found in O(1) time. v
17 I.S. nalysis Existence of large size, low degree IS follows from Euler s formula for lanar grahs. triangulated lanar grah on n vertices has e = 3n 6 edges. Summing over the vertex degrees, we get deg(v) = e = 6n 1 < 6n. v We now claim that at least n/ vertices have degree 8. Suose otherwise. Then n/ vertices all have degree 9. The remaining have degree at least 3. (Why?) Thus, the sum of degrees will be at least 9 n + 3n = 6n, which contradicts the degree bound above. So, in the beginning, at least n/ nodes are unmarked. Each chosen v marks at most 8 other nodes (total 9 counting itself.) Thus, the node selection ste can be reeated at least n/18 times. So, there is a I.S. of size n/18, where each node has degree 8.
18 Traezoidal Mas randomized oint location scheme, with (exected) uery O(log n), sace O(n), and construction time O(n log n). The exectation does not deend on the olygonal subdivision. The bounds holds for any subdivision. It aears simler to imlement, and its constant factors are better than Kirkatrick s. The algorithm is based on traezoidal mas, or decomositions, also encountered earlier in triangulation.
19 Traezoidal Mas Inut a set of nonintersecting line segments S = {,,..., s n }. Query: given oint, reort the segment directly above. The region label can be easily encoded into the line segments. Ma is created by shooting a ray vertically from each vertex, u and down, until a segment is hit. In order to avoid degeneracies, assume that no segment is vertical. The resulting rays lus the segments define the traezoidal ma.
20 Traezoidal Mas Enclose S into a bounding box to avoid infinite rays. ll faces of the subdivision are traezoids, with vertical sides. Size Claim: If S has n segments, the ma has at most 6n + 4 vertices and 3n + 1 tras. Each vertex shoots one ray, each resulting in two new vertices, so at most 6n vertices, lus 4 for the outer box. The left boundary of each traezoid is defined by a segment endoint, or lower left corner of enclosing box. The corner of box acts as leftoint for one tra; the right endoint of any segment also for one tra; and left endoint of any segment for at most traezoids. So total of 3n + 1.
21 Construction Plane swee ossible, but not helful for oint location. Instead we use randomized incremental construction. Historically, invented for randomized segment intersection. Point location an intermediate roblem. Start with outer box, one traezoid. Then, add one segment at a time, in an arbitrary, not sorted, order. / s / / i efore fter inserting s
22 Construction Let S i = {,,..., s i } be first i segments, and T i be their traezoidal ma. Suose T i 1 built, and we add s i. ind the traezoid containing the left endoint of s i. Defer for now: this is oint location. Walk through T i 1, identifying traezoids that are cut. Then, fix them u. ixing u means, shoot rays from left and right endoints of s i, and trim the earlier rays that are cut by s i. / s / / i efore fter inserting s
23 nalysis Observation: inal structure of tra ma does not deend on the order of segments. (Why?) Claim: Ignoring oint location, segment i s insertion takes O(k i ) time if k i new traezoids created. Proof: Each endoint of s i shoots two rays. dditionally, suose s i interruts K existing ray shots, so total of K + 4 rays need rocessing. If K = 0, we get exactly 4 new traezoids. or each interruted ray shot, a new traezoid created. With DCEL, udate takes O(1) er ray. efore fter
24 Worst Case In a worstcase, k i can be Θ(i). This can haen for all i, making the worstcase run time n i=1 i = Θ(n ). Using randomization, we rove that if segments are inserted in random order, then exected value of k i is O(1)! So, for each segment s i, the exected number of new traezoids created is a constant. igure below shows a worstcase examle. How will randomization hel? n/ + 1 n 1 n/
25 Randomization Theorem: ssume,,..., s n is a random ermutation. Then, E[k i ] = O(1), where k i traezoids created uon s i s insertion, and the exectation is over all ermutations. Proof. 1. Consider T i, the ma after s i s insertion.. T i does not deend on the order in which segments,..., s i were added. 3. Reshuffle,..., s i. What s the robability that a articular s was the last segment added? 4. The robability i/i. 5. We want to comute the number of traezoids that would have been created if s were the last segment. s The traezoids that deend on s The segments that the traezoid deends on.
26 Proof Say traezoid deends on s if would be created by s if s were added last. Want to count traezoids that deend on each segment, and then find the average over all segments. Define δ(, s) = 1 if deends on s; otherwise, δ(, s) = 0. s The traezoids that deend on s The exected comlexity is E[k i ] = 1 ix s S i The segments that the traezoid deends on. Xδ(, s) T i Some segments create a lot of traezoids; others very few. X X Switch the order of summation: E[k i ] = 1 δ(, s) i s S i T i
27 Proof s The segments that the traezoid The traezoids that deend on s deends on. Now we are counting number Xof segments X each traezoid deents on. E[k i ] = 1 δ(, s) i s S i T i This is much easier each deends on at most 4 segments. To and bottom of defined by two segments; if either of them added last, then comes into existence. Left and right sides defined by two segments endoints, and if either one added last, is created. Thus,Ps S δ(, s) 4. i T i X has O(i) traezoids, so E[k i ] = = i i 4 T i = 1 O(i) = O(1). i T i End of roof.
28 Point Location Like Kirkatrick s, oint location structure is a rooted directed acyclic grah. To uery rocessor, it looks like a binary tree, but subtree may be shared. Tree has two tyes of nodes: xnode: contains the xcoordinate of a segment endoint. (Circle) ynode: ointer to a segment. (Hexagon) leaf for each trazedoid. 1 C D 1 E G 1 C D 1 E G
29 Point Location Children of xnode corresond to oints lying to the left and right of x coord. Children of ynode corresond to sace below and above the segment. ynode searched only when uery s xcoordinate is within segment s san. Examle: uery in region D. 1 C D 1 E G 1 C D 1 E G Encodes the tra decomosition, and enables oint location during the construction as well.
30 uilding the Structure Incremental construction, mirroring the traezoidal ma. When a segment s added, modify the tree to account for changes in traezoids. Essentially, some leaves will be relaced by new subtrees. Like Kirkatrick s, each old traezoid will overla O(1) new traezoids. 1 C D 1 E G 1 C D 1 E G Each traezoid aears exactly once as a leaf. or instance,.
31 dding a Segment Consider adding segment s 3. 1 C D 1 E G 1 C D 1 E G K 1 1 s I 1 s N L M H J H 1 1 s 3 s 3 3 s 3 s 3 3 M N I J K L
32 dding a Segment Changes are highly local. If segment s asses entirely through an old traezoid t, then t is relaced by two tras t, t. During search, we need to comare uery oint to s to decide above/below. So, a new ynode added which is the arent of t and t. If an endoint of s lies in t, then we add a xnode to decide left/right and a ynode for the segment. K 1 1 s I 1 s N L M H J H 1 1 s 3 s 3 3 s 3 s 3 3 M N I J K L
33 nalysis Sace is O(n), and uery time is O(log n), both in exectation. Exected bound deends on the random ermutation, and not on the choice of inut segments or the uery oint. The data structure size number of traezoids, which is O(n), since O(1) exected number of tras created when a new segment inserted. In order to analyze uery bound, fix a uery. We consider how moves incrementally through the traezoidal ma as new segments are inserted. Search comlexity number of traezoids encountered by.
34 Search nalysis Let i be traezoid containing after insertion of ith segment. If i = i 1 then new insertion does not affect s traezoid. (E.g. and s 3 s insertion.) If i i 1, then new segment deleted s traezoid, and needs to locate itself among the (at most 4) new tras. could fall 3 levels in the tree. E.g. C falling to J after s 3 s insertion. K 1 1 s I 1 s N L M H J H 1 1 s 3 s 3 3 s 3 s 3 3 M N I J K L
35 Search nalysis Let P i be robability that i i 1, over all random ermutation. Since can dro 3 levels, exected search ath length is n i=1 3P i. We will show that P i 4/i. That will imly that exected search ath length is n n 4 3 i = 1 1 = 1 ln n i i=1 i=1 Why is P i 4/i? Use backward analysis. The traezoid i deends on at most 4 segments. The robability that ith segment is one of these 4 is at most 4/i. 1 C D 1 E G 1 C D 1 E G
36 inal Remarks Exectation only says that average search ath is small. It can still have large variance. The traezoidal ma data structure has bounds on variance too. See the textbook for comlete analysis. Theorem: or any λ > 0, the robability that deth of the randomized seach structure exceeds 3λ ln(n + 1) is at most (n + 1) λ ln More careful analysis can rovide better constants for the data structure.
The Online Freezetag Problem
The Online Freezetag Problem Mikael Hammar, Bengt J. Nilsson, and Mia Persson Atus Technologies AB, IDEON, SE3 70 Lund, Sweden mikael.hammar@atus.com School of Technology and Society, Malmö University,
More informationIntroduction to NPCompleteness Written and copyright c by Jie Wang 1
91.502 Foundations of Comuter Science 1 Introduction to Written and coyright c by Jie Wang 1 We use timebounded (deterministic and nondeterministic) Turing machines to study comutational comlexity of
More informationThe Priority RTree: A Practically Efficient and WorstCase Optimal RTree
The Priority RTree: A Practically Efficient and WorstCase Otimal RTree Lars Arge Deartment of Comuter Science Duke University, ox 90129 Durham, NC 277080129 USA large@cs.duke.edu Mark de erg Deartment
More information6.042/18.062J Mathematics for Computer Science December 12, 2006 Tom Leighton and Ronitt Rubinfeld. Random Walks
6.042/8.062J Mathematics for Comuter Science December 2, 2006 Tom Leighton and Ronitt Rubinfeld Lecture Notes Random Walks Gambler s Ruin Today we re going to talk about onedimensional random walks. In
More informationThe Optimal Sequenced Route Query
The Otimal Sequenced Route Query Mehdi Sharifzadeh, Mohammad Kolahdouzan, Cyrus Shahabi Comuter Science Deartment University of Southern California Los Angeles, CA 900890781 [sharifza, kolahdoz, shahabi]@usc.edu
More informationAutomatic Search for Correlated Alarms
Automatic Search for Correlated Alarms KlausDieter Tuchs, Peter Tondl, Markus Radimirsch, Klaus Jobmann Institut für Allgemeine Nachrichtentechnik, Universität Hannover Aelstraße 9a, 0167 Hanover, Germany
More informationMemory management. Chapter 4: Memory Management. Memory hierarchy. In an ideal world. Basic memory management. Fixed partitions: multiple programs
Memory management Chater : Memory Management Part : Mechanisms for Managing Memory asic management Swaing Virtual Page relacement algorithms Modeling age relacement algorithms Design issues for aging systems
More informationSQUARE GRID POINTS COVERAGED BY CONNECTED SOURCES WITH COVERAGE RADIUS OF ONE ON A TWODIMENSIONAL GRID
International Journal of Comuter Science & Information Technology (IJCSIT) Vol 6, No 4, August 014 SQUARE GRID POINTS COVERAGED BY CONNECTED SOURCES WITH COVERAGE RADIUS OF ONE ON A TWODIMENSIONAL GRID
More informationStatic and Dynamic Properties of Smallworld Connection Topologies Based on Transitstub Networks
Static and Dynamic Proerties of Smallworld Connection Toologies Based on Transitstub Networks Carlos Aguirre Fernando Corbacho Ramón Huerta Comuter Engineering Deartment, Universidad Autónoma de Madrid,
More informationOn Multicast Capacity and Delay in Cognitive Radio Mobile Adhoc Networks
On Multicast Caacity and Delay in Cognitive Radio Mobile Adhoc Networks Jinbei Zhang, Yixuan Li, Zhuotao Liu, Fan Wu, Feng Yang, Xinbing Wang Det of Electronic Engineering Det of Comuter Science and Engineering
More informationA Modified Measure of Covert Network Performance
A Modified Measure of Covert Network Performance LYNNE L DOTY Marist College Deartment of Mathematics Poughkeesie, NY UNITED STATES lynnedoty@maristedu Abstract: In a covert network the need for secrecy
More informationLargeScale IP Traceback in HighSpeed Internet: Practical Techniques and Theoretical Foundation
LargeScale IP Traceback in HighSeed Internet: Practical Techniques and Theoretical Foundation Jun Li Minho Sung Jun (Jim) Xu College of Comuting Georgia Institute of Technology {junli,mhsung,jx}@cc.gatech.edu
More informationwhere a, b, c, and d are constants with a 0, and x is measured in radians. (π radians =
Introduction to Modeling 3.61 3.6 Sine and Cosine Functions The general form of a sine or cosine function is given by: f (x) = asin (bx + c) + d and f(x) = acos(bx + c) + d where a, b, c, and d are constants
More informationX How to Schedule a Cascade in an Arbitrary Graph
X How to Schedule a Cascade in an Arbitrary Grah Flavio Chierichetti, Cornell University Jon Kleinberg, Cornell University Alessandro Panconesi, Saienza University When individuals in a social network
More informationPOISSON PROCESSES. Chapter 2. 2.1 Introduction. 2.1.1 Arrival processes
Chater 2 POISSON PROCESSES 2.1 Introduction A Poisson rocess is a simle and widely used stochastic rocess for modeling the times at which arrivals enter a system. It is in many ways the continuoustime
More informationThe MagnusDerek Game
The MagnusDerek Game Z. Nedev S. Muthukrishnan Abstract We introduce a new combinatorial game between two layers: Magnus and Derek. Initially, a token is laced at osition 0 on a round table with n ositions.
More information1 Gambler s Ruin Problem
Coyright c 2009 by Karl Sigman 1 Gambler s Ruin Problem Let N 2 be an integer and let 1 i N 1. Consider a gambler who starts with an initial fortune of $i and then on each successive gamble either wins
More informationENFORCING SAFETY PROPERTIES IN WEB APPLICATIONS USING PETRI NETS
ENFORCING SAFETY PROPERTIES IN WEB APPLICATIONS USING PETRI NETS Liviu Grigore Comuter Science Deartment University of Illinois at Chicago Chicago, IL, 60607 lgrigore@cs.uic.edu Ugo Buy Comuter Science
More informationCABRS CELLULAR AUTOMATON BASED MRI BRAIN SEGMENTATION
XI Conference "Medical Informatics & Technologies"  2006 Rafał Henryk KARTASZYŃSKI *, Paweł MIKOŁAJCZAK ** MRI brain segmentation, CT tissue segmentation, Cellular Automaton, image rocessing, medical
More informationProject Management and. Scheduling CHAPTER CONTENTS
6 Proect Management and Scheduling HAPTER ONTENTS 6.1 Introduction 6.2 Planning the Proect 6.3 Executing the Proect 6.7.1 Monitor 6.7.2 ontrol 6.7.3 losing 6.4 Proect Scheduling 6.5 ritical Path Method
More informationMachine Learning with Operational Costs
Journal of Machine Learning Research 14 (2013) 19892028 Submitted 12/11; Revised 8/12; Published 7/13 Machine Learning with Oerational Costs Theja Tulabandhula Deartment of Electrical Engineering and
More informationLocal Connectivity Tests to Identify Wormholes in Wireless Networks
Local Connectivity Tests to Identify Wormholes in Wireless Networks Xiaomeng Ban Comuter Science Stony Brook University xban@cs.sunysb.edu Rik Sarkar Comuter Science Freie Universität Berlin sarkar@inf.fuberlin.de
More informationIdentity based and CCAsecure encryption
Identity based and CCAsecure encrytion By Ilia Lotosh Based on [BF 03], [BCHK 07] Agenda Definition of IDbased encrytion Possible alications CCAsecure encrytion based on IBE BonehFranklin construction
More informationSoftware Cognitive Complexity Measure Based on Scope of Variables
Software Cognitive Comlexity Measure Based on Scoe of Variables Kwangmyong Rim and Yonghua Choe Faculty of Mathematics, Kim Il Sung University, D.P.R.K mathchoeyh@yahoo.com Abstract In this aer, we define
More informationAssignment 9; Due Friday, March 17
Assignment 9; Due Friday, March 17 24.4b: A icture of this set is shown below. Note that the set only contains oints on the lines; internal oints are missing. Below are choices for U and V. Notice that
More informationGreeting Card Boxes. Preparation and Materials. Planning chart
Leader Overview ACTIVITY 13 Greeting Card Boxes In this activity, members of your grou make cool boxes out of old (or new) greeting cards or ostcards. But first, they ractice making boxes from grid aer,
More informationRisk and Return. Sample chapter. e r t u i o p a s d f CHAPTER CONTENTS LEARNING OBJECTIVES. Chapter 7
Chater 7 Risk and Return LEARNING OBJECTIVES After studying this chater you should be able to: e r t u i o a s d f understand how return and risk are defined and measured understand the concet of risk
More informationAlgorithms for Constructing ZeroDivisor Graphs of Commutative Rings Joan Krone
Algorithms for Constructing ZeroDivisor Grahs of Commutative Rings Joan Krone Abstract The idea of associating a grah with the zerodivisors of a commutative ring was introduced in [3], where the author
More informationA MOST PROBABLE POINTBASED METHOD FOR RELIABILITY ANALYSIS, SENSITIVITY ANALYSIS AND DESIGN OPTIMIZATION
9 th ASCE Secialty Conference on Probabilistic Mechanics and Structural Reliability PMC2004 Abstract A MOST PROBABLE POINTBASED METHOD FOR RELIABILITY ANALYSIS, SENSITIVITY ANALYSIS AND DESIGN OPTIMIZATION
More informationApproximation Algorithms
Approximation Algorithms or: How I Learned to Stop Worrying and Deal with NPCompleteness Ong Jit Sheng, Jonathan (A0073924B) March, 2012 Overview Key Results (I) General techniques: Greedy algorithms
More informationEECS 122: Introduction to Communication Networks Homework 3 Solutions
EECS 22: Introduction to Communication Networks Homework 3 Solutions Solution. a) We find out that onelayer subnetting does not work: indeed, 3 deartments need 5000 host addresses, so we need 3 bits (2
More information4 Perceptron Learning Rule
Percetron Learning Rule Objectives Objectives  Theory and Examles  Learning Rules  Percetron Architecture 3 SingleNeuron Percetron 5 MultileNeuron Percetron 8 Percetron Learning Rule 8 Test Problem
More informationCoin ToGa: A CoinTossing Game
Coin ToGa: A CoinTossing Game Osvaldo Marrero and Paul C Pasles Osvaldo Marrero OsvaldoMarrero@villanovaedu studied mathematics at the University of Miami, and biometry and statistics at Yale University
More informationERDŐS SZEKERES THEOREM WITH FORBIDDEN ORDER TYPES. II
ERDŐS SEKERES THEOREM WITH FORBIDDEN ORDER TYPES. II GYULA KÁROLYI Institute of Mathematics, Eötvös University, Pázmány P. sétány /C, Budaest, H 7 Hungary GÉA TÓTH Alfréd Rényi Institute of Mathematics,
More informationSynopsys RURAL ELECTRICATION PLANNING SOFTWARE (LAPER) Rainer Fronius Marc Gratton Electricité de France Research and Development FRANCE
RURAL ELECTRICATION PLANNING SOFTWARE (LAPER) Rainer Fronius Marc Gratton Electricité de France Research and Develoment FRANCE Synosys There is no doubt left about the benefit of electrication and subsequently
More informationCSI:FLORIDA. Section 4.4: Logistic Regression
SI:FLORIDA Section 4.4: Logistic Regression SI:FLORIDA Reisit Masked lass Problem.5.5 2 .5  .5 .5  .5.5.5 We can generalize this roblem to two class roblem as well! SI:FLORIDA Reisit Masked lass
More informationTRANSCENDENTAL NUMBERS
TRANSCENDENTAL NUMBERS JEREMY BOOHER. Introduction The Greeks tried unsuccessfully to square the circle with a comass and straightedge. In the 9th century, Lindemann showed that this is imossible by demonstrating
More informationA Note on Integer Factorization Using Lattices
A Note on Integer Factorization Using Lattices Antonio Vera To cite this version: Antonio Vera A Note on Integer Factorization Using Lattices [Research Reort] 2010, 12 HAL Id: inria00467590
More informationImproved Symmetric Lists
Imroved Symmetric Lists Technical Reort MIP49 October, 24 Christian Bachmaier and Marcus Raitner University of Passau, 943 Passau, Germany Fax: +49 85 59 332 {bachmaier,raitner}@fmi.uniassau.de Abstract.
More informationAn Introduction to Risk Parity Hossein Kazemi
An Introduction to Risk Parity Hossein Kazemi In the aftermath of the financial crisis, investors and asset allocators have started the usual ritual of rethinking the way they aroached asset allocation
More informationThe risk of using the Q heterogeneity estimator for software engineering experiments
Dieste, O., Fernández, E., GarcíaMartínez, R., Juristo, N. 11. The risk of using the Q heterogeneity estimator for software engineering exeriments. The risk of using the Q heterogeneity estimator for
More informationArrangements And Duality
Arrangements And Duality 3.1 Introduction 3 Point configurations are tbe most basic structure we study in computational geometry. But what about configurations of more complicated shapes? For example,
More informationFinding a Needle in a Haystack: Pinpointing Significant BGP Routing Changes in an IP Network
Finding a Needle in a Haystack: Pinointing Significant BGP Routing Changes in an IP Network Jian Wu, Zhuoqing Morley Mao University of Michigan Jennifer Rexford Princeton University Jia Wang AT&T Labs
More informationComputational Finance The Martingale Measure and Pricing of Derivatives
1 The Martingale Measure 1 Comutational Finance The Martingale Measure and Pricing of Derivatives 1 The Martingale Measure The Martingale measure or the Risk Neutral robabilities are a fundamental concet
More informationF inding the optimal, or valuemaximizing, capital
Estimating RiskAdjusted Costs of Financial Distress by Heitor Almeida, University of Illinois at UrbanaChamaign, and Thomas Philion, New York University 1 F inding the otimal, or valuemaximizing, caital
More informationThe Cubic Formula. The quadratic formula tells us the roots of a quadratic polynomial, a polynomial of the form ax 2 + bx + c. The roots (if b 2 b+
The Cubic Formula The quadratic formula tells us the roots of a quadratic olynomial, a olynomial of the form ax + bx + c. The roots (if b b+ 4ac 0) are b 4ac a and b b 4ac a. The cubic formula tells us
More informationRisk in Revenue Management and Dynamic Pricing
OPERATIONS RESEARCH Vol. 56, No. 2, March Aril 2008,. 326 343 issn 0030364X eissn 15265463 08 5602 0326 informs doi 10.1287/ore.1070.0438 2008 INFORMS Risk in Revenue Management and Dynamic Pricing Yuri
More informationAn important observation in supply chain management, known as the bullwhip effect,
Quantifying the Bullwhi Effect in a Simle Suly Chain: The Imact of Forecasting, Lead Times, and Information Frank Chen Zvi Drezner Jennifer K. Ryan David SimchiLevi Decision Sciences Deartment, National
More informationDesign of A Knowledge Based Trouble Call System with Colored Petri Net Models
2005 IEEE/PES Transmission and Distribution Conference & Exhibition: Asia and Pacific Dalian, China Design of A Knowledge Based Trouble Call System with Colored Petri Net Models HuiJen Chuang, ChiaHung
More informationStochastic Derivation of an Integral Equation for Probability Generating Functions
Journal of Informatics and Mathematical Sciences Volume 5 (2013), Number 3,. 157 163 RGN Publications htt://www.rgnublications.com Stochastic Derivation of an Integral Equation for Probability Generating
More informationMultiperiod Portfolio Optimization with General Transaction Costs
Multieriod Portfolio Otimization with General Transaction Costs Victor DeMiguel Deartment of Management Science and Oerations, London Business School, London NW1 4SA, UK, avmiguel@london.edu Xiaoling Mei
More informationPRIME NUMBERS AND THE RIEMANN HYPOTHESIS
PRIME NUMBERS AND THE RIEMANN HYPOTHESIS CARL ERICKSON This minicourse has two main goals. The first is to carefully define the Riemann zeta function and exlain how it is connected with the rime numbers.
More information2D Modeling of the consolidation of soft soils. Introduction
D Modeling of the consolidation of soft soils Matthias Haase, WISMUT GmbH, Chemnitz, Germany Mario Exner, WISMUT GmbH, Chemnitz, Germany Uwe Reichel, Technical University Chemnitz, Chemnitz, Germany Abstract:
More informationA Study of Active Queue Management for Congestion Control
In IEEE INFOCOM 2 A Study of Active Queue Management for Congestion Control Victor Firoiu Marty Borden 1 vfiroiu@nortelnetworks.com mborden@tollbridgetech.com Nortel Networks TollBridge Technologies 6
More informationUnited Arab Emirates University College of Sciences Department of Mathematical Sciences HOMEWORK 1 SOLUTION. Section 10.1 Vectors in the Plane
United Arab Emirates University College of Sciences Deartment of Mathematical Sciences HOMEWORK 1 SOLUTION Section 10.1 Vectors in the Plane Calculus II for Engineering MATH 110 SECTION 0 CRN 510 :00 :00
More informationTimeCost TradeOffs in ResourceConstraint Project Scheduling Problems with Overlapping Modes
TimeCost TradeOffs in ResourceConstraint Proect Scheduling Problems with Overlaing Modes François Berthaut Robert Pellerin Nathalie Perrier Adnène Hai February 2011 CIRRELT201110 Bureaux de Montréal
More informationDiscrete Stochastic Approximation with Application to Resource Allocation
Discrete Stochastic Aroximation with Alication to Resource Allocation Stacy D. Hill An otimization roblem involves fi nding the best value of an obective function or fi gure of merit the value that otimizes
More informationWeb Application Scalability: A ModelBased Approach
Coyright 24, Software Engineering Research and Performance Engineering Services. All rights reserved. Web Alication Scalability: A ModelBased Aroach Lloyd G. Williams, Ph.D. Software Engineering Research
More informationModeling and Simulation of an Incremental Encoder Used in Electrical Drives
10 th International Symosium of Hungarian Researchers on Comutational Intelligence and Informatics Modeling and Simulation of an Incremental Encoder Used in Electrical Drives János Jób Incze, Csaba Szabó,
More informationA Simple Model of Pricing, Markups and Market. Power Under Demand Fluctuations
A Simle Model of Pricing, Markus and Market Power Under Demand Fluctuations Stanley S. Reynolds Deartment of Economics; University of Arizona; Tucson, AZ 85721 Bart J. Wilson Economic Science Laboratory;
More informationThe Fundamental Incompatibility of Scalable Hamiltonian Monte Carlo and Naive Data Subsampling
The Fundamental Incomatibility of Scalable Hamiltonian Monte Carlo and Naive Data Subsamling Michael Betancourt Deartment of Statistics, University of Warwick, Coventry, UK CV4 7A BETANAPHA@GMAI.COM Abstract
More informationA 60,000 DIGIT PRIME NUMBER OF THE FORM x 2 + x Introduction StarkHeegner Theorem. Let d > 0 be a squarefree integer then Q( d) has
A 60,000 DIGIT PRIME NUMBER OF THE FORM x + x + 4. Introduction.. Euler s olynomial. Euler observed that f(x) = x + x + 4 takes on rime values for 0 x 39. Even after this oint f(x) takes on a high frequency
More informationLarge firms and heterogeneity: the structure of trade and industry under oligopoly
Large firms and heterogeneity: the structure of trade and industry under oligooly Eddy Bekkers University of Linz Joseh Francois University of Linz & CEPR (London) ABSTRACT: We develo a model of trade
More informationBranchandPrice for Service Network Design with Asset Management Constraints
BranchandPrice for Servicee Network Design with Asset Management Constraints Jardar Andersen Roar Grønhaug Mariellee Christiansen Teodor Gabriel Crainic December 2007 CIRRELT200755 BranchandPrice
More informationEffect Sizes Based on Means
CHAPTER 4 Effect Sizes Based on Means Introduction Raw (unstardized) mean difference D Stardized mean difference, d g Resonse ratios INTRODUCTION When the studies reort means stard deviations, the referred
More informationMultiChannel Opportunistic Routing in MultiHop Wireless Networks
MultiChannel Oortunistic Routing in MultiHo Wireless Networks ANATOLIJ ZUBOW, MATHIAS KURTH and JENSPETER REDLICH Humboldt University Berlin Unter den Linden 6, D99 Berlin, Germany (zubow kurth jr)@informatik.huberlin.de
More informationA Multivariate Statistical Analysis of Stock Trends. Abstract
A Multivariate Statistical Analysis of Stock Trends Aril Kerby Alma College Alma, MI James Lawrence Miami University Oxford, OH Abstract Is there a method to redict the stock market? What factors determine
More informationMonitoring Streams A New Class of Data Management Applications
Brown Comuter Science Technical Reort, TRCS004 Monitoring Streams A New Class o Data Management Alications Don Carney Brown University dc@csbrownedu Ugur Cetintemel Brown University ugur@csbrownedu
More informationIEEM 101: Inventory control
IEEM 101: Inventory control Outline of this series of lectures: 1. Definition of inventory. Examles of where inventory can imrove things in a system 3. Deterministic Inventory Models 3.1. Continuous review:
More informationRealTime MultiStep View Reconstruction for a Virtual Teleconference System
EURASIP Journal on Alied Signal Processing 00:0, 067 087 c 00 Hindawi Publishing Cororation RealTime MultiSte View Reconstruction for a Virtual Teleconference System B. J. Lei Information and Communication
More informationFinding and counting given length cycles
Finding and counting given length cycles Noga Alon Raphael Yuster Uri Zwick Abstract We present an assortment of methods for finding and counting simple cycles of a given length in directed and undirected
More informationInt. J. Advanced Networking and Applications Volume: 6 Issue: 4 Pages: 23862392 (2015) ISSN: 09750290
2386 Survey: Biological Insired Comuting in the Network Security V Venkata Ramana Associate Professor, Deartment of CSE, CBIT, Proddatur, Y.S.R (dist), A.P516360 Email: ramanacsecbit@gmail.com Y.Subba
More informationSynchronizing Time Servers. Leslie Lamport June 1, 1987
Synchronizing Time Servers Leslie Lamort June 1, 1987 c Digital Equiment Cororation 1987 This work may not be coied or reroduced in whole or in art for any commercial urose. Permission to coy in whole
More informationBinary Heaps * * * * * * * / / \ / \ / \ / \ / \ * * * * * * * * * * * / / \ / \ / / \ / \ * * * * * * * * * *
Binary Heaps A binary heap is another data structure. It implements a priority queue. Priority Queue has the following operations: isempty add (with priority) remove (highest priority) peek (at highest
More informationMonitoring Frequency of Change By Li Qin
Monitoring Frequency of Change By Li Qin Abstract Control charts are widely used in rocess monitoring roblems. This aer gives a brief review of control charts for monitoring a roortion and some initial
More information(This result should be familiar, since if the probability to remain in a state is 1 p, then the average number of steps to leave the state is
How many coin flis on average does it take to get n consecutive heads? 1 The rocess of fliing n consecutive heads can be described by a Markov chain in which the states corresond to the number of consecutive
More informationLECTURE 3: BDI LOGICS
are mutually exclusive LECTURE 3: BDI LOGICS Marc Pauly & Mike Wooldridge University of Liverool, UK What is intention? Two sorts: resent directed attitude to an action function causally in roducing behaviour
More informationService Network Design with Asset Management: Formulations and Comparative Analyzes
Service Network Design with Asset Management: Formulations and Comarative Analyzes Jardar Andersen Teodor Gabriel Crainic Marielle Christiansen October 2007 CIRRELT200740 Service Network Design with
More informationMinimizing the Communication Cost for Continuous Skyline Maintenance
Minimizing the Communication Cost for Continuous Skyline Maintenance Zhenjie Zhang, Reynold Cheng, Dimitris Paadias, Anthony K.H. Tung School of Comuting National University of Singaore {zhenjie,atung}@com.nus.edu.sg
More informationThis document is downloaded from DRNTU, Nanyang Technological University Library, Singapore.
This document is downloaded from DRNTU, Nanyang Technological University Library, Singaore. Title Automatic Robot Taing: AutoPath Planning and Maniulation Author(s) Citation Yuan, Qilong; Lembono, Teguh
More informationComplex Conjugation and Polynomial Factorization
Comlex Conjugation and Polynomial Factorization Dave L. Renfro Summer 2004 Central Michigan University I. The Remainder Theorem Let P (x) be a olynomial with comlex coe cients 1 and r be a comlex number.
More informationReDispatch Approach for Congestion Relief in Deregulated Power Systems
ReDisatch Aroach for Congestion Relief in Deregulated ower Systems Ch. Naga Raja Kumari #1, M. Anitha 2 #1, 2 Assistant rofessor, Det. of Electrical Engineering RVR & JC College of Engineering, Guntur522019,
More informationAdaptive Routing Using a Virtual Waiting Time Technique
76 EEE TRANSACTONS ON SOFTWARE ENGNEERNG, VOL. SE8, NO. 1, JANUARY 1982 Adative Routing Using a Virtual Waiting Time Technique ASHOK K. AGRAWALA, SENOR MEMBER, EEE, SATSH K. TRPATH, AND GLENN RCART, MEMBER,
More informationCBus Voltage Calculation
D E S I G N E R N O T E S CBus Voltage Calculation Designer note number: 3121256 Designer: Darren Snodgrass Contact Person: Darren Snodgrass Aroved: Date: Synosis: The guidelines used by installers
More informationPersistent Data Structures and Planar Point Location
Persistent Data Structures and Planar Point Location Inge Li Gørtz Persistent Data Structures Ephemeral Partial persistence Full persistence Confluent persistence V1 V1 V1 V1 V2 q ue V2 V2 V5 V2 V4 V4
More informationSoftmax Model as Generalization upon Logistic Discrimination Suffers from Overfitting
Journal of Data Science 12(2014),563574 Softmax Model as Generalization uon Logistic Discrimination Suffers from Overfitting F. Mohammadi Basatini 1 and Rahim Chiniardaz 2 1 Deartment of Statistics, Shoushtar
More informationALGEBRAIC SIGNATURES FOR SCALABLE WEB DATA INTEGRATION FOR ELECTRONIC COMMERCE TRANSACTIONS
ALGEBRAIC SIGNATURES FOR SCALABLE WEB DATA INTEGRATION FOR ELECTRONIC COMMERCE TRANSACTIONS Chima Adiele Deartment of Comuter Science University of Manitoba adiele@cs.umanitoba.ca Sylvanus A. Ehikioya
More informationPartialOrder Planning Algorithms todomainfeatures. Information Sciences Institute University ofwaterloo
Relating the Performance of PartialOrder Planning Algorithms todomainfeatures Craig A. Knoblock Qiang Yang Information Sciences Institute University ofwaterloo University of Southern California Comuter
More informationSage Timberline Office
Sage Timberline Office Get Started Document Management 9.8 NOTICE This document and the Sage Timberline Office software may be used only in accordance with the accomanying Sage Timberline Office End User
More informationPinhole Optics. OBJECTIVES To study the formation of an image without use of a lens.
Pinhole Otics Science, at bottom, is really antiintellectual. It always distrusts ure reason and demands the roduction of the objective fact. H. L. Mencken (18801956) OBJECTIVES To study the formation
More informationComparing Dissimilarity Measures for Symbolic Data Analysis
Comaring Dissimilarity Measures for Symbolic Data Analysis Donato MALERBA, Floriana ESPOSITO, Vincenzo GIOVIALE and Valentina TAMMA Diartimento di Informatica, University of Bari Via Orabona 4 76 Bari,
More informationMultistage Human Resource Allocation for Software Development by Multiobjective Genetic Algorithm
The Oen Alied Mathematics Journal, 2008, 2, 9503 95 Oen Access Multistage Human Resource Allocation for Software Develoment by Multiobjective Genetic Algorithm Feng Wen a,b and ChiMing Lin*,a,c a Graduate
More informationTitle: Stochastic models of resource allocation for services
Title: Stochastic models of resource allocation for services Author: Ralh Badinelli,Professor, Virginia Tech, Deartment of BIT (235), Virginia Tech, Blacksburg VA 2461, USA, ralhb@vt.edu Phone : (54) 2317688,
More informationChapter 4. Simplification of Boolean Functions
4. Simlification of Boolean Functions 4 Chater 4. Simlification of Boolean Functions Boolean Cubes and Boolean Functions (a) n = (b) n = 2 (c) n = (d) n = 4 Figure : Boolean cubes [Gajski]. c ChengWen
More informationMigration to Object Oriented Platforms: A State Transformation Approach
Migration to Object Oriented Platforms: A State Transformation Aroach Ying Zou, Kostas Kontogiannis Det. of Electrical & Comuter Engineering University of Waterloo Waterloo, ON, N2L 3G1, Canada {yzou,
More informationSECTION 6: FIBER BUNDLES
SECTION 6: FIBER BUNDLES In this section we will introduce the interesting class o ibrations given by iber bundles. Fiber bundles lay an imortant role in many geometric contexts. For examle, the Grassmaniann
More informationProvable Ownership of File in Deduplication Cloud Storage
1 Provable Ownershi of File in Dedulication Cloud Storage Chao Yang, Jian Ren and Jianfeng Ma School of CS, Xidian University Xi an, Shaanxi, 710071. Email: {chaoyang, jfma}@mail.xidian.edu.cn Deartment
More informationBuffer Capacity Allocation: A method to QoS support on MPLS networks**
Buffer Caacity Allocation: A method to QoS suort on MPLS networks** M. K. Huerta * J. J. Padilla X. Hesselbach ϒ R. Fabregat O. Ravelo Abstract This aer describes an otimized model to suort QoS by mean
More informationTHE WELFARE IMPLICATIONS OF COSTLY MONITORING IN THE CREDIT MARKET: A NOTE
The Economic Journal, 110 (Aril ), 576±580.. Published by Blackwell Publishers, 108 Cowley Road, Oxford OX4 1JF, UK and 50 Main Street, Malden, MA 02148, USA. THE WELFARE IMPLICATIONS OF COSTLY MONITORING
More information! Solve problem to optimality. ! Solve problem in polytime. ! Solve arbitrary instances of the problem. !approximation algorithm.
Approximation Algorithms Chapter Approximation Algorithms Q Suppose I need to solve an NPhard problem What should I do? A Theory says you're unlikely to find a polytime algorithm Must sacrifice one of
More information