# TU e. Advanced Algorithms: experimentation project. The problem: load balancing with bounded look-ahead. Input: integer m 2: number of machines

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1 The problem: load balancing with bounded look-ahead Input: integer m 2: number of machines integer k 0: the look-ahead numbers t 1,..., t n : the job sizes Problem: assign jobs to machines machine to which job J i is assigned should only depend on jobs J 1,..., J i 1, J i, J i+1,... J i+k Goal: minimize makespan

2 The project Your task: design two (or more) algorithms for the problem if possible: theoretical analysis of run time and approximation ratio implement algorithms and perform experimental evalution... and write a paper about it Goals: investigate algorithms from an experimental / practical point of view practice writing a scientific paper

3 The paper Strict requirements: 8 10 pages, 11 pt, normal margins in LaTex: \usepackage{a4wide} Write report as a scientific paper. (Not: For the course Advanced Algorithms we had to write... )

4 Suggested structure of the paper: Abstract (one short paragraph) 1 Introduction (1 1.5 pages) Motivation, problem description, embedding in existing literature. Short discussion of main results/conclusions. 2 The algorithms (2 3 pages) Description of algorithms and theoretical analysis. Use subsections when appropriate. 3 Experimental Evaluation (4 5 pages) Description of data sets and experiments. Hypotheses, results (graphs and/or tables), and discussion of results. Use subsections when appropriate. 4 Concluding remarks (one ore two paragraphs) Very brief summary, future research/open problems. References

5 Suggested structure of the paper: Abstract (one short paragraph) 1 Introduction (1 1.5 pages) Motivation, problem description, embedding in existing literature. Short discussion of main results/conclusions. 2 The algorithms (2 3 pages) Description of algorithms and theoretical analysis. Use subsections when appropriate. 3 Experimental Evaluation (4 5 pages) Description of data sets and experiments. Hypotheses, results (graphs and/or tables), and discussion of results. Use subsections when appropriate. 4 Concluding remarks (one ore two paragraphs) Very brief summary, future research/open problems. References no Table of Contents

6 Grading scheme abstract, introduction, concluding remarks: max 1 point algorithms (max 3 points): description: 1.5 point choice of algorithms: 1.5 points experimental evaluation (max 4 points): data sets (description, variety) and experiments: 2 points discussion of results: 2 points presentation (max 2 points): layout, formatting: 0.5 point language: 1 point graphs / tables: 0.5 point overall impression: -1 to +1

7 Points to consider make sure graphs are readable, and axes are clearly labeled use different types of data sets (distribution large versus small jobs, order, etc) it is useful to (also) generate data sets such that you know OPT focus on quality of results (approximation ratio), but investigation of run time may also be nice compare experimental results to theoretical analysis when possible cite relevant literature (5 10 references, say, mainly for intro)

8 About writing papers proofread, proofread, proofread! at level of sections and subsections at the paragraph level at sentence level... and rewrite, rewrite, rewrite

9 Proofreading at sentence level Some (real-life) examples: This situation is the easiest method for solving the problem. We assume the set of points does not have the same x-coordinate. Therefore we change the weight of edge e to e + f.

10 Notation use consistent notation

11 Notation use consistent notation For example: upper case roman for sets (A, B, V, E, etc) lower case roman for elements in sets (a, b, etc.) calligraphic for structures (T for tree, L for list)

12 Notation use consistent notation For example: upper case roman for sets (A, B, V, E, etc) lower case roman for elements in sets (a, b, etc.) calligraphic for structures (T for tree, L for list) keep it simple, don t overdo it

13 Notation use consistent notation For example: upper case roman for sets (A, B, V, E, etc) lower case roman for elements in sets (a, b, etc.) calligraphic for structures (T for tree, L for list) keep it simple, don t overdo it G = (V (G), E(G)) is usually not needed, G = (V, E) will do just fine

14 Notation don t deviate from standard conventions, unless you have a very good reason

15 Notation don t deviate from standard conventions, unless you have a very good reason don t use ε to denote an integer and i to number close to zero.

16 Notation don t deviate from standard conventions, unless you have a very good reason don t use ε to denote an integer and i to number close to zero. even standard notation should be defined

17 Notation don t deviate from standard conventions, unless you have a very good reason don t use ε to denote an integer and i to number close to zero. even standard notation should be defined Let S be a set of segments in the plane. We describe an algorithm to compute a binary space partition for S of size O(n).

18 Notation don t deviate from standard conventions, unless you have a very good reason don t use ε to denote an integer and i to number close to zero. even standard notation should be defined Let S be a set of segments in the plane. We describe an algorithm to compute a binary space partition for S of size O(n). n is undefined

19 Notation don t deviate from standard conventions, unless you have a very good reason don t use ε to denote an integer and i to number close to zero. even standard notation should be defined Let S be a set of segments in the plane. We describe an algorithm to compute a binary space partition for S of size O(n). n is undefined avoid using too many sub/superscripts, like in p x j i

20 Level of formality mathematics / computer science texts should be precise and unambiguous but they should also be as clear and easy to read as possible

21 Level of formality mathematics / computer science texts should be precise and unambiguous but they should also be as clear and easy to read as possible being precise does not mean you always must write complicated formulas!

22 Let G = (V, E) be an unweighted, undirected graph. The problem we study is to find a subset C E satisfying the following condition: ( e = (u, v) E : w C : (w = u w = v)) ( C E : ( e = (u, v) E : w C : (w = u w = v)) C C )

23 Let G = (V, E) be an unweighted, undirected graph. The problem we study is to find a subset C E satisfying the following condition: ( e = (u, v) E : w C : (w = u w = v)) ( C E : ( e = (u, v) E : w C : (w = u w = v)) C C ) Let G = (V, E) be an unweighted, undirected graph. We call a subset C E a vertex cover for G if, for every edge (u, v) E, either u or v (or both) are in C. The problem we study is to find the smallest possible vertex cover for G, that is, a vertex cover for G with a minimum number of vertices.

24 Pay attention to detail use same font in figures as in text Suppose you want to write something about a certain point p. Then it looks ugly when the letter p is not on the same line as the word point. format your formulas nicely cos x( 3x xy 6 7) = π sin y versus ( 3x 2 ) + 5 4xy 6 7 cos x = π sin y

25 When writing with multiple authors make sure notation, style, etc are consistent proofread and comment on text written by your co-authors: when you are one of the authors you should understand every sentence (and be happy with the way it is written)

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### The x-intercepts of the graph are the x-values for the points where the graph intersects the x-axis. A parabola may have one, two, or no x-intercepts.

Chapter 10-1 Identify Quadratics and their graphs A parabola is the graph of a quadratic function. A quadratic function is a function that can be written in the form, f(x) = ax 2 + bx + c, a 0 or y = ax

### 14. GEOMETRY AND COORDINATES

14. GEOMETRY AND COORDINATES We define. Given we say that the x-coordinate is while the y-coordinate is. We can view the coordinates as mappings from to : Coordinates take in a point in the plane and output