LOW ENERGY MAPPING TECHNIQUE FOR HIERARCHICAL NETWORK-ON-CHIP

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1 Journal of Theoretcal and Appled Informaton Technology JATIT & LLS. All rghts reserved. ISSN: E-ISSN: LOW ENERGY MAPPING TECHNIQUE FOR HIERARCHICAL NETWORK-ON-CHIP 1 XIAONA XIE, 2 QINGXIN ZHU, 3 ZHENGWEI CHANG, 3 YU FANG 1 School of Computer Scence and Engneerng, Unversty of Electronc Scence and Technology of Chna, Chengdu , Schuan, Chna; Physcal Educaton College of Zhengzhou Unversty, Zhengzhou , Henan, Chna 2 School of Computer Scence and Engneerng, Unversty of Electronc Scence and Technology of Chna, Chengdu , Schuan, Chna 3 Schuan Electrc Power Research Insttute, Chengdu , Schuan, Chna E-mal: 1 xnxeok@163.com, 2 qxzhu@uestc.edu.cn ABSTRACT Intellectual property (IP) core-to-node mappng s an mportant but ntractable optmzaton problem n Network-on-Chp (NoC) applcaton desgn. In ths paper, we present an approach to map cores onto herarchcal NoC archtecture whch conssts of two levels. The top-level nterconnecton network s realzed by a 2D mesh of communcatng routers, and a tree based topology s used at the second level of nterconnecton herarchy. We formulate the problem of low energy mappng, and ntroduce a three-phase optmzaton strategy to solve t. The cores are clustered frstly, and a tabu search based mappng technque s proposed to map the core clusters to the top-level nterconnecton network. Then the cores wthn each cluster are mapped to the nodes of every sub-network. Expermental results show that the proposed method s very fast and effectve n terms of energy optmzaton. Keywords: Herarchcal Network-on-Chp, Low Energy, Mappng, Cluster, Tabu Search 1. INTRODUCTION Wth the advance of ntegrated crcuts and the semconductor technology, bllons of transstors and hundreds of computaton resources or ntellectual property (IP) cores are allowed to be put on a sngle chp. System-on-chps (SoCs) wth these capabltes requre effcent communcaton archtecture to offer scalable bandwdth and parallelsm. Network-on-chp (NoC) [1, 2] has been proposed to overcome the complex on-chp communcaton problem of SoC desgn. For these complex NoCs, power consumpton becomes the most pressng desgn problem. An mportant phase n the desgn flow of NoCs s to map a set of IPs onto a set of resource nodes whch connected to local ports of routers to optmze a cost functon (e.g. energy consumpton). Generally, consder a system composed of n IPs, ths mappng problem allows n! possble solutons. Even for a small problem sze, the entre search space of ths problem s huge. In [3], a heurstc branch-and-bound algorthm s developed to tackle mappng for tle-based NoC. In addton, a lot of works wth dfferent obectves have been conducted n NoC mappng [4-6], and a survey s gven n [7]. Most of the exstng approaches assume a mesh NoC topology, snce t s straghtforward for chp surface layout. On the other way, applcaton specfc NoC s an emergng paradgm handle the communcaton problem between the set of computatonal resources n modern embedded system applcatons. Ths type of NoC optmzes desgn of the on-chp network to comply wth the applcaton specfc SoC requrements. Herarchcal NoC archtecture [8] can acheve the trade-off of regular and custom network topology, and s more sutable for larger sze or applcaton specfc systems. Moreover, t can reduce the complexty of herarchcal NoC desgn usng platform-based desgn technques or dvde-and-conquer methods. In ths work, we assume herarchcal NoC archtecture whch conssts of two levels. The top-level nterconnecton network s realzed by a 2D mesh of communcatng routers, and a tree based topology s used at the 850

2 Journal of Theoretcal and Appled Informaton Technology JATIT & LLS. All rghts reserved. ISSN: E-ISSN: second level of nterconnecton herarchy. Trees are natural for explotng localty of traffc. So the IPs wthn a sub-network could communcate effcently [9]. In ths paper, we address energy-aware mappng of IPs onto herarchcal NoC archtecture. We frst descrbe the NoC model and the assocated energy model, and then formulate the low energy mappng problem. A three-phase clusterng and tabu search based mappng approach s proposed to map the IPs to the resource nodes of a gven NoC, such that the total communcaton energy s mnmzed. The rest of ths paper s organzed as follows. Secton 2 descrbes the problem defnton. Secton 3 presents the low energy mappng algorthm of herarchcal NoC archtecture. Secton 4 shows expermental results. Fnally, Secton 5 gves the conclusons. 2. PROBLEM DEFINITION In ths secton, we descrbe the two-level herarchcal NoC archtectures and ts assocated energy model. Then the low energy mappng problem formulaton s gven. 2.1 NoC Model As shown n Fg. 1, the on-chp communcaton archtecture under consderaton n ths study s composed of two levels. At the top level, the man network s nterconnected by a 2D mesh of communcatng routers. We call these routers as global routers. Each global router s also connected to the four neghborng routers va lnks. A local sub-network s connected to a global router. A global router may connect to other global routers only IP Core Communcaton Communcaton Task Graph Mappng Local Router Resource Node Lnk Global Local Network Router NoC Archtecture Fg.1: The Mappng Problem Models At the second level, all the leaves and vertces are nterconnected by a bnary tree as shown n Fg. 1. Besdes bnary tree based topology, the k-ary trees (k > 2) or fat trees such as SPIN [10] may be used n the sub-networks. In our model, the leaf nodes do all computaton, and the rest of the nodes (routers) are used only for communcaton. We call these non-leaf routers n the sub-networks as local routers. In other words, the resources are placed at the leaves and the local routers placed at the vertces. The routng of the local network s qute easy as the best path s defned by the topology tself. The messages are generated by the computaton resources. When a packet comes from a downlnk, the local router has to see f t belongs to ts sub-tree. If t sn t the router must address t to the father router n the hgh level. Statc XY routng s assumed for the global communcaton. It frst routes packets along the X-axs. Once t reaches the column under whch the destnaton tle s located, the packet s then routed along the Y-axs. 2.2 Energy Model When packets travel on the nterconnecton network, both the routers and the nter-routers lnks wll result n energy dsspaton. We are concerned wth the dynamc energy dsspaton caused by the communcaton tasks. Consder the communcatons between two resource nodes of n hops, the energy consumpton of sendng one bt of data s modeled as: E ( n) = n E + ( n 1) E (1) bt r bt l bt where n s the number of routers the data passes on ts way along a path, and E r and E bt l represent bt the energy consumed by a router and a lnk per bt, respectvely. 2.3 Problem Formulaton As Fg.1 shown, the obectve of the mappng problems s to select IPs from a communcaton task graph and assgn them to dfferent resource nodes of the NoC archtecture, such that the total communcaton energy consumpton s mnmzed. More formally, ths problem can be formulated as follows. Gven: a drected communcaton task graph CTG(C,A), where each c C denotes a IP core, and the drected edge a A denotes the communcaton from c to c. For every a 851

3 Journal of Theoretcal and Appled Informaton Technology JATIT & LLS. All rghts reserved. ISSN: E-ISSN: A, v(a ) denotes the communcaton volume n bts from c to c. a herarchcal NoC archtecture defned as a tuple NA = ( CN, GR, SR, GP, CP), where each cn CN gr GR sr SR denotes a resource node, each denotes a global router, each denotes a local router of the subnetwork connected gr drectly, each gp GP denotes the routng path from a global router gr to another global router gr, and each cp CP denotes the routng path from resource node cn to cn. For every gp GP, e gp ) denotes the average ( energy consumpton of sendng one bt of data from global router gr to gr. For every cp CP, e ( cp ) denotes the average energy consumpton of sendng one bt of data from resource node cn to cn. When C CN, the problem of mnmzng the total communcaton energy s to obtan a one to one mappng functon φ : C CN whch: ( v( a ) e( cp ) mn E ( φ ) = ) φ ( c ), φ ( c ) (2) a A such that: c C, cn = φ ( c ) CN (3) c c C, φ( cn ) φ( cn ) (4) Therefore, the communcaton energy consumpton can be mnmzed by mnmzng the cumulatve traffc flowng through each routng paths. Moreover, the traffc flowng along GP has more mpacts on the total energy consumptons. So the IPs communcate frequently should be mapped on to a common sub-network. 3. THE MAPPING ALGORITHM Fndng an optmal mappng for NoC that consumes the least energy s kn to be NP-hard. For the large-sze herarchcal NoC system, the mappng problem s even harder. In ths work, we combne two technques, namely, cores clusterng and clusters mappng to address the IP mappng problem of herarchcal NoC. Clusterng can greatly smplfy the mappng problem because the mappng can be conducted cluster wse nstead of node wse. As shown n Fg.2, we propose a three-phase mappng approach. In the frst phase, the IP cores that communcate wth each other frequently are clustered nto a group, such that the nter-cluster communcaton volumes are less. In the second phase, a tabu search algorthm s used to mappng the clusters on to the global routers. Fnally, n the thrd phase, the IP cores wthn each cluster are mapped to the resource nodes of the tree based sub-networks. NoC & Energy Model IP Core Clusterng Phase 1 Tabu Search based Cluster Mappng IP Mappng onto Tree based Sub-network Optmzed Soluton Fg.2: Three-phase Mappng Algorthm Phase 2 Phase IP Core Clusterng Clusterng s a general technque to partton nodes (cores) nto groups accordng to dstance property. Here, the clusterng explots the kledge about the communcaton demands of the tasks to acheve communcaton localty. The dstance of a core depends on the number of connectons and the communcaton volume for each connecton [11]. The frst phase s to partton IP cores nto clusters, matchng the number of global routers GR. And the sze of each cluster equals the number of resource nodes of a sub-network. The mplementaton of IP cores clusterng s omtted here. Formally, as the output of the frst phase, we defne the cluster communcaton task graph TG (, AC), where = { cl GR } 1 s a set of IP clusters, and each cl s a set of IP cores. And the drected edge ac AC denotes the communcaton from c to c. So n the second phase, we should fnd a cores cluster to global router mappng φ : GR, such that the 852

4 Journal of Theoretcal and Appled Informaton Technology JATIT & LLS. All rghts reserved. ISSN: E-ISSN: communcaton energy consumpton of the top level man network E φ ) s mnmzed. ( 3.2 Tabu Search based Cluster Mappng The second phase s to make a one-to-one mappng φ usng tabu search. Tabu search s a heurstc ntroduce by Glover [12]. Ths method has been successfully appled to a varety of problems. Several researchers have compared tabu search wth other optmzaton heurstcs, such as smulated annealng and genetc algorthms, and t s observed that tabu search s superor wth regard to optmzaton tme and qualty of results [13, 14]. The man deas of tabu search may be sketched as follows. Tabu search starts from an ntal soluton S, and moves repeatedly from a soluton to a neghborng one. At each step of the procedure, a set N( S) of the neghborng solutons of the current soluton S s consdered and the move that mproves most the obectve functon value s chosen. If there are no mprovng moves, tabu search chooses one that least degrades the obectve functon. In order to avod returnng to the local optmal ust vsted, the reverse move must be forbdden. Ths s done by storng the move or a characterzaton of the move n a memory called a tabu lst. The tabu lst keeps nformaton on the last h moves durng the search process. The parameter h s called the tabu lst sze. However, the tabu lst may forbd certan relevant or nterestng moves. Consequently, an aspraton crteron s ntroduced to allow tabu moves to be chosen. As a result, the tabu search approach accepts uphll moves and smulates convergence toward a global optmum by takng advantage of the search hstory at selecton of the move. The key elements of tabu search are obect functon, neghborhood, tabu lst, tabu lst sze, and aspraton functon. In addton, n ths work dversfcaton s ntroduced to search more effcently. (1) Obect functon. Let φ represent the current confguraton of IP cluster mappng, and ts obect functon s gven by E( φ ). (2) Neghborhood. A move from one soluton to another soluton conssts of exchangng two IP clusters so that each occupes the global router formerly occuped by the other. Let N( φ ) denote the neghborhood of φ n the soluton space, whch s the set of all the neghbors ofφ. Startng from a placement φ, a neghborng placement φ N( φ ) s obtaned by permutng IP cl and cl : φ cl ) = φ ( cl ) (5) ( φ cl ) = φ ( cl ) (6) k ( k { cl cl }, φ ( cl ) = φ ( cl ) cl cl (7), k k (3) Tabu lst. The tabu lst s consttuted of pars ( cl, cl ) of IP clusters that cannot be exchanged. The prohbton of the lst s mplemented wth a 2- dmental array TL of ntegers where the element TL[, ] dentfes the value of the future teratons at whch the two IPs may agan be exchanged wth each other. By ths means, testng whether a move s tabu or not requre only one comparson. (4) Tabu lst sze. The tabu lst sze h vares randomly between 0.4 and 0.6. (5) Aspraton functon. We gnore the tabu status of a move f the soluton produced s better than the best found so far. (6) Dversfcaton. If the best soluton has not been updated for 0.2 teratons, tabu search may trap nto a local optmum. In ths case, a dversfcaton phase follows n whch a rarely used move s performed n order to force the heurstc to escape the current regon and explore dfferent regon n the desgn space. A dversfcaton of the current soluton φ s acheved by performng a rare move n the neghborhood N( φ ). The steps of the tabu search algorthm for cluster mappng can be summarzed as follows: (1) Intalzaton: Generate ntal cluster mappng confguraton φ randomly, and calculate the obect functon E( φ ). Intalze the best-so-far best soluton, setφ = φ. Intalze the tabu lst, set TL[, ] = 0, for 1 and 1. (2) Calculate the obect functon E( φ ). (3) For each φ n ncreasng order of E( φ ), represent the move as (cl m, cl n ), and repeat the followng steps 853

5 Journal of Theoretcal and Appled Informaton Technology JATIT & LLS. All rghts reserved. ISSN: E-ISSN: best (3.1) If E( φ ) < E( φ ), then set φ = φ, best φ = φ, and go to step (4) (3.2) If φ s not tabu,.e. TL[m, n] < 0, then set φ = φ, and go to step (4) (4) Update the tabu lst: Set TL[, ] = TL[, ] 1, for 1 and 1 ; Generate h randomly, set TL[m, n] = h. (5) If teratons snce prevous best soluton > 0.2, then perform dversfcaton: let TL[m, n] = mn{ TL[, ] 1 and 1 }, generate ntal cluster mappng φ by permutng cl m and cl n, and set TL[, ] = 0, for 1 and 1. (6) If restarts < max_restart_tmes, then go to step (2). best (7) Returnφ. Obvously, the above tabu search algorthm can be appled to IP mappng problem of 2D mesh or other type of NoC topology well. 3.3 IP Mappng n the Sub-networks In the thrd phase, after every cluster has been mapped to a global router,.e. a sub-network, then a recursve b-parttonng algorthm s used to map the IPs wthn a cluster to the resource nodes of the correspondng sub-network [9]. As a result, the total energy consumpton s: base lne. All algorthms were mplemented n C++, runnng on a notebook wth a 2.5 GHz processor, and 2 GB man memory. 10 applcatons of 36, 64, 100, 144, 196 IPs were generated by TGFF [15], mapped onto NoC of 3 3, 4 4, 5 5, 6 6, and 7 7 mesh man network, respectvely. Each sub-network s based on bnary tree topology, ncludng 4 resource nodes and 3 local routers. We compare the qualty of the soluton of two algorthms: (1) Cluster & Mappng. Ths s our proposed three-phase algorthm combned clusterng and tabu search based clusters mappng. (2) IP Mappng. Ths s the tabu search based IP mappng algorthm as llustrated n secton 3.2. The nput of ths mplementaton s CTG ( C, A), and the output of IP mappng φ s E (φ). Fg. 3 shows how our algorthm performs as the system sze scales up. For each problem, IP Mappng algorthm has been set to run same tme as Cluster & Mappng. In Fg.3, the energy of Cluster & Mappng s normalzed aganst IP Mappng. As we can see, our proposed method produces better solutons, especally for large sze problem. In the best case, t saves 27% energy over IP mappng. GR E( φ ) = E( φ ) + E( φ ) (8) = 1 where E( φ ) s the communcaton consumpton of the sub-network connected gr, and φ s the optmzed mappng functon of the IPs mapped onto ths sub-network. 4. EXPERIMENTAL RESULTS The purpose of our experments s to valdate the advantages of our method n runtme and qualty of solutons. In ths secton, we present the results obtaned by the executon of our technque on the benchmark applcatons wth dfferent sze and characterstcs. We have also mplemented the tabu search based IP mappng wthout clusterng as the Fg.3: Comparson of Energy Optmzaton Table 1 shows the computatonal tme rato of the two algorthms for obtanng the almost same energy optmzaton results. As Table 1shown, our method takes less tme than IP Mappng. When the system sze s 196, the runtme rato of IP Mappng to Cluster & Mappng s almost

6 Journal of Theoretcal and Appled Informaton Technology JATIT & LLS. All rghts reserved. ISSN: E-ISSN: Table 1: Comparson of Computaton Tme Rato System Sze (Number of IPs) Runtme of IP Mappng / Runtme of Cluster & Mappng CONUSIONS In ths paper, a computatonally effcent threephase algorthm for energy-aware mappng IPs onto herarchcal two-level NoC archtecture has been presented. The algorthm combned IP cores clusterng and tabu search based clusters mappng. The effectveness of ths algorthm s evaluated by comparng wth pure tabu search based IP mappng algorthm. Expermental results have shown, our method obtans hgh qualty of solutons, but requres sgnfcantly less computatonal tme. ACKNOWLEDGMENT Ths work was supported by: the Natural Scence Foundaton of Chna (No , ), and Artfcal Intellgence Key Laboratory of Schuan Provnce of Chna (No. 2010RY010, 2011RYJ05). REFRENCES: [1] T. Berregaard and S. Mahadevan, "A survey of research and practces of Network-on-chp," ACM Computng Surveys, vol. 38, No.2, 2006, pp [2] U. Y. Ogras, J. Hu, and R. Marculescu, "Key research problems n NoC desgn: a holstc perspectve," Proceedngs of the 3rd IEEE/ACM/IFIP nternatonal conference on Hardware/software codesgn and system synthess, 2005, pp [3] J. Hu and R. Marculescu, "Energy-aware mappng for tle-based NoC archtectures under performance constrants," Proceedngs of the 2003 conference on Asa South Pacfc desgn automaton, 2003, pp [4] S. Mural and G. De Mchel, "Bandwdth- Constraned Mappng of Cores onto NoC Archtectures," Proceedngs of the Desgn, Automaton and Test n Europe Conference and Exhbton, 2004, pp [5] G. Asca, V. Catana, and M. Pales, "Multobectve mappng for mesh-based NoC archtectures," Proceedngs of the 2nd IEEE/ACM/IFIP nternatonal conference on Hardware/software codesgn and system synthess, 2004, pp [6] R. Chae-Eun, J. Han-You, and H. Soonho, "Many-to-many core-swtch mappng n 2-D mesh NoC archtectures," Proceedngs of IEEE Internatonal Conference on Computer Desgn, 2004, pp [7] P. K. Sahu and S. Chattopadhyay, "A Survey on Applcaton Mappng Strateges for Networkon-Chp Desgn," Journal of Systems Archtecture, vol. 59, No.1, 2013, pp [8] T. Hollsten and M. Glesner, "Advanced hardware/software co-desgn on reconfgurable network-on-chp based hyper-platforms," Computers & Electrcal Engneerng, vol. 33, No.4, 2007, pp ,. [9] Z. Chang, G. Xong, and N. Sang, "Energyaware Mappng for Tree-based NoC Archtectures by Recursve Bparttonng," Proceedngs of Internatonal Conference on Embedded Software and Systems, 2008, pp [10] P. Guerrer and A. Grener, "A generc archtecture for on-chp packet-swtched nterconnectons," Proceedngs of the conference on Desgn, automaton and test n Europe, 2000, pp [11] Z. Lu, L. Xa, and A. Jantsch, "Cluster-based smulated annealng for mappng cores onto 2D mesh networks on chp," Proceedngs of 11th IEEE Workshop on Desgn and Dagnostcs of Electronc Crcuts and Systems, 2008, pp [12] F. Glover and M. Laguna, Tabu search: Sprnger, [13] P. Eles, Z. Peng, K. Kuchcnsk, and A. Dobol, "System Level Hardware/Software Parttonng Based on Smulated Annealng and Tabu Search," Desgn Automaton for Embedded Systems, vol. 2, pp. 5-32, [14] O. Ha, S. Brsset, and P. Brochet, "Comparng stochastc optmzaton methods used n electrcal engneerng," Proceedngs of IEEE Internatonal Conference on Systems, Man and Cybernetcs, [15] R. P. Dck, D. L. Rhodes, and W. Wolf, "TGFF: task graphs for free," Proceedngs of the 6th nternatonal workshop on Hardware/software codesgn, 1998, pp