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Parallel Algorithms for Graph Optimization Using Tree Decompositions

Blair D. Sullivan, Dinesh Weerapurage, Chris Groer
2013 2013 IEEE International Symposium on Parallel & Distributed Processing, Workshops and Phd Forum  
For their help with the MADNESS parallel runtime, we thank Robert Harrison, Rebecca Hartman-Baker and Benjamin Mintz.  ...  We would also like to thank Josh Lothian for his help with getting INDDGO to a releasable state.  ...  An optimal tree decomposition for a graph G is one with width τ (G). An important class of graphs of class used in this paper are the k-trees, which are defined recursively.  ... 
doi:10.1109/ipdpsw.2013.242 dblp:conf/ipps/SullivanWG13 fatcat:vvu3wqxhfnhn3awwxsllsrddna

Towards systematic parallel programming of graph problems via tree decomposition and tree parallelism

Qi Wang, Meixian Chen, Yu Liu, Zhenjiang Hu
2013 Proceedings of the 2nd ACM SIGPLAN workshop on Functional high-performance computing - FHPC '13  
We propose to derive bottom-up dynamic programming algorithms on tree decompositions from the user-specified GTA algorithms, and further transform the bottom-up algorithms to parallel ones which run in  ...  Besides, balanced tree partition strategies are discussed for efficient parallel computing.  ...  Tree parallelization Using tree decomposition, we are able to reduce algorithms for some graph problems to algorithms on tree decompositions (trees).  ... 
doi:10.1145/2502323.2502331 dblp:conf/icfp/WangCLH13 fatcat:3ypmn7swrrho7nplv23xbfgjle

Page 6812 of Mathematical Reviews Vol. , Issue 2002I [page]

2002 Mathematical Reviews  
“Additionally, we present experimental evidence that computing an optimal orientation of a decomposition tree is useful in practice.  ...  For | /3-balanced decomposition trees of bounded degree graphs, the time complex- ity of our algorithm is O(n?*), where n denotes the number of vertices.  ... 

On local elimination algorithms for sparse discrete optimization problems

Daria Lemtyuzhnikova, Aleksandr Sviridenko, Oleg Shcherbina
2012 2012 IV International Conference "Problems of Cybernetics and Informatics" (PCI)  
Strategies for parallelizing a sequential local elimination algorithm for sparse discrete optimization problems are analyzed.  ...  We discuss local elimination algorithms that compute global information using local computations.  ...  This research should analyze and develop new parallel methodology using using structural decomposition combined with linear algebra approaches for solving large-scale DO problems.  ... 
doi:10.1109/icpci.2012.6486427 fatcat:f2uxkwellncebhmovq5euxzkri

Using PRAM Algorithms on a Uniform-Memory-Access Shared-Memory Architecture [chapter]

David A. Bader, Ajith K. Illendula, Bernard M. E. Moret, Nina R. Weisse-Bernstein
2001 Lecture Notes in Computer Science  
The example we present in detail here is a graph decomposition algorithm that also requires the computation of a spanning tree; this problem is not only of interest in its own right, but is representative  ...  Our results thus offer promise for bridging the gap between the theory and practice of shared-memory parallel algorithms.  ...  The ear decomposition algorithm first computes the spanning tree, then labels non-tree edges using independent LCA searches, and finally labels tree edges in parallel.  ... 
doi:10.1007/3-540-44688-5_11 fatcat:7kxngeka6ze25eqx2rk7zv2dx4

Treewidth Computation and Kernelization in the Parallel External Memory Model [chapter]

Riko Jacob, Tobias Lieber, Matthias Mnich
2014 Lecture Notes in Computer Science  
We present a randomized algorithm which computes, for any fixed k, a tree decomposition of width at most k of any input graph.  ...  Our algorithm has sorting complexity, which we prove to be optimal for a large parameter range. We use this algorithm as part of a PEM-efficient kernelization algorithm.  ...  For efficient parallelization, the algorithm obtains a balanced tree decomposition of width for a graph of size n.  ... 
doi:10.1007/978-3-662-44602-7_7 fatcat:tjzng5qyhbbmtmyc5c4chgqeue

Combinatorial Optimization on Graphs of Bounded Treewidth

H. L. Bodlaender, A. M. C. A. Koster
2007 Computer journal  
For combinatorial optimization problems, this is a useful approach for obtaining fixed-parameter tractable algorithms.  ...  tree decompositions with optimal or close to optimal treewidth.  ...  In Section 2.3, we discuss the general shape of many algorithms that use tree decompositions, and define a special form of tree decompositions, called nice tree decompositions, that are useful for the  ... 
doi:10.1093/comjnl/bxm037 fatcat:maq7rjwstvfw7jsda7zrn62zha

Simple heuristics for efficient parallel tensor contraction and quantum circuit simulation [article]

Roman Schutski, Dmitry Kolmakov, Taras Khakhulin, Ivan Oseledets
2020 arXiv   pre-print
Here we propose a parallel algorithm for the contraction of tensor networks using probabilistic graphical models.  ...  We apply the resulting algorithm to the simulation of random quantum circuits and discuss the extensions for general tensor network contractions.  ...  We also provided algorithms to calculate treewidth using either tree decomposition or any of its associated elimination orders.  ... 
arXiv:2004.10892v2 fatcat:nxenvej5bvfo5exzdc7xrsa5zi

Scheduling UET-UCT series-parallel graphs on two processors

Lucian Finta, Zhen Liu, Ioannis Mills, Evripidis Bampis
1996 Theoretical Computer Science  
A quadratic algorithm is proposed to compute an optimal schedule for a class of series-parallel graphs, called SPl graphs, which includes in particular in-forests and out-forests.  ...  The scheduling of task graphs on two identical processors is considered. It is assumed that tasks have unit-execution-time, and arcs are associated with unit-communication-time delays.  ...  Acknowledgements The authors are grateful to the referees for carefully reading the first draft of the paper and pointing out errors therein.  ... 
doi:10.1016/0304-3975(96)00035-7 fatcat:n6prmtmyvzbunnthwrdrkd5zwa

Greedy concepts for network flow problems

Wolfgang W. Bein, Peter Brucker
1986 Discrete Applied Mathematics  
We provide a general theoretical framework to prove greedy results for the optimal cost flow problem. We also draw the border line to problems where greedy is not valid.  ...  In some cases polymatroid explanations can be given for the greedy behaviour.  ...  They would also like to express their sincere thanks to the referees for their useful comments which improved the presentation of the paper.  ... 
doi:10.1016/0166-218x(86)90037-5 fatcat:ys5ylbfzg5hy7i33mf23f2bzii

Minimum cost flow algorithms for series-parallel networks

Wolfgang W. Bein, Peter Brucker, Arie Tamir
1985 Discrete Applied Mathematics  
It is shown that an acyclic multigraph with a single source and a single sink is series-parallel if and only if for arbitrary linear cost functions and arbitrary capacities the corresponding minimum cost  ...  Furthermore, for networks of this type with m edges and n vertices, two O(mn + m log m)-algorithms are presented. One of them is based on the greedy scheme.  ...  In a decomposition tree sets of parallel edges of the graph are represented by the leaves of the tree.  ... 
doi:10.1016/0166-218x(85)90006-x fatcat:kvbdulzsbrg3dmebwj7j7s4vye

Real-time minimum vertex cover for two-terminal series-parallel graphs

Marius Nagy, Selim G. Akl
2006 International Journal of High Performance Computing and Networking  
Sequentially, this can be done in linear time with respect to the size of the input graph. In parallel, e cient and even cost optimal tree contraction algorithms have also been developed.  ...  Speci cally, there are cases in which the solution produced by a parallel algorithm that uses p processors is better than the output of any sequential algorithm for this problem, by a factor superlinear  ...  A closer look at a decomposition algorithm for TTSP graphs will help us answer this question.  ... 
doi:10.1504/ijhpcn.2006.013490 fatcat:byzl36lsyfbb3aestyspw6hqci

Embedding graphs with bounded treewidth into optimal hypercubes [chapter]

Volker Heun, Ernst W. Mayr
1996 Lecture Notes in Computer Science  
Moreover, if the given graph has constant treewidth or is represented by a tree-decomposition of width t, this embedding can be efficiently implemented on the optimal hypercube itself. 2  ...  The given embedding is a generalization of our method to embed arbitrary binary trees into their optimal hypercubes given in [HM93] .  ...  If the given graph has constant treewidth, a minimal tree-decomposition for this graph can be computed on the optimal hypercube in time O(log 3 (n) loglog 2 (n)), using a result in [BH95] .  ... 
doi:10.1007/3-540-60922-9_14 fatcat:olbl6l2tunatjb7nsecjzosdi4

Embedding Graphs with Bounded Treewidth into Their Optimal Hypercubes

Volker Heun, Ernst W. Mayr
2002 Journal of Algorithms  
For graphs with constant treewidth, a minimal tree-decomposition can be computed efficiently in parallel due to a result of Bodlaender and Hagerup.  ...  Provided that the graph is given by its tree-decomposition the embedding can be computed efficiently on the hypercube itself.  ...  For graphs with constant treewidth an algorithm for constructing a minimal tree-decomposition is described in [6] . This algorithm works in time O log 2 n using O n operations on a EREW PRAM.  ... 
doi:10.1006/jagm.2002.1217 fatcat:j2udl5lcufh3jekk54aax4upue

Bethe-ADMM for Tree Decomposition based Parallel MAP Inference [article]

Qiang Fu, Huahua Wang, Arindam Banerjee
2013 arXiv   pre-print
We present a parallel MAP inference algorithm called Bethe-ADMM based on two ideas: tree-decomposition of the graph and the alternating direction method of multipliers (ADMM).  ...  However, unlike the standard ADMM, we use an inexact ADMM augmented with a Bethe-divergence based proximal function, which makes each subproblem in ADMM easy to solve in parallel using the sum-product  ...  Snyder for the helpful discussion on the CRU experiment. The authors are grateful for the technical support from the University of Minnesota Supercomputing Institute (MSI).  ... 
arXiv:1309.6829v1 fatcat:j46qkdak3zemvpopfda45lieji
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