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Parallel Algorithms for Graph Optimization Using Tree Decompositions

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. ...

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

2013
*
Proceedings of the 2nd ACM SIGPLAN workshop on Functional high-performance computing - FHPC '13
*

We propose to derive bottom-up dynamic programming

doi:10.1145/2502323.2502331
dblp:conf/icfp/WangCLH13
fatcat:3ypmn7swrrho7nplv23xbfgjle
*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*). ...##
###
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

2012
*
2012 IV International Conference "Problems of Cybernetics and Informatics" (PCI)
*

Strategies

doi:10.1109/icpci.2012.6486427
fatcat:f2uxkwellncebhmovq5euxzkri
*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. ...##
###
Using PRAM Algorithms on a Uniform-Memory-Access Shared-Memory Architecture
[chapter]

2001
*
Lecture Notes in Computer Science
*

The example we present in detail here is a

doi:10.1007/3-540-44688-5_11
fatcat:7kxngeka6ze25eqx2rk7zv2dx4
*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*. ...##
###
Treewidth Computation and Kernelization in the Parallel External Memory Model
[chapter]

2014
*
Lecture Notes in Computer Science
*

We present a randomized

doi:10.1007/978-3-662-44602-7_7
fatcat:tjzng5qyhbbmtmyc5c4chgqeue
*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. ...##
###
Combinatorial Optimization on Graphs of Bounded Treewidth

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 ...

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

2020
*
arXiv
*
pre-print

Here we propose a

arXiv:2004.10892v2
fatcat:nxenvej5bvfo5exzdc7xrsa5zi
*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. ...##
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Scheduling UET-UCT series-parallel graphs on two processors

1996
*
Theoretical Computer Science
*

A quadratic

doi:10.1016/0304-3975(96)00035-7
fatcat:n6prmtmyvzbunnthwrdrkd5zwa
*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. ...##
###
Greedy concepts for network flow problems

1986
*
Discrete Applied Mathematics
*

We provide a general theoretical framework to prove greedy results

doi:10.1016/0166-218x(86)90037-5
fatcat:ys5ylbfzg5hy7i33mf23f2bzii
*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. ...##
###
Minimum cost flow algorithms for series-parallel networks

1985
*
Discrete Applied Mathematics
*

It is shown that an acyclic multigraph with a single source and a single sink is series-

doi:10.1016/0166-218x(85)90006-x
fatcat:kvbdulzsbrg3dmebwj7j7s4vye
*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*. ...##
###
Real-time minimum vertex cover for two-terminal series-parallel graphs

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

doi:10.1504/ijhpcn.2006.013490
fatcat:byzl36lsyfbb3aestyspw6hqci
*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. ...##
###
Embedding graphs with bounded treewidth into optimal hypercubes
[chapter]

1996
*
Lecture Notes in Computer Science
*

Moreover, if the given

doi:10.1007/3-540-60922-9_14
fatcat:olbl6l2tunatjb7nsecjzosdi4
*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] . ...##
###
Embedding Graphs with Bounded Treewidth into Their Optimal Hypercubes

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. ...

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

2013
*
arXiv
*
pre-print

We present a

arXiv:1309.6829v1
fatcat:j46qkdak3zemvpopfda45lieji
*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). ...
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