A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Inapproximability of Treewidth, One-Shot Pebbling, and Related Layout Problems
[chapter]

2012
*
Lecture Notes in Computer Science
*

We study the

doi:10.1007/978-3-642-32512-0_2
fatcat:cykgo367bfdb5k3slkwvopqtxm
*approximability**of**a*number*of*graph problems:*treewidth*and pathwidth*of*graphs, one-shot black (and black-white) pebbling costs*of*directed acyclic graphs, and*a*variety*of*different graph ... We show that, assuming the recently introduced Small Set Expansion Conjecture, all*of*these problems are hard to*approximate*within any*constant**factor*. Research supported by NSERC. ...*A*central open problem is to determine whether or not there exists*a*polynomial time*constant**factor**approximation**algorithm*for*treewidth*(see e.g., [9, 13, 8] ). ...##
###
A Note on Multiflows and Treewidth

2007
*
Algorithmica
*

We consider multicommodity flow problems in capacitated graphs where the

doi:10.1007/s00453-007-9129-z
fatcat:addxk77fejhatpd3v5vufqfy24
*treewidth**of*the underlying graph is bounded by r. The parameter r is allowed to be*a*function*of*the input size. ... We obtain the following results in such graphs. • An O(r log r log n)*approximation*for EDP and UFP. • The integrality gap*of*the multicommodity flow*relaxation*for EDP and UFP is O(min{r log n, √ n}). ... Using by now standard ideas [25] an*algorithm*for EDP based on the flow*relaxation*can be extended to obtain an*algorithm*with*a*comparable performance (to within*constant**factors*) for UFP if d max ≤ ...##
###
Relax, Compensate and Then Recover
[chapter]

2011
*
Lecture Notes in Computer Science
*

First, our notion

doi:10.1007/978-3-642-25655-4_16
fatcat:vrsjf5zs2nhdtmg4spleghv4vu
*of*an*approximation*is based on "*relaxing*" equality constraints, for the purposes*of*simplifying*a*problem so that it can be solved more readily. ... We present in this paper*a*framework*of**approximate*probabilistic inference which is based on three simple concepts. ... Discussion The performance*of*our system in the UAI'10*approximate*inference evaluation was clearly*a*strong demonstration*of*the*practical*effectiveness*of*the*relax*, compensate and then recover framework ...##
###
Large-Scale Traffic Signal Offset Optimization
[article]

2019
*
arXiv
*
pre-print

Specifically, we solve

arXiv:1911.08368v1
fatcat:ekkipngoindhrfw4yxi66kvkti
*a*convex*relaxation**of*the nonconvex problem using*a*tree decomposition reduction, and use randomized rounding to recover*a*near-global solution. ... In this paper, we present*a*novel*algorithm*to solve this new formulation to near-global optimality on*a*large-scale. ... In*practice*, the resulting*algorithm*is about*a**constant**factor**of*10 times slower than the one proposed in this paper. ...##
###
Constant Congestion Routing of Symmetric Demands in Planar Directed Graphs

2018
*
SIAM Journal on Discrete Mathematics
*

The main technical contribution is to show that

doi:10.1137/17m1150694
fatcat:qzb4xwxhbrctjk6wgsxvnxlrlm
*a*planar digraph with directed*treewidth*h contains*a**constant*congestion crossbar*of*size Ω(h/polylog(h)). paths. ... It is known that even the simpler case*of*ANF and with congestion c allowed is hard to*approximate*to within*a**factor**of*n Ω(1/c) [15] ; moreover this holds in acyclic graphs. ... 7:13 Does*a*planar directed graph with*treewidth*h have*a**constant*congestion crossbar*of*size Ω(h). This would strengthen our result. In particular, is there*a*cylindrical grid minor*of*size Ω(h)? ...##
###
Convex Relaxations for Learning Bounded Treewidth Decomposable Graphs
[article]

2012
*
arXiv
*
pre-print

*A*supergradient method is used to solve the dual problem, with

*a*run-time complexity

*of*O(k^3 n^k+2 n) for each iteration, where n is the number

*of*variables and k is

*a*bound on the

*treewidth*. ... We consider the problem

*of*learning the structure

*of*undirected graphical models with bounded

*treewidth*, within the maximum likelihood framework. ... We would also like to thank other members

*of*the SIERRA and WILLOW project-teams for helpful discussions. ...

##
###
Inapproximability of Treewidth and Related Problems

2014
*
The Journal of Artificial Intelligence Research
*

We show that, assuming the recently introduced Small Set Expansion Conjecture, all

doi:10.1613/jair.4030
fatcat:zyqijghvife2zlvgkhnhpjwfcm
*of*these problems are NP-hard to*approximate*to within any*constant**factor*in polynomial time. ... Therefore, finding or*approximating*the*Treewidth**of**a*graph is*a*fundamental problem related to inference in graphical models. ... It is*a*longstanding open question whether or not there is*a**constant**factor**approximation**algorithm*for*Treewidth*. ...##
###
Maximizing submodular functions using probabilistic graphical models
[article]

2013
*
arXiv
*
pre-print

based on outer

arXiv:1309.2593v1
fatcat:x4ckgjwbnnehfl7ypcgvmzl4ni
*approximations**of*the marginal polytope and maximum likelihood bounded*treewidth*structures. ... In*a*graphical model, the entropy*of*the joint distribution decomposes as*a*sum*of*marginal entropies*of*subsets*of*variables; moreover, for any distribution, the entropy*of*the closest distribution*factorizing*... [10] proposed*constant**factor**approximation**algorithms*for maximizing non-negative submodular functions. ...##
###
Tree Diet: Reducing the Treewidth to Unlock FPT Algorithms in RNA Bioinformatics
[article]

2021
*
bioRxiv
*
pre-print

Our rationale is that the time gained thanks to

doi:10.1101/2021.04.30.442158
fatcat:ovpvupwbfbftzb5radjf2iriri
*a*smaller*treewidth*in*a*parameterized*algorithm*compensates the extra post-processing needed to take deleted edges into account. ... This work paves the way for*a*wider adoption*of*tree-decomposition-based*algorithms*in Bioinformatics. ... However it seems unlikely to induce*a*175 "*practical*" exact*algorithms*. ...##
###
Improved Approximation Algorithms for Minimum Weight Vertex Separators

2008
*
SIAM journal on computing (Print)
*

For graphs excluding

doi:10.1137/05064299x
fatcat:hedhyzomrjdwpojnnall7heg3y
*a*fixed graph as*a*minor (which includes, e.g. bounded genus graphs), we give*a**constant*-*factor**approximation*for the*treewidth*; this can be used to obtain the first polynomial-time ... Likewise, we obtain improved*approximation*ratios for*treewidth*: In any graph*of**treewidth*k, we show how to find*a*tree decomposition*of*width at most O(k √ log k), whereas previous*algorithms*yielded ...*A*wellknown open problem is whether*treewidth*can be*approximated*within*a**constant**factor*. ...##
###
Improved approximation algorithms for minimum-weight vertex separators

2005
*
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing - STOC '05
*

For graphs excluding

doi:10.1145/1060590.1060674
dblp:conf/stoc/FeigeHL05
fatcat:ad2nkwcizzeynmbucegyxvyrdi
*a*fixed graph as*a*minor (which includes, e.g. bounded genus graphs), we give*a**constant*-*factor**approximation*for the*treewidth*; this can be used to obtain the first polynomial-time ... Likewise, we obtain improved*approximation*ratios for*treewidth*: In any graph*of**treewidth*k, we show how to find*a*tree decomposition*of*width at most O(k √ log k), whereas previous*algorithms*yielded ...*A*wellknown open problem is whether*treewidth*can be*approximated*within*a**constant**factor*. ...##
###
Faster Algorithms for Quantitative Verification in Constant Treewidth Graphs
[chapter]

2015
*
Lecture Notes in Computer Science
*

First, for

doi:10.1007/978-3-319-21690-4_9
fatcat:246qqug5l5bolp7jo6o2jorsai
*constant**treewidth*graphs we present an*algorithm*that*approximates*the mean-payoff value within*a*multiplicative*factor**of*in time O(n · log(n/ )) and linear space, as compared to the classical ... Beyond the mathematical elegance*of*the*treewidth*property for graphs, there are many classes*of*graphs which arise in*practice*and have*constant**treewidth*. ... First, we present*a*linear-time*algorithm*that computes c * exactly (if c * ≥ 0) or*approximate*within*a*polynomial*factor*(if c * < 0). ...##
###
Algorithmic Meta-Theorems for Monotone Submodular Maximization
[article]

2018
*
arXiv
*
pre-print

Formally, we prove the following three '

arXiv:1807.04575v1
fatcat:ye2o43726zfyvfc7vijifqaptm
*algorithmic*metatheorems.' (1) If the constraint is specified by*a*monadic second-order logic on*a*graph*of*bounded*treewidth*, the problem is solved in n^O(1) time ...*factor**of*2. (3) If the constraint is specified by*a*first-order logic on*a*graph*of*bounded expansion, the problem is solved in n^O( k) time with an*approximation**factor**of*O( k), where k is the number ... Acknowledgment We thank Antoine Amarilli for confirming the structuredness*of*their construction*of*DNNF in [1] . ...##
###
An Improvement of Reed's Treewidth Approximation
[article]

2020
*
arXiv
*
pre-print

Reed simply claims time O(n log n) for bounded k for his

arXiv:2010.03105v1
fatcat:xhy2egcprzdqrg5sbsrbh32324
*constant**factor**approximation**algorithm*, but the bound*of*2^Ω(k log k) n log n is well known. ... We present*a*new*approximation**algorithm*for the*treewidth*problem which constructs*a*corresponding tree decomposition as well. Our*algorithm*is*a*faster variation*of*Reed's classical*algorithm*. ... Then, the running time*of*our*algorithm*has another*factor**of*1/ . ...##
###
Prize-collecting Network Design on Planar Graphs
[article]

2010
*
arXiv
*
pre-print

More precisely, we show any α-

arXiv:1006.4339v1
fatcat:tnfakl2efvdzneuc2hn64wgrje
*approximation**algorithm*for these problems on graphs*of*bounded*treewidth*gives an (α + ϵ)-*approximation**algorithm*for these problems on planar graphs (and more generally ... is known to be polynomially solvable on series-parallel graphs and admits*a*PTAS on graphs*of*bounded*treewidth*. ... For any given*constant*> 0, an α-*approximation**algorithm*for SPCSF on graphs*of*bounded*treewidth*gives*a*(α + )-*approximation**algorithm*for SPCSF on planar graphs. ...
« Previous

*Showing results 1 — 15 out of 604 results*