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Inapproximability of Treewidth, One-Shot Pebbling, and Related Layout Problems
[chapter]
2012
Lecture Notes in Computer Science
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We study the 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] ). ...
doi:10.1007/978-3-642-32512-0_2
fatcat:cykgo367bfdb5k3slkwvopqtxm
A Note on Multiflows and Treewidth
2007
Algorithmica
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We consider multicommodity flow problems in capacitated graphs where the 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 ≤ ...
doi:10.1007/s00453-007-9129-z
fatcat:addxk77fejhatpd3v5vufqfy24
Relax, Compensate and Then Recover
[chapter]
2011
Lecture Notes in Computer Science
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First, our notion 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 ...
doi:10.1007/978-3-642-25655-4_16
fatcat:vrsjf5zs2nhdtmg4spleghv4vu
Large-Scale Traffic Signal Offset Optimization
[article]
2019
arXiv
pre-print
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Specifically, we solve 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. ...
arXiv:1911.08368v1
fatcat:ekkipngoindhrfw4yxi66kvkti
Constant Congestion Routing of Symmetric Demands in Planar Directed Graphs
2018
SIAM Journal on Discrete Mathematics
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The main technical contribution is to show that 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)? ...
doi:10.1137/17m1150694
fatcat:qzb4xwxhbrctjk6wgsxvnxlrlm
Convex Relaxations for Learning Bounded Treewidth Decomposable Graphs
[article]
2012
arXiv
pre-print
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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. ...
arXiv:1212.2573v1
fatcat:s7h5odxm6bd6hncumavdiypat4
Inapproximability of Treewidth and Related Problems
2014
The Journal of Artificial Intelligence Research
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We show that, assuming the recently introduced Small Set Expansion Conjecture, all 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. ...
doi:10.1613/jair.4030
fatcat:zyqijghvife2zlvgkhnhpjwfcm
Maximizing submodular functions using probabilistic graphical models
[article]
2013
arXiv
pre-print
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based on outer 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. ...
arXiv:1309.2593v1
fatcat:x4ckgjwbnnehfl7ypcgvmzl4ni
Tree Diet: Reducing the Treewidth to Unlock FPT Algorithms in RNA Bioinformatics
[article]
2021
bioRxiv
pre-print
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Our rationale is that the time gained thanks to 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. ...
doi:10.1101/2021.04.30.442158
fatcat:ovpvupwbfbftzb5radjf2iriri
Improved Approximation Algorithms for Minimum Weight Vertex Separators
2008
SIAM journal on computing (Print)
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For graphs excluding 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. ...
doi:10.1137/05064299x
fatcat:hedhyzomrjdwpojnnall7heg3y
Improved approximation algorithms for minimum-weight vertex separators
2005
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing - STOC '05
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For graphs excluding 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. ...
doi:10.1145/1060590.1060674
dblp:conf/stoc/FeigeHL05
fatcat:ad2nkwcizzeynmbucegyxvyrdi
Faster Algorithms for Quantitative Verification in Constant Treewidth Graphs
[chapter]
2015
Lecture Notes in Computer Science
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First, for 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). ...
doi:10.1007/978-3-319-21690-4_9
fatcat:246qqug5l5bolp7jo6o2jorsai
Algorithmic Meta-Theorems for Monotone Submodular Maximization
[article]
2018
arXiv
pre-print
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Formally, we prove the following three '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] . ...
arXiv:1807.04575v1
fatcat:ye2o43726zfyvfc7vijifqaptm
An Improvement of Reed's Treewidth Approximation
[article]
2020
arXiv
pre-print
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Reed simply claims time O(n log n) for bounded k for his 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/ . ...
arXiv:2010.03105v1
fatcat:xhy2egcprzdqrg5sbsrbh32324
Prize-collecting Network Design on Planar Graphs
[article]
2010
arXiv
pre-print
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More precisely, we show any α-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. ...
arXiv:1006.4339v1
fatcat:tnfakl2efvdzneuc2hn64wgrje
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