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Approximability of 3- and 4-Hop Bounded Disjoint Paths Problems [chapter]

Andreas Bley, Jose Neto
2010 Lecture Notes in Computer Science  
In the weighted edge-or node-disjoint path problems WEDP( ) and WNDP( ), we are also given an integer k ∈ N and non-negative edge weights ce ∈ N, e ∈ E, and seek for a minimum weight subgraph of G that  ...  In this paper, we settle the complexity status of all open cases showing that WNDP(3) can be solved in polynomial time, that MEDP(4) is APXcomplete and approximable within a factor of 2, and that WNDP(  ...  In addition, we presented a 2-approximation algorithm for WEDP(4) and a 4k-approximation algorithm WNDP (4) .  ... 
doi:10.1007/978-3-642-13036-6_16 fatcat:fdm6obkdxvc4bmdqioaxb7pwxm

Solving the Minimum-Cost Satisfiability Problem Using SAT Based Branch-and-Bound Search

Zhaohui Fu, Sharad Malik
2006 Computer-Aided Design (ICCAD), IEEE International Conference on  
In this paper we consider one important variation, the Minimum-Cost Satisfiability Problem (MinCostSAT). MinCostSAT is a SAT problem which minimizes the cost of the satisfying assignment.  ...  The resulting solver MinCostChaff shows order of magnitude improvement over several current best known branchand-bound solvers for a large class of problems, ranging from Minimum Test Pattern Generation  ...  We also thank several anonymous reviewers for their invaluable suggestions and comments on this paper.  ... 
doi:10.1109/iccad.2006.320089 fatcat:oiajc7aozreztls2aoaasirese

Solving the minimum-cost satisfiability problem using SAT based branch-and-bound search

Zhaohui Fu, Sharad Malik
2006 Computer-Aided Design (ICCAD), IEEE International Conference on  
In this paper we consider one important variation, the Minimum-Cost Satisfiability Problem (MinCostSAT). MinCostSAT is a SAT problem which minimizes the cost of the satisfying assignment.  ...  The resulting solver MinCostChaff shows order of magnitude improvement over several current best known branchand-bound solvers for a large class of problems, ranging from Minimum Test Pattern Generation  ...  We also thank several anonymous reviewers for their invaluable suggestions and comments on this paper.  ... 
doi:10.1145/1233501.1233681 dblp:conf/iccad/FuM06 fatcat:e575tusipbdvta4tjsmvb3wu4q

Approximating the single source unsplittable min-cost flow problem

Martin Skutella
2002 Mathematical programming  
Moreover, all our results dominate the best known bicriteria approximations. Finally, we provide results on the hardness of approximation for several variants of the problem.  ...  Moreover, the total cost must not exceed a given budget.  ...  Thanks to Cliff Stein for sending us a copy of a preliminary version of [9] . We are grateful to two anonymous referees for many helpful comments.  ... 
doi:10.1007/s101070100260 fatcat:7ghnp6k4xfbrrewm3q5jxrxmom

On the Approximability of Robust Network Design [article]

Yacine Al-Najjar, and Walid Ben-Ameur, Jeremie Leguay
2021 arXiv   pre-print
Then, using the ETH conjecture, we get a Ω(log n/loglog n) lower bound for the approximability of this problem.  ...  Finally, we show that even if only two given paths are allowed for each commodity, the robust network design problem with minimum congestion or linear cost is hard to approximate within some constant.  ...  with linear costs directly leads to an α-approximation for the problem with minimum congestion.  ... 
arXiv:2009.12291v3 fatcat:js4qvptq3zhmrgdjfouym4o2sa

A New Solver for the Minimum Weighted Vertex Cover Problem [chapter]

Hong Xu, T. K. Satish Kumar, Sven Koenig
2016 Lecture Notes in Computer Science  
In this paper, we present a new solver for the MWVC problem based on a novel reformulation to a series of SAT instances using a primal-dual approximation algorithm as a starting point.  ...  Given a vertex-weighted graph G = V, E , the minimum weighted vertex cover (MWVC) problem is to choose a subset of vertices with minimum total weight such that every edge in the graph has at least one  ...  Acknowledgments The research at USC was supported by NSF under grant numbers 1409987 and 1319966 and a MURI under grant number N00014-09-1-1031.  ... 
doi:10.1007/978-3-319-33954-2_28 fatcat:jyqb3a37nvgk5oxqe63rqqwgei

Page 7552 of Mathematical Reviews Vol. , Issue 2002J [page]

2002 Mathematical Reviews  
“We use the local-ratio technique to develop 2-approximation algorithms for the first two variants of the problem.  ...  In particular, we present the first (linear time) 2-approximation algorithm for the edge clique complement problem.  ... 

Finding a minimum medial axis of a discrete shape is NP-hard

David Coeurjolly, Jérôme Hulin, Isabelle Sivignon
2008 Theoretical Computer Science  
In this article, we first prove that finding a minimum medial axis is an NP-hard problem for the Euclidean distance.  ...  Then, we compare two algorithms which compute an approximation of the minimum medial axis, one of them providing bounded approximation results.  ...  Acknowledgement The second author was supported in part by ANR grant BLAN06-1-138894 (projet OPTICOMB).  ... 
doi:10.1016/j.tcs.2008.06.013 fatcat:5elzyd4uqvgzdlidhqnmhidn3m

On the complexity of graph tree partition problems

Roberto Cordone, Francesco Maffioli
2004 Discrete Applied Mathematics  
We achieve a complete characterization of its computational complexity, previously studied only for special cases: a polynomial algorithm based on a new matroid solves the easy cases; the others are strongly  ...  We consider di erent objectives, depending on the cost of the trees spanning the clusters.  ...  Min-max problem: we impose = 2 and an upper bound K = 2n + 2mn on the cost of each tree. 4. Max-min problem: we impose = 1=2 and a lower bound K = 2n + 2mn on the cost of each tree.  ... 
doi:10.1016/s0166-218x(03)00340-8 fatcat:45rtgu27wrh5vjdewzmdb46xee

On the approximability of minmax (regret) network optimization problems [article]

Adam Kasperski, Pawel Zielinski
2008 arXiv   pre-print
It is shown that if the number of scenarios is unbounded, then the problems under consideration are not approximable within ^1-ϵ K for any ϵ>0 unless NP ⊆ DTIME(n^poly n), where K is the number of scenarios  ...  In this paper the minmax (regret) versions of some basic polynomially solvable deterministic network problems are discussed.  ...  Acknowledgements This work was partially supported by Polish Committee for Scientific Research, grant N N111 1464 33.  ... 
arXiv:0804.0396v3 fatcat:nsesz4ejxvb3xcvciosjile5oy

Reload cost problems: minimum diameter spanning tree

Hans-Christoph Wirth, Jan Steffan
2001 Discrete Applied Mathematics  
We consider the problem of ÿnding a spanning tree of minimum diameter with respect to the reload costs. We present lower bounds for the approximability even on graphs with maximum degree 5.  ...  We examine a network design problem under the reload cost model.  ...  In [6] , the authors give both a logarithmic approximation algorithm and a logarithmic lower bound for the minimum label spanning tree problem.  ... 
doi:10.1016/s0166-218x(00)00392-9 fatcat:nbung2c6h5dxhkhgjzamyop5fu

Solving Weighted Max-SAT Problems in a Reduced Search Space: A Performance Analysis1

Knot Pipatsrisawat, Akop Palyan, Mark Chavira, Arthur Choi, Adnan Darwiche, Ewald Speckenmeyer, Chu Min Li, Vasco Manquinho, Armando Tacchella
2008 Journal on Satisfiability, Boolean Modeling and Computation  
Clone utilizes a novel bound computation based on formula compilation that allows it to search in a reduced search space.  ...  We analyze, in this work, the performance of a recently introduced weighted Max-SAT solver, Clone, in the Max-SAT evaluation 2007.  ...  Reducing Max-SAT to Minimum Cardinality Given a CNF formula and a cost for each literal of the formula, the weighted minimum cardinality problem asks for a satisfying assignment that costs the least.  ... 
doi:10.3233/sat190044 fatcat:dkx5duodpnh5pc7r7chagvv4vq

Quantum Optimization [article]

Tad Hogg, Dmitriy Portnov
2000 arXiv   pre-print
We present a quantum algorithm for combinatorial optimization using the cost structure of the search states.  ...  Simulations with randomly generated problem instances show each step of the algorithm shifts amplitude preferentially towards lower cost states, thereby concentrating amplitudes into low-cost states, on  ...  We also thank Weixiong Zhang for providing his TSP search program and helpful comments on its behavior.  ... 
arXiv:quant-ph/0006090v1 fatcat:w24x6ixnmzezbfhb3ow5nncbmi

Fixed-Parameter and Approximation Algorithms: A New Look [chapter]

Rajesh Chitnis, MohammadTaghi Hajiaghayi, Guy Kortsarz
2013 Lecture Notes in Computer Science  
Our results indicate a potential separation between the classes W[1] and W[2]; since no W[2]-hard problem is known to have a polynomial time f (OPT)-approximation for any function f .  ...  size of the universe and M is the number of sets. • Unless NP ⊆ SUBEXP, for every 1 > δ > 0 there exists a constant F(δ ) > 0 such that Clique has no FPT cost approximation with ratio k 1−δ in 2 k F ·  ...  If at most ε-fraction of edges of I 1 can be satisfied, then the size of a minimum set cover for I 2 is at least |V 1 |+|V 2 | √ 32ε 5 SAT is the standard Boolean satisfiability problem 3.  ... 
doi:10.1007/978-3-319-03898-8_11 fatcat:okiqr5f655au7owy4ij7wtz3y4

Approximation Strategies for Incomplete MaxSAT [chapter]

Saurabh Joshi, Prateek Kumar, Ruben Martins, Sukrut Rao
2018 Lecture Notes in Computer Science  
In this paper, we propose two approximation strategies for improving incomplete MaxSAT solving. In one of the strategies, we cluster the weights and approximate them with a representative weight.  ...  In another strategy, we break up the problem of minimizing the sum of weights of unsatisfiable clauses into multiple minimization subproblems.  ...  Authors would like to thank the anonymous reviewers for their helpful comments, and Saketha Nath for lending his servers for the experiments.  ... 
doi:10.1007/978-3-319-98334-9_15 fatcat:d6sv54jifraxvadcnfqlyawgmu
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