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744
Tight Gaps for Vertex Cover in the SheraliAdams SDP Hierarchy
, 2011
"... We give the first tight integrality gap for Vertex Cover in the SheraliAdams SDP system. More precisely, we show that for every ɛ> 0, the standard SDP for Vertex Cover that is strengthened with the level6 SheraliAdams system has integrality gap 2 − ɛ. To the best of our knowledge this is the f ..."
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Cited by 6 (2 self)
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We give the first tight integrality gap for Vertex Cover in the SheraliAdams SDP system. More precisely, we show that for every ɛ> 0, the standard SDP for Vertex Cover that is strengthened with the level6 SheraliAdams system has integrality gap 2 − ɛ. To the best of our knowledge
Using Symmetry to Optimize Over the SheraliAdams Relaxation
, 2013
"... In this paper we examine the impact of using the SheraliAdams procedure on highly symmetric integer programming problems. Linear relaxations of the extended formulations gen) many variables for the leveld erated by SheraliAdams can be very large, containing O ( ( n d closure. When large amounts ..."
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programming problems. We also present a class of constraints, called counting constraints, that further improves the bound, and in some cases provides a tight formulation. A major advantage of the SheraliAdams formulation over the traditional formulation is that symmetrybreaking constraints can be more
SheraliAdams Relaxations and Indistinguishability in Counting Logics
, 2012
"... Two graphs with adjacency matrices A and B are isomorphic if there exists a permutation matrix P for which the identity P T AP = B holds. Multiplying through by P and relaxing the permutation matrix to a doubly stochastic matrix leads to the linear programming relaxation known as fractional isomorph ..."
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Cited by 10 (0 self)
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isomorphism. We show that the levels of the SheraliAdams (SA) hierarchy of linear programming relaxations applied to fractional isomorphism interleave in power with the levels of a wellknown colorrefinementheuristic for graph isomorphism called the WeisfeilerLehman algorithm, orequivalently
Robust algorithms for Max Independent Set on Minorfree graphs based on the SheraliAdams Hierarchy
"... Abstract. This work provides a Linear Programmingbased Polynomial Time Approximation Scheme (PTAS) for two classical NPhard problems on graphs when the input graph is guaranteed to be planar, or more generally Minor Free. The algorithm applies a sufficiently large number (some function of 1/ɛ when ..."
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Cited by 2 (1 self)
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when 1 + ɛ approximation is required) of rounds of the socalled SheraliAdams LiftandProject system. needed to obtain a (1 + ɛ)approximation, where f is some function that depends only on the graph that should be avoided as a minor. The problem we discuss are the wellstudied problems, the Max
ControlFlow Analysis of HigherOrder Languages
, 1991
"... representing the official policies, either expressed or implied, of ONR or the U.S. Government. Keywords: dataflow analysis, Scheme, LISP, ML, CPS, type recovery, higherorder functions, functional programming, optimising compilers, denotational semantics, nonstandard Programs written in powerful, ..."
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Cited by 362 (10 self)
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, higherorder languages like Scheme, ML, and Common Lisp should run as fast as their FORTRAN and C counterparts. They should, but they don’t. A major reason is the level of optimisation applied to these two classes of languages. Many FORTRAN and C compilers employ an arsenal of sophisticated global
Free Bits, PCPs and NonApproximability  Towards Tight Results
, 1996
"... This paper continues the investigation of the connection between proof systems and approximation. The emphasis is on proving tight nonapproximability results via consideration of measures like the "free bit complexity" and the "amortized free bit complexity" of proof systems. ..."
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Cited by 224 (39 self)
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This paper continues the investigation of the connection between proof systems and approximation. The emphasis is on proving tight nonapproximability results via consideration of measures like the "free bit complexity" and the "amortized free bit complexity" of proof systems.
EXACT AND APPROXIMATE ALGORITHMS FOR PARTIALLY OBSERVABLE MARKOV DECISION PROCESSES
, 1998
"... Automated sequential decision making is crucial in many contexts. In the face of uncertainty, this task becomes even more important, though at the same time, computing optimal decision policies becomes more complex. The more sources of uncertainty there are, the harder the problem becomes to solve. ..."
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Cited by 183 (2 self)
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. In this work, we look at sequential decision making in environments where the actions have probabilistic outcomes and in which the system state is only partially observable. We focus on using a model called a partially observable Markov decision process (POMDP) and explore algorithms which address computing
A proof of Alon’s second eigenvalue conjecture
, 2003
"... A dregular graph has largest or first (adjacency matrix) eigenvalue λ1 = d. Consider for an even d ≥ 4, a random dregular graph model formed from d/2 uniform, independent permutations on {1,...,n}. We shall show that for any ɛ>0 we have all eigenvalues aside from λ1 = d are bounded by 2 √ d − 1 ..."
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Cited by 168 (1 self)
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A dregular graph has largest or first (adjacency matrix) eigenvalue λ1 = d. Consider for an even d ≥ 4, a random dregular graph model formed from d/2 uniform, independent permutations on {1,...,n}. We shall show that for any ɛ>0 we have all eigenvalues aside from λ1 = d are bounded by 2 √ d
Potential Function Methods for Approximately Solving Linear Programming Problems: Theory and Practice
, 2001
"... After several decades of sustained research and testing, linear programming has evolved into a remarkably reliable, accurate and useful tool for handling industrial optimization problems. Yet, large problems arising from several concrete applications routinely defeat the very best linear programming ..."
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Cited by 158 (4 self)
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programming, has been to solve problems "to optimality." In concrete implementations, this has always meant the solution ofproblems to some finite accuracy (for example, eight digits). An alternative approach would be to explicitly, and rigorously, trade o# accuracy for speed. One motivating factor
Results 1  10
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744