Open AccessProceedings Article
Backbones in optimization and approximation
John Slaney,Toby Walsh +1 more
- 04 Aug 2001
- pp 254-259
TL;DR: The impact of backbones in optimization and approximation problems is studied to find that to observe the impact of backbone size on problem hardness, it is necessary to eliminate some symmetries, perform trivial reductions and factor out the effective problem size.
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Abstract: We study the impact of backbones in optimization and approximation problems. We show that some optimization problems like graph coloring resemble decision problems, with problem hardness positively correlated with backbone size. For other optimization problems like blocks world planning and traveling salesperson problems, problem hardness is weakly and negatively correlated with backbone size, while the cost of finding optimal and approximate solutions is positively correlated with backbone size. A third class of optimization problems like number partitioning have regions of both types of behavior. We find that to observe the impact of backbone size on problem hardness, it is necessary to eliminate some symmetries, perform trivial reductions and factor out the effective problem size.
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Citations
Partial Compilation of SAT Using Selective Backbones
Andy Balogh,Guillaume Escamocher,Barry O'Sullivan +2 more
TL;DR: This paper proposes a partial compilation method for SAT instances, reducing compiled size while preserving solution information, by assigning values to a subset of variables, called the selective backbone, to achieve a smaller representation with minimal solution loss.
Mining Potentially Explanatory Patterns via Partial Solutions
GianCarlo Catalano,Alexander E. I. Brownlee,David Cairns,John Mccall,Russell Ainslie +4 more
TL;DR: Mining potentially explanatory patterns via partial solutions improves explainability of solutions to combinatorial optimization problems without significantly impacting search performance.
A preference-based approach to backbone computation with application to argumentation
Alessandro Previti,Matti Järvisalo +1 more
- 09 Apr 2018
TL;DR: This paper proposes a new backbone algorithm which makes use of a "SAT with preferences" solver, i.e., a SAT solver which is guaranteed to output a most preferred satisfying assignment w.r.t. a given preference over literals of the SAT instance at hand.
Leveraging cluster backbones for improving MAP inference in statistical relational models
TL;DR: A novel family of extended factor graphs that are parameterized by a smoothing parameter χ ∈ [0,1] are introduced, and applying belief propagation (BP) message-passing to this family formulates a new family of WSP- χ algorithms applicable to relational domains.
Effective Tour Searching for TSP by Contraction of Pseudo Backbone Edges
Changxing Dong,Gerold Jäger,Dirk Richter,Paul Molitor +3 more
- 18 Jun 2009
TL;DR: A reduction technique for the well-known TSP that can set world records and find better tours than the best tours known so far, mainly due to the effective reduction of the problem size so that the more important tour subspace is searched more intensively.
References
New methods to color the vertices of a graph
TL;DR: An exact method is given which performs better than the Randall-Brown algorithm and is able to color larger graphs and the new heuristic methods, the classical methods, and the exact method are compared.
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•Proceedings Article
Where the really hard problems are
Peter Cheeseman,Bob Kanefsky,Will Taylor +2 more
- 24 Aug 1991
TL;DR: It is shown that NP-complete problems can be summarized by at least one "order parameter", and that the hard problems occur at a critical value of such a parameter.
•Proceedings Article
Hard and easy distributions of SAT problems
David G. Mitchell,Bart Selman,Hector J. Levesque +2 more
- 12 Jul 1992
TL;DR: It is shown that by using the right distribution of instances, and appropriate parameter values, it is possible to generate random formulas that are hard, that is, for which satisfiability testing is quite difficult.
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Determining computational complexity from characteristic 'phase transitions.'
TL;DR: An analytic solution and experimental investigation of the phase transition in K -satisfiability, an archetypal NP-complete problem, is reported and the nature of these transitions may explain the differing computational costs, and suggests directions for improving the efficiency of search algorithms.
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