13 research outputs found
Another look at graph coloring via propositional satisfiability
AbstractThis paper studies the solution of graph coloring problems by encoding into propositional satisfiability problems. The study covers three kinds of satisfiability solvers, based on postorder reasoning (e.g., grasp, chaff), preorder reasoning (e.g., 2cl, 2clsEq), and back-chaining (modoc). The study evaluates three encodings, one of them believed to be new. Some new symmetry-breaking methods, specific to coloring, are used to reduce the redundancy of solutions. A by-product of this research is an implemented lower-bound technique that has shown improved lower bounds for the chromatic numbers of the long-standing unsolved random graphs known as DSJC125.5 and DSJC125.9. Independent-set analysis shows that the chromatic numbers of DSJC125.5 and DSJC125.9 are at least 18 and 40, respectively, but satisfiability encoding was able to demonstrate only that the chromatic numbers are at least 13 and 38, respectively, within available time and space
IGraph/M: graph theory and network analysis for Mathematica
IGraph/M is an efficient general purpose graph theory and network analysis
package for Mathematica. IGraph/M serves as the Wolfram Language interfaces to
the igraph C library, and also provides several unique pieces of functionality
not yet present in igraph, but made possible by combining its capabilities with
Mathematica's. The package is designed to support both graph theoretical
research as well as the analysis of large-scale empirical networks.Comment: submitted to Journal of Open Source Software on August 30, 202
Computation with Polynomial Equations and Inequalities arising in Combinatorial Optimization
The purpose of this note is to survey a methodology to solve systems of
polynomial equations and inequalities. The techniques we discuss use the
algebra of multivariate polynomials with coefficients over a field to create
large-scale linear algebra or semidefinite programming relaxations of many
kinds of feasibility or optimization questions. We are particularly interested
in problems arising in combinatorial optimization.Comment: 28 pages, survey pape
ASlib: A Benchmark Library for Algorithm Selection
The task of algorithm selection involves choosing an algorithm from a set of
algorithms on a per-instance basis in order to exploit the varying performance
of algorithms over a set of instances. The algorithm selection problem is
attracting increasing attention from researchers and practitioners in AI. Years
of fruitful applications in a number of domains have resulted in a large amount
of data, but the community lacks a standard format or repository for this data.
This situation makes it difficult to share and compare different approaches
effectively, as is done in other, more established fields. It also
unnecessarily hinders new researchers who want to work in this area. To address
this problem, we introduce a standardized format for representing algorithm
selection scenarios and a repository that contains a growing number of data
sets from the literature. Our format has been designed to be able to express a
wide variety of different scenarios. Demonstrating the breadth and power of our
platform, we describe a set of example experiments that build and evaluate
algorithm selection models through a common interface. The results display the
potential of algorithm selection to achieve significant performance
improvements across a broad range of problems and algorithms.Comment: Accepted to be published in Artificial Intelligence Journa
On the Quest for an Acyclic Graph
The paper aims at finding acyclic graphs under a given set of
constraints. More specifically, given a propositional formula
? over edges of a fixed-size graph, the objective is to find a model of
? that corresponds to a graph that is acyclic. The paper proposes several encodings of the
problem and compares them in an experimental evaluation using stateof-the-art
SAT solvers
The Configurable SAT Solver Challenge (CSSC)
It is well known that different solution strategies work well for different
types of instances of hard combinatorial problems. As a consequence, most
solvers for the propositional satisfiability problem (SAT) expose parameters
that allow them to be customized to a particular family of instances. In the
international SAT competition series, these parameters are ignored: solvers are
run using a single default parameter setting (supplied by the authors) for all
benchmark instances in a given track. While this competition format rewards
solvers with robust default settings, it does not reflect the situation faced
by a practitioner who only cares about performance on one particular
application and can invest some time into tuning solver parameters for this
application. The new Configurable SAT Solver Competition (CSSC) compares
solvers in this latter setting, scoring each solver by the performance it
achieved after a fully automated configuration step. This article describes the
CSSC in more detail, and reports the results obtained in its two instantiations
so far, CSSC 2013 and 2014
SATzilla: Portfolio-based Algorithm Selection for SAT
It has been widely observed that there is no single "dominant" SAT solver;
instead, different solvers perform best on different instances. Rather than
following the traditional approach of choosing the best solver for a given
class of instances, we advocate making this decision online on a per-instance
basis. Building on previous work, we describe SATzilla, an automated approach
for constructing per-instance algorithm portfolios for SAT that use so-called
empirical hardness models to choose among their constituent solvers. This
approach takes as input a distribution of problem instances and a set of
component solvers, and constructs a portfolio optimizing a given objective
function (such as mean runtime, percent of instances solved, or score in a
competition). The excellent performance of SATzilla was independently verified
in the 2007 SAT Competition, where our SATzilla07 solvers won three gold, one
silver and one bronze medal. In this article, we go well beyond SATzilla07 by
making the portfolio construction scalable and completely automated, and
improving it by integrating local search solvers as candidate solvers, by
predicting performance score instead of runtime, and by using hierarchical
hardness models that take into account different types of SAT instances. We
demonstrate the effectiveness of these new techniques in extensive experimental
results on data sets including instances from the most recent SAT competition