451 research outputs found
The Design of a Relational Engine
The key design challenges in the construction of a SAT-based relational engine are described, and novel techniques are proposed to address them. An efficient engine must have a mechanism for specifying partial solutions, an effective symmetry detection and breaking scheme, and an economical translation from relational to boolean logic. These desiderata are addressed with three new techniques: a symmetry detection algorithm that works in the presence of partial solutions, a sparse-matrix representation of relations, and a compact representation of boolean formulas inspired by boolean expression diagrams and reduced boolean circuits. The presented techniques have been implemented and evaluated, with promising results
The Symmetry Method for Coloured Petri Nets
This booklet is the author's PhD-dissertation
A SAT Approach to Clique-Width
Clique-width is a graph invariant that has been widely studied in
combinatorics and computer science. However, computing the clique-width of a
graph is an intricate problem, the exact clique-width is not known even for
very small graphs. We present a new method for computing the clique-width of
graphs based on an encoding to propositional satisfiability (SAT) which is then
evaluated by a SAT solver. Our encoding is based on a reformulation of
clique-width in terms of partitions that utilizes an efficient encoding of
cardinality constraints. Our SAT-based method is the first to discover the
exact clique-width of various small graphs, including famous graphs from the
literature as well as random graphs of various density. With our method we
determined the smallest graphs that require a small pre-described clique-width.Comment: proofs in section 3 updated, results remain unchange
The SCIP Optimization Suite 9.0
The SCIP Optimization Suite provides a collection of software packages for
mathematical optimization, centered around the constraint integer programming
(CIP) framework SCIP. This report discusses the enhancements and extensions
included in the SCIP Optimization Suite 9.0. The updates in SCIP 9.0 include
improved symmetry handling, additions and improvements of nonlinear handlers
and primal heuristics, a new cut generator and two new cut selection schemes, a
new branching rule, a new LP interface, and several bug fixes. The SCIP
Optimization Suite 9.0 also features new Rust and C++ interfaces for SCIP, new
Python interface for SoPlex, along with enhancements to existing interfaces.
The SCIP Optimization Suite 9.0 also includes new and improved features in the
LP solver SoPlex, the presolving library PaPILO, the parallel framework UG, the
decomposition framework GCG, and the SCIP extension SCIP-SDP. These additions
and enhancements have resulted in an overall performance improvement of SCIP in
terms of solving time, number of nodes in the branch-and-bound tree, as well as
the reliability of the solver.Comment: The release report of the SCIP Optimization Suite version 9.
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