5,916 research outputs found
Graphs, Matrices, and the GraphBLAS: Seven Good Reasons
The analysis of graphs has become increasingly important to a wide range of
applications. Graph analysis presents a number of unique challenges in the
areas of (1) software complexity, (2) data complexity, (3) security, (4)
mathematical complexity, (5) theoretical analysis, (6) serial performance, and
(7) parallel performance. Implementing graph algorithms using matrix-based
approaches provides a number of promising solutions to these challenges. The
GraphBLAS standard (istc- bigdata.org/GraphBlas) is being developed to bring
the potential of matrix based graph algorithms to the broadest possible
audience. The GraphBLAS mathematically defines a core set of matrix-based graph
operations that can be used to implement a wide class of graph algorithms in a
wide range of programming environments. This paper provides an introduction to
the GraphBLAS and describes how the GraphBLAS can be used to address many of
the challenges associated with analysis of graphs.Comment: 10 pages; International Conference on Computational Science workshop
on the Applications of Matrix Computational Methods in the Analysis of Modern
Dat
Combining Relational Algebra, SQL, Constraint Modelling, and Local Search
The goal of this paper is to provide a strong integration between constraint
modelling and relational DBMSs. To this end we propose extensions of standard
query languages such as relational algebra and SQL, by adding constraint
modelling capabilities to them. In particular, we propose non-deterministic
extensions of both languages, which are specially suited for combinatorial
problems. Non-determinism is introduced by means of a guessing operator, which
declares a set of relations to have an arbitrary extension. This new operator
results in languages with higher expressive power, able to express all problems
in the complexity class NP. Some syntactical restrictions which make data
complexity polynomial are shown. The effectiveness of both extensions is
demonstrated by means of several examples. The current implementation, written
in Java using local search techniques, is described. To appear in Theory and
Practice of Logic Programming (TPLP)Comment: 30 pages, 5 figure
Simplicial blowups and discrete normal surfaces in simpcomp
simpcomp is an extension to GAP, the well known system for computational
discrete algebra. It allows the user to work with simplicial complexes. In the
latest version, support for simplicial blowups and discrete normal surfaces was
added, both features unique to simpcomp. Furthermore, new functions for
constructing certain infinite series of triangulations have been implemented
and interfaces to other software packages have been improved to previous
versions.Comment: 10 page
A combinatorial approach to knot recognition
This is a report on our ongoing research on a combinatorial approach to knot
recognition, using coloring of knots by certain algebraic objects called
quandles. The aim of the paper is to summarize the mathematical theory of knot
coloring in a compact, accessible manner, and to show how to use it for
computational purposes. In particular, we address how to determine colorability
of a knot, and propose to use SAT solving to search for colorings. The
computational complexity of the problem, both in theory and in our
implementation, is discussed. In the last part, we explain how coloring can be
utilized in knot recognition
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