8,564 research outputs found
On realization graphs of degree sequences
Given the degree sequence of a graph, the realization graph of is the
graph having as its vertices the labeled realizations of , with two vertices
adjacent if one realization may be obtained from the other via an
edge-switching operation. We describe a connection between Cartesian products
in realization graphs and the canonical decomposition of degree sequences
described by R.I. Tyshkevich and others. As applications, we characterize the
degree sequences whose realization graphs are triangle-free graphs or
hypercubes.Comment: 10 pages, 5 figure
JGraphT -- A Java library for graph data structures and algorithms
Mathematical software and graph-theoretical algorithmic packages to
efficiently model, analyze and query graphs are crucial in an era where
large-scale spatial, societal and economic network data are abundantly
available. One such package is JGraphT, a programming library which contains
very efficient and generic graph data-structures along with a large collection
of state-of-the-art algorithms. The library is written in Java with stability,
interoperability and performance in mind. A distinctive feature of this library
is the ability to model vertices and edges as arbitrary objects, thereby
permitting natural representations of many common networks including
transportation, social and biological networks. Besides classic graph
algorithms such as shortest-paths and spanning-tree algorithms, the library
contains numerous advanced algorithms: graph and subgraph isomorphism; matching
and flow problems; approximation algorithms for NP-hard problems such as
independent set and TSP; and several more exotic algorithms such as Berge graph
detection. Due to its versatility and generic design, JGraphT is currently used
in large-scale commercial, non-commercial and academic research projects. In
this work we describe in detail the design and underlying structure of the
library, and discuss its most important features and algorithms. A
computational study is conducted to evaluate the performance of JGraphT versus
a number of similar libraries. Experiments on a large number of graphs over a
variety of popular algorithms show that JGraphT is highly competitive with
other established libraries such as NetworkX or the BGL.Comment: Major Revisio
Space-Efficient Approximation Scheme for Maximum Matching in Sparse Graphs
We present a Logspace Approximation Scheme (LSAS), i.e. an approximation algorithm for maximum matching in planar graphs (not necessarily bipartite) that achieves an approximation ratio arbitrarily close to one, using only logarithmic space. This deviates from the well known Baker\u27s approach for approximation in planar graphs by avoiding the use of distance computation - which is not known to be in Logspace. Our algorithm actually works for any "recursively sparse" graph class which contains a linear size matching and also for certain other classes like bounded genus graphs.
The scheme is based on an LSAS in bounded degree graphs which are not known to be amenable to Baker\u27s method. We solve the bounded degree case by parallel augmentation of short augmenting paths. Finding a large number of such disjoint paths can, in turn, be reduced to finding a large independent set in a bounded degree graph. The bounded degree assumption allows us to obtain a Logspace algorithm
Composite Graph Coloring Algorithms and Applications
A vertex-composite graph is a graph that can have unequal chromaticities on its vertices. Vertex-composite graph coloring or composite graph coloring involves coloring each vertex of a composite graph with consecutive colors according to the vertex\u27s chromaticity with no two vertices adjacent to one another having the same color(s).
New heuristic algorithms including the use of the saturation degree method have been developed in this research. All eleven heuristic algorithms including Clementson and Elphick algorithms were then tested using random composite graphs with five different chromaticity distributions. The best algorithm which uses the least average colors from the experiment is the MLF1I algorithm follow very closely by the MLF2I algorithm.
Four applications, Timetabling, Job Shop Scheduling, CPU Scheduling and Network Assignment Problem, have been formulated as composite graph coloring problems and solved using heuristic composite graph coloring algorithms
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