8 research outputs found
GraphCombEx: A Software Tool for Exploration of Combinatorial Optimisation Properties of Large Graphs
We present a prototype of a software tool for exploration of multiple
combinatorial optimisation problems in large real-world and synthetic complex
networks. Our tool, called GraphCombEx (an acronym of Graph Combinatorial
Explorer), provides a unified framework for scalable computation and
presentation of high-quality suboptimal solutions and bounds for a number of
widely studied combinatorial optimisation problems. Efficient representation
and applicability to large-scale graphs and complex networks are particularly
considered in its design. The problems currently supported include maximum
clique, graph colouring, maximum independent set, minimum vertex clique
covering, minimum dominating set, as well as the longest simple cycle problem.
Suboptimal solutions and intervals for optimal objective values are estimated
using scalable heuristics. The tool is designed with extensibility in mind,
with the view of further problems and both new fast and high-performance
heuristics to be added in the future. GraphCombEx has already been successfully
used as a support tool in a number of recent research studies using
combinatorial optimisation to analyse complex networks, indicating its promise
as a research software tool
Hierarchical Partial Planarity
In this paper we consider graphs whose edges are associated with a degree of
{\em importance}, which may depend on the type of connections they represent or
on how recently they appeared in the scene, in a streaming setting. The goal is
to construct layouts of these graphs in which the readability of an edge is
proportional to its importance, that is, more important edges have fewer
crossings. We formalize this problem and study the case in which there exist
three different degrees of importance. We give a polynomial-time testing
algorithm when the graph induced by the two most important sets of edges is
biconnected. We also discuss interesting relationships with other
constrained-planarity problems.Comment: Conference version appeared in WG201
Planarity of Streamed Graphs
In this paper we introduce a notion of planarity for graphs that are
presented in a streaming fashion. A is a stream of
edges on a vertex set . A streamed graph is
- with respect to a positive integer window
size if there exists a sequence of planar topological drawings
of the graphs such that
the common graph is drawn the same in
and in , for . The Problem with window size asks whether a given streamed
graph is -stream planar. We also consider a generalization, where there
is an additional whose edges have to be present
during each time step. These problems are related to several well-studied
planarity problems.
We show that the Problem is NP-complete even when
the window size is a constant and that the variant with a backbone graph is
NP-complete for all . On the positive side, we provide
-time algorithms for (i) the case and (ii) all
values of provided the backbone graph consists of one -connected
component plus isolated vertices and no stream edge connects two isolated
vertices. Our results improve on the Hanani-Tutte-style -time
algorithm proposed by Schaefer [GD'14] for .Comment: 21 pages, 9 figures, extended version of "Planarity of Streamed
Graphs" (9th International Conference on Algorithms and Complexity, 2015
Drawing Trees in a Streaming Model
We introduce a data stream model of computation for Graph Drawing, where a source produces a graph one edge at a time. When an edge is produced, it is immediately drawn and its drawing can not be altered. The drawing has an image persistence, that controls the lifetime of edges. If the persistence is k, an edge remains in the drawing for the time spent by the source to generate k edges, then it fades away. In this model we study the area requirement of planar straight-line grid drawings of trees, with different streaming orders, layout models, and quality criteria. We assess the output quality of the presented algorithms by computing the competitive ratio with respect to the best known offline algorithms