13,183 research outputs found
A Solution Merging Heuristic for the Steiner Problem in Graphs Using Tree Decompositions
Fixed parameter tractable algorithms for bounded treewidth are known to exist
for a wide class of graph optimization problems. While most research in this
area has been focused on exact algorithms, it is hard to find decompositions of
treewidth sufficiently small to make these al- gorithms fast enough for
practical use. Consequently, tree decomposition based algorithms have limited
applicability to large scale optimization. However, by first reducing the input
graph so that a small width tree decomposition can be found, we can harness the
power of tree decomposi- tion based techniques in a heuristic algorithm, usable
on graphs of much larger treewidth than would be tractable to solve exactly. We
propose a solution merging heuristic to the Steiner Tree Problem that applies
this idea. Standard local search heuristics provide a natural way to generate
subgraphs with lower treewidth than the original instance, and subse- quently
we extract an improved solution by solving the instance induced by this
subgraph. As such the fixed parameter tractable algorithm be- comes an
efficient tool for our solution merging heuristic. For a large class of sparse
benchmark instances the algorithm is able to find small width tree
decompositions on the union of generated solutions. Subsequently it can often
improve on the generated solutions fast
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Variable neighbourhood search for the minimum labelling Steiner tree problem
We present a study on heuristic solution approaches to the minimum labelling Steiner tree problem, an NP-hard graph problem related to the minimum labelling spanning tree problem. Given an undirected labelled connected graph, the aim is to find a spanning tree covering a given subset of nodes of the graph, whose edges have the smallest number of distinct labels. Such a model may be used to represent many real world problems in telecommunications and multimodal transportation networks. Several metaheuristics are proposed and evaluated. The approaches are compared to the widely adopted Pilot Method and it is shown that the Variable Neighbourhood Search that we propose is the most effective metaheuristic for the problem, obtaining high quality solutions in short computational running time
The Minimum Wiener Connector
The Wiener index of a graph is the sum of all pairwise shortest-path
distances between its vertices. In this paper we study the novel problem of
finding a minimum Wiener connector: given a connected graph and a set
of query vertices, find a subgraph of that connects all
query vertices and has minimum Wiener index.
We show that The Minimum Wiener Connector admits a polynomial-time (albeit
impractical) exact algorithm for the special case where the number of query
vertices is bounded. We show that in general the problem is NP-hard, and has no
PTAS unless . Our main contribution is a
constant-factor approximation algorithm running in time
.
A thorough experimentation on a large variety of real-world graphs confirms
that our method returns smaller and denser solutions than other methods, and
does so by adding to the query set a small number of important vertices
(i.e., vertices with high centrality).Comment: Published in Proceedings of the 2015 ACM SIGMOD International
Conference on Management of Dat
A parallel genetic algorithm for the Steiner Problem in Networks
This paper presents a parallel genetic algorithm to the
Steiner Problem in Networks. Several previous papers
have proposed the adoption of GAs and others
metaheuristics to solve the SPN demonstrating the
validity of their approaches. This work differs from them
for two main reasons: the dimension and the
characteristics of the networks adopted in the experiments
and the aim from which it has been originated. The reason
that aimed this work was namely to build a comparison
term for validating deterministic and computationally
inexpensive algorithms which can be used in practical
engineering applications, such as the multicast
transmission in the Internet. On the other hand, the large
dimensions of our sample networks require the adoption
of a parallel implementation of the Steiner GA, which is
able to deal with such large problem instances
Approximate Closest Community Search in Networks
Recently, there has been significant interest in the study of the community
search problem in social and information networks: given one or more query
nodes, find densely connected communities containing the query nodes. However,
most existing studies do not address the "free rider" issue, that is, nodes far
away from query nodes and irrelevant to them are included in the detected
community. Some state-of-the-art models have attempted to address this issue,
but not only are their formulated problems NP-hard, they do not admit any
approximations without restrictive assumptions, which may not always hold in
practice.
In this paper, given an undirected graph G and a set of query nodes Q, we
study community search using the k-truss based community model. We formulate
our problem of finding a closest truss community (CTC), as finding a connected
k-truss subgraph with the largest k that contains Q, and has the minimum
diameter among such subgraphs. We prove this problem is NP-hard. Furthermore,
it is NP-hard to approximate the problem within a factor , for
any . However, we develop a greedy algorithmic framework,
which first finds a CTC containing Q, and then iteratively removes the furthest
nodes from Q, from the graph. The method achieves 2-approximation to the
optimal solution. To further improve the efficiency, we make use of a compact
truss index and develop efficient algorithms for k-truss identification and
maintenance as nodes get eliminated. In addition, using bulk deletion
optimization and local exploration strategies, we propose two more efficient
algorithms. One of them trades some approximation quality for efficiency while
the other is a very efficient heuristic. Extensive experiments on 6 real-world
networks show the effectiveness and efficiency of our community model and
search algorithms
Variable neighbourhood search for the minimum labelling Steiner tree problem
We present a study on heuristic solution approaches to the minimum labelling Steiner
tree problem, an NP-hard graph problem related to the minimum labelling spanning tree
problem. Given an undirected labelled connected graph, the aim is to find a spanning
tree covering a given subset of nodes of the graph, whose edges have the smallest number
of distinct labels. Such a model may be used to represent many real world problems in
telecommunications and multimodal transportation networks. Several metaheuristics are
proposed and evaluated. The approaches are compared to the widely adopted Pilot Method
and it is shown that the Variable Neighbourhood Search metaheuristic is the most effective
approach to the problem, obtaining high quality solutions in short computational running
times
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