18,180 research outputs found
Cut Size Statistics of Graph Bisection Heuristics
We investigate the statistical properties of cut sizes generated by heuristic
algorithms which solve approximately the graph bisection problem. On an
ensemble of sparse random graphs, we find empirically that the distribution of
the cut sizes found by ``local'' algorithms becomes peaked as the number of
vertices in the graphs becomes large. Evidence is given that this distribution
tends towards a Gaussian whose mean and variance scales linearly with the
number of vertices of the graphs. Given the distribution of cut sizes
associated with each heuristic, we provide a ranking procedure which takes into
account both the quality of the solutions and the speed of the algorithms. This
procedure is demonstrated for a selection of local graph bisection heuristics.Comment: 17 pages, 5 figures, submitted to SIAM Journal on Optimization also
available at http://ipnweb.in2p3.fr/~martin
Algorithms for Graph-Constrained Coalition Formation in the Real World
Coalition formation typically involves the coming together of multiple,
heterogeneous, agents to achieve both their individual and collective goals. In
this paper, we focus on a special case of coalition formation known as
Graph-Constrained Coalition Formation (GCCF) whereby a network connecting the
agents constrains the formation of coalitions. We focus on this type of problem
given that in many real-world applications, agents may be connected by a
communication network or only trust certain peers in their social network. We
propose a novel representation of this problem based on the concept of edge
contraction, which allows us to model the search space induced by the GCCF
problem as a rooted tree. Then, we propose an anytime solution algorithm
(CFSS), which is particularly efficient when applied to a general class of
characteristic functions called functions. Moreover, we show how CFSS can
be efficiently parallelised to solve GCCF using a non-redundant partition of
the search space. We benchmark CFSS on both synthetic and realistic scenarios,
using a real-world dataset consisting of the energy consumption of a large
number of households in the UK. Our results show that, in the best case, the
serial version of CFSS is 4 orders of magnitude faster than the state of the
art, while the parallel version is 9.44 times faster than the serial version on
a 12-core machine. Moreover, CFSS is the first approach to provide anytime
approximate solutions with quality guarantees for very large systems of agents
(i.e., with more than 2700 agents).Comment: Accepted for publication, cite as "in press
Partitioning networks into cliques: a randomized heuristic approach
In the context of community detection in social networks, the term community can be grounded in the strict way that simply everybody should know each other within the community. We consider the corresponding community detection problem. We search for a partitioning of a network into the minimum number of non-overlapping cliques, such that the cliques cover all vertices. This problem is called the clique covering problem (CCP) and is one of the classical NP-hard problems. For CCP, we propose a randomized heuristic approach. To construct a high quality solution to CCP, we present an iterated greedy (IG) algorithm. IG can also be combined with a heuristic used to determine how far the algorithm is from the optimum in the worst case. Randomized local search (RLS) for maximum independent set was proposed to find such a bound. The experimental results of IG and the bounds obtained by RLS indicate that IG is a very suitable technique for solving CCP in real-world graphs. In addition, we summarize our basic rigorous results, which were developed for analysis of IG and understanding of its behavior on several relevant graph classes
Recent Advances in Graph Partitioning
We survey recent trends in practical algorithms for balanced graph
partitioning together with applications and future research directions
Sonet Network Design Problems
This paper presents a new method and a constraint-based objective function to
solve two problems related to the design of optical telecommunication networks,
namely the Synchronous Optical Network Ring Assignment Problem (SRAP) and the
Intra-ring Synchronous Optical Network Design Problem (IDP). These network
topology problems can be represented as a graph partitioning with capacity
constraints as shown in previous works. We present here a new objective
function and a new local search algorithm to solve these problems. Experiments
conducted in Comet allow us to compare our method to previous ones and show
that we obtain better results
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