3,575 research outputs found
Finding Connected Dense -Subgraphs
Given a connected graph on vertices and a positive integer ,
a subgraph of on vertices is called a -subgraph in . We design
combinatorial approximation algorithms for finding a connected -subgraph in
such that its density is at least a factor
of the density of the densest -subgraph
in (which is not necessarily connected). These particularly provide the
first non-trivial approximations for the densest connected -subgraph problem
on general graphs
Finding long cycles in graphs
We analyze the problem of discovering long cycles inside a graph. We propose
and test two algorithms for this task. The first one is based on recent
advances in statistical mechanics and relies on a message passing procedure.
The second follows a more standard Monte Carlo Markov Chain strategy. Special
attention is devoted to Hamiltonian cycles of (non-regular) random graphs of
minimal connectivity equal to three
Enumerating Top-k Quasi-Cliques
Quasi-cliques are dense incomplete subgraphs of a graph that generalize the
notion of cliques. Enumerating quasi-cliques from a graph is a robust way to
detect densely connected structures with applications to bio-informatics and
social network analysis. However, enumerating quasi-cliques in a graph is a
challenging problem, even harder than the problem of enumerating cliques. We
consider the enumeration of top-k degree-based quasi-cliques, and make the
following contributions: (1) We show that even the problem of detecting if a
given quasi-clique is maximal (i.e. not contained within another quasi-clique)
is NP-hard (2) We present a novel heuristic algorithm KernelQC to enumerate the
k largest quasi-cliques in a graph. Our method is based on identifying kernels
of extremely dense subgraphs within a graph, following by growing subgraphs
around these kernels, to arrive at quasi-cliques with the required densities
(3) Experimental results show that our algorithm accurately enumerates
quasi-cliques from a graph, is much faster than current state-of-the-art
methods for quasi-clique enumeration (often more than three orders of magnitude
faster), and can scale to larger graphs than current methods.Comment: 10 page
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