2,662 research outputs found
Approximating the Minimum Equivalent Digraph
The MEG (minimum equivalent graph) problem is, given a directed graph, to
find a small subset of the edges that maintains all reachability relations
between nodes. The problem is NP-hard. This paper gives an approximation
algorithm with performance guarantee of pi^2/6 ~ 1.64. The algorithm and its
analysis are based on the simple idea of contracting long cycles. (This result
is strengthened slightly in ``On strongly connected digraphs with bounded cycle
length'' (1996).) The analysis applies directly to 2-Exchange, a simple ``local
improvement'' algorithm, showing that its performance guarantee is 1.75.Comment: conference version in ACM-SIAM Symposium on Discrete Algorithms
(1994
The maximum disjoint paths problem on multi-relations social networks
Motivated by applications to social network analysis (SNA), we study the
problem of finding the maximum number of disjoint uni-color paths in an
edge-colored graph. We show the NP-hardness and the approximability of the
problem, and both approximation and exact algorithms are proposed. Since short
paths are much more significant in SNA, we also study the length-bounded
version of the problem, in which the lengths of paths are required to be upper
bounded by a fixed integer . It is shown that the problem can be solved in
polynomial time for and is NP-hard for . We also show that the
problem can be approximated with ratio in polynomial time
for any . Particularly, for , we develop an efficient
2-approximation algorithm
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