An algorithm for computing the edge-connectivity of a multigraph, where p ( \leqq | E | )$ is the number of pairs of nodes between which G has an edge, is proposed and consists only of times of graph searches and edge contractions.Expand

The computational complexity and algorithms of the core are studied to answer important questions about the cores of various games on graphs, such as maximum flow, connectivity, maximum matching, minimum vertex cover, minimum edge cover, maximum independent set, and minimum coloring.Expand

The problem of finding a smallest 2-edge-connected spanning subgraph (V,F ∪ E') of G + T containing T is shown to be (1.875 + e)-approximable in O(n½m + n2) time for any constant e < 0.Expand

A simple and unified framework for developing and analyzing approximation algorithms for various MPPs and their generalizations in hypergraphs is presented.Expand

It is shown that all cuts of weights less than $k\lambda({\cal N})$ can be enumerated in $O(m^2n+n^{2k}m)$ time without using the maximum flow algorithm.Expand

This work focuses on the perfect packing problem (PP), which is a special case of 2SP, wherein all given rectangles are required to be packed without wasted space, and design branch-and-bound algorithms introducing several branching rules and bounding operations.Expand

The authors comprehensively discuss new concepts and algorithms that allow for quicker and more efficient computing, such as maximum adjacency ordering of vertices.Expand

This work opens up the question of fully characterizing the combinatorial structures of totally balanced packing and covering games, for which some interesting examples are presented: the totally balanced matching, vertex cover, and minimum coloring games.Expand

It is proved that every internally triconnected clustered plane graph with a completely connected clustering structure admits a ''fully convex drawing,'' a planar straight-line drawing such that both clusters and facial cycles are drawn as convex polygons.Expand

We present an O^*(1.0836^n)-time algorithm for finding a maximum independent set in an n-vertex graph with degree bounded by 3, which improves all previous running time bounds for this problem. Our… Expand