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Computing Edge-Connectivity in Multigraphs and Capacitated Graphs
TLDR
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.
Algorithmic Aspects of the Core of Combinatorial Optimization Games
TLDR
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.
An approximation for finding a smallest 2-edge-connected subgraph containing a specified spanning tree
  • H. Nagamochi
  • Computer Science, Mathematics
    Discret. Appl. Math.
  • 26 July 1999
TLDR
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.
Greedy splitting algorithms for approximating multiway partition problems
TLDR
A simple and unified framework for developing and analyzing approximation algorithms for various MPPs and their generalizations in hypergraphs is presented.
Computing All Small Cuts in an Undirected Network
TLDR
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.
Exact algorithms for the two-dimensional strip packing problem with and without rotations
TLDR
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.
Algorithmic Aspects of Graph Connectivity
TLDR
The authors comprehensively discuss new concepts and algorithms that allow for quicker and more efficient computing, such as maximum adjacency ordering of vertices.
Totally balanced combinatorial optimization games
TLDR
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.
Convex drawings of hierarchical planar graphs and clustered planar graphs
TLDR
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.
Confining sets and avoiding bottleneck cases: A simple maximum independent set algorithm in degree-3 graphs
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
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