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Compact Encodings of Planar Graphs via Canonical Orderings and Multiple Parentheses
Three sets of coding schemes which all take linear time for encoding and decoding are presented which are significantly shorter than the previously known results in each case.
Approximating Maximum Leaf Spanning Trees in Almost Linear Time
This paper gives a new greedy 3-approximation algorithm for maximum leaf spanning trees, where the running timeO((m+n)?(m,n)) required by the algorithm, where m is the number of edges and n is thenumber of nodes, is almost linear in the size of the graph.
Orderly Spanning Trees with Applications
- Yi-Ting Chiang, Ching-Chi Lin, Hsueh-I Lu
- Mathematics, Computer ScienceSIAM J. Comput.
- 7 February 2001
An algorithm to compute an orderly pair for any connected planar graphs G, consisting of an embedded planar graph H isomorphic to G, and an orderly spanning tree of H.
Multicast routing with multiple QoS constraints in ATM networks
An Optimal Algorithm for the Maximum-Density Segment Problem
The algorithm has the capability to process the input sequence in an online manner, which is an important feature for dealing with genome-scale sequences and shows how to exploit the sparsity of S and solve the maximum-density segment problem for S in O(k) time.
Orderly spanning trees with applications to graph encoding and graph drawing
The technique of orderly spanning trees of connected planar graphs yields the best known encoding of G, with query support, and the first area-optimal 2-visibility drawing of G.
Linear-Time Succinct Encodings of Planar Graphs via Canonical Orderings
Two schemes to encode and decode an embedded planar undirected graph that has n vertices, m edges, and f faces but has no self-loop or multiple edge and take O(n) time for encoding and decoding are presented.
Efficient approximation algorithms for semidefinite programs arising from MAX CUT and COLORING
An approximation algorithm for graph coloring that also involves solving a semidefinite program and derives a graph cut from that solution is given.
The Power of Local Optimization: Approximation Algorithms for Maximum-Leaf Spanning Tree
This work uses the simple technique of local optimization to provide the first approximation algorithms for this problem and proves that such locally optimal solutions to this problem are globally near-optimal.