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All-Pairs Shortest Paths for Unweighted Undirected Graphs in o(mn) Time

by Timothy M. Chan - Proc. ACM-SIAM Symposium on Discrete Algorithms (SODA , 2006
"... Abstract We revisit the all-pairs-shortest-paths problem for an unweighted undirected graph with n vertices and m edges. We present new algorithms with the following running times: O(mn = log n) if m? n log ..."
Abstract - Cited by 23 (1 self) - Add to MetaCart
Abstract We revisit the all-pairs-shortest-paths problem for an unweighted undirected graph with n vertices and m edges. We present new algorithms with the following running times: O(mn = log n) if m? n log

An algorithm for drawing general undirected graphs

by Tomihisa Kamada, Satoru Kawai - Information Processing Letters , 1989
"... Graphs (networks) are very common data structures which are handled in computers. Diagrams are widely used to represent the graph structures visually in many information systems. In order to automatically draw the diagrams which are, for example, state graphs, data-flow graphs, Petri nets, and entit ..."
Abstract - Cited by 698 (2 self) - Add to MetaCart
Graphs (networks) are very common data structures which are handled in computers. Diagrams are widely used to represent the graph structures visually in many information systems. In order to automatically draw the diagrams which are, for example, state graphs, data-flow graphs, Petri nets

Depth first search and linear graph algorithms

by Robert Tarjan - SIAM JOURNAL ON COMPUTING , 1972
"... The value of depth-first search or "backtracking" as a technique for solving problems is illustrated by two examples. An improved version of an algorithm for finding the strongly connected components of a directed graph and ar algorithm for finding the biconnected components of an undirect ..."
Abstract - Cited by 1406 (19 self) - Add to MetaCart
of an undirect graph are presented. The space and time requirements of both algorithms are bounded by k 1V + k2E d- k for some constants kl, k2, and k a, where Vis the number of vertices and E is the number of edges of the graph being examined.

Fast Edge Orientation for Unweighted Graphs

by Anand Bhalgat , Ramesh Hariharan
"... Abstract We consider an unweighted undirected graph with n vertices, m edges, and edge connectivity 2k. The weak edge orientation problem requires that the edges of this graph be oriented so the resulting directed graph is at least k edge-connected. Nash-Williams proved the existence of such orient ..."
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Abstract We consider an unweighted undirected graph with n vertices, m edges, and edge connectivity 2k. The weak edge orientation problem requires that the edges of this graph be oriented so the resulting directed graph is at least k edge-connected. Nash-Williams proved the existence

Succinct Oracles for Exact Distances in Undirected Unweighted Graphs Succinct Oracles for Exact Distances in Undirected Unweighted Graphs

by Paolo Ferragina , Igor Nitto , Rossano Venturini , Paolo Ferragina , Igor Nitto , Rossano Venturini
"... Abstract. Let G be an unweighted and undirected graph of n nodes, and let D be the n × n matrix storing the All-Pairs-Shortest-Path distances in G. Since D contains integers in [n], its plain storage takes n 2 log(n + 1) bits. However, a simple counting argument shows that n 2 /2 bits are necessary ..."
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Abstract. Let G be an unweighted and undirected graph of n nodes, and let D be the n × n matrix storing the All-Pairs-Shortest-Path distances in G. Since D contains integers in [n], its plain storage takes n 2 log(n + 1) bits. However, a simple counting argument shows that n 2 /2 bits

Loopy belief propagation for approximate inference: An empirical study. In:

by Kevin P Murphy , Yair Weiss , Michael I Jordan - Proceedings of Uncertainty in AI, , 1999
"... Abstract Recently, researchers have demonstrated that "loopy belief propagation" -the use of Pearl's polytree algorithm in a Bayesian network with loops -can perform well in the context of error-correcting codes. The most dramatic instance of this is the near Shannon-limit performanc ..."
Abstract - Cited by 676 (15 self) - Add to MetaCart
with loops (undirected cycles). The algorithm is an exact inference algorithm for singly connected networks -the beliefs converge to the cor rect marginals in a number of iterations equal to the diameter of the graph.1 However, as Pearl noted, the same algorithm will not give the correct beliefs for mul

Fast Edge Orientation for Unweighted Graphs

by Bhalgat Ramesh Hariharan
"... We consider an unweighted undirected graph with n vertices, m edges, and edge-connectivity 2k. The weak edge orientation problem requires that the edges of this graph be oriented so the resulting directed graph is at least k edge-connected. Nash-Williams proved the existence of such orientations and ..."
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We consider an unweighted undirected graph with n vertices, m edges, and edge-connectivity 2k. The weak edge orientation problem requires that the edges of this graph be oriented so the resulting directed graph is at least k edge-connected. Nash-Williams proved the existence of such orientations

A distributed algorithm for minimum-weight spanning trees

by R. G. Gallager, P. A. Humblet, P. M. Spira , 1983
"... A distributed algorithm is presented that constructs he minimum-weight spanning tree in a connected undirected graph with distinct edge weights. A processor exists at each node of the graph, knowing initially only the weights of the adjacent edges. The processors obey the same algorithm and exchange ..."
Abstract - Cited by 435 (3 self) - Add to MetaCart
A distributed algorithm is presented that constructs he minimum-weight spanning tree in a connected undirected graph with distinct edge weights. A processor exists at each node of the graph, knowing initially only the weights of the adjacent edges. The processors obey the same algorithm

Approximate distance oracles for unweighted graphs . . .

by Surender Baswana, Sandeep Sen
"... ������������ � Let be an undirected graph � on vertices, and ���������� � let denote the distance � in between two � vertices � and. Thorup and Zwick showed that for any +ve � integer, the � graph can be preprocessed to build a data-structure that can efficiently � report-approximate distance betwee ..."
Abstract - Cited by 53 (10 self) - Add to MetaCart
������������ � Let be an undirected graph � on vertices, and ���������� � let denote the distance � in between two � vertices � and. Thorup and Zwick showed that for any +ve � integer, the � graph can be preprocessed to build a data-structure that can efficiently � report-approximate distance

Variational algorithms for approximate Bayesian inference

by Matthew J. Beal , 2003
"... The Bayesian framework for machine learning allows for the incorporation of prior knowledge in a coherent way, avoids overfitting problems, and provides a principled basis for selecting between alternative models. Unfortunately the computations required are usually intractable. This thesis presents ..."
Abstract - Cited by 440 (9 self) - Add to MetaCart
theorems are presented to pave the road for automated VB derivation procedures in both directed and undirected graphs (Bayesian and Markov networks, respectively). Chapters 3-5 derive and apply the VB EM algorithm to three commonly-used and important models: mixtures of factor analysers, linear dynamical
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