Results 1  10
of
243
Loopy belief propagation for approximate inference: An empirical study. In:
 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 errorcorrecting codes. The most dramatic instance of this is the near Shannonlimit 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
A general approximation technique for constrained forest problems
 SIAM J. COMPUT.
, 1995
"... We present a general approximation technique for a large class of graph problems. Our technique mostly applies to problems of covering, at minimum cost, the vertices of a graph with trees, cycles, or paths satisfying certain requirements. In particular, many basic combinatorial optimization proble ..."
Abstract

Cited by 414 (21 self)
 Add to MetaCart
problems fit in this framework, including the shortest path, minimumcost spanning tree, minimumweight perfect matching, traveling salesman, and Steiner tree problems. Our technique produces approximation algorithms that run in O(n log n) time and come within a factor of 2 of optimal for most
FASTER ALGORITHMS FOR ALLPAIRS APPROXIMATE SHORTEST PATHS IN UNDIRECTED GRAPHS
, 2006
"... Let G = (V, E) be a weighted undirected graph having nonnegative edge weights. An estimate ˆ δ(u, v) of the actual distance δ(u, v) between u, v ∈ V is said to be of stretch t iff δ(u, v) ≤ ˆ δ(u, v) ≤ t · δ(u, v). Computing allpairs small stretch distances efficiently (both in terms of time ..."
Abstract

Cited by 9 (2 self)
 Add to MetaCart
and space) is a wellstudied problem in graph algorithms. We present a simple, novel and generic scheme for allpairs approximate shortest paths. Using this scheme and some new ideas and tools, we design faster algorithms for allpairs tstretch distances for a whole range of stretch t, and also answer
A faster algorithm for Minimum Cycle Basis of graphs
 In Proc. of ICALP, LNCS 3142
, 2004
"... Abstract. In this paper we consider the problem of computing a minimum cycle basis in a graph G with m edges and n vertices. The edges of G have nonnegative weights on them. The previous best result for this problem was an O(mωn) algorithm, where ω is the best exponent of matrix multiplication. It ..."
Abstract

Cited by 22 (10 self)
 Add to MetaCart
; 0, we also design a 1 + approximation algorithm to compute a cycle basis which is at most 1+ times the weight of a minimum cycle basis. The running time of this algorithm is O(m ω log(W/)) for reasonably dense graphs, where W is the largest edge weight.
Faster approximation of distances in graphs
 IN PROC. WADS
, 2007
"... Let G = (V, E) be an weighted undirected graph on n vertices and m edges, and let dG be its shortest path metric. We present two simple deterministic algorithms for approximating allpairs shortest paths in G. Our first algorithm runs in Õ(n2) time, and for any u, v ∈ V reports distance no greater th ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
Let G = (V, E) be an weighted undirected graph on n vertices and m edges, and let dG be its shortest path metric. We present two simple deterministic algorithms for approximating allpairs shortest paths in G. Our first algorithm runs in Õ(n2) time, and for any u, v ∈ V reports distance no greater
FASTER ALGORITHMS FOR MINIMUM CYCLE BASIS IN DIRECTED GRAPHS
, 2008
"... We consider the problem of computing a minimum cycle basis in a directed graph. The input to this problem is a directed graph G whose edges have nonnegative weights. A cycle in this graph is actually a cycle in the underlying undirected graph with edges traversable in both directions. A {−1, 0, 1} ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
basis for this vector space. We seek a cycle basis where the sum of weights of the cycles is minimum. The current fastest algorithm for computing a minimum cycle basis in a directed graph with m edges and n vertices runs in Õ(mω+1n) time, where ω<2.376 is the exponent of matrix multiplication. We
Approximating Weighted Shortest Paths on Polyhedral Surfaces
 In 6th Annual Video Review of Computational Geometry, Proc. 13th ACM Symp. Computational Geometry
, 1996
"... Consider a simple polyhedron P, possibly nonconvex, composed of n triangular regions (faces), each assigned a positive weight indicating the cost of travel in that region. We present and experimentally study several algorithms to compute an approximate weighted geodesic shortest path, ß 0 (s; t) ..."
Abstract

Cited by 58 (6 self)
 Add to MetaCart
Consider a simple polyhedron P, possibly nonconvex, composed of n triangular regions (faces), each assigned a positive weight indicating the cost of travel in that region. We present and experimentally study several algorithms to compute an approximate weighted geodesic shortest path, ß 0 (s; t
Faster Shortest Paths in Dense Distance Graphs, with Applications
, 2014
"... We show how to combine two techniques for efficiently computing shortest paths in directed planar graphs. The first is the lineartime shortestpath algorithm of Henzinger, Klein, Subramanian, and Rao [STOC’94]. The second is Fakcharoenphol and Rao’s algorithm [FOCS’01] for emulating Dijkstra’s alg ..."
Abstract
 Add to MetaCart
time, algorithms for problems such as minimumcut, maximumflow, and shortest paths with negative arc lengths. As immediate applications, we show how to compute maximum flow in directed weighted planar graphs in O(n log p) time, where p is the minimum number of edges on any path from the source to the sink. We
Faster shortest noncontractible cycles in directed surface graphs
 CoRR
"... Let G be a directed graph embedded on a surface of genus g with b boundary cycles. We describe an algorithm to compute the shortest noncontractible cycle in G in O((g 3 + g b)n log n) time. Our algorithm improves the previous best known time bound of (g + b) O(g+b) n log n for all positive g and b. ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Let G be a directed graph embedded on a surface of genus g with b boundary cycles. We describe an algorithm to compute the shortest noncontractible cycle in G in O((g 3 + g b)n log n) time. Our algorithm improves the previous best known time bound of (g + b) O(g+b) n log n for all positive g and b
Faster Algorithms for Some Geometric Graph Problems in Higher Dimensions
, 1993
"... We show how to apply the wellseparated pair decomposition of a pointset P in ! d to significantly improve known time bounds on several geometric graph problems. We first present an algorithm to find an approximate Euclidean minimum spanning tree of P whose weight is at most 1 + ffl times the exa ..."
Abstract

Cited by 66 (2 self)
 Add to MetaCart
We show how to apply the wellseparated pair decomposition of a pointset P in ! d to significantly improve known time bounds on several geometric graph problems. We first present an algorithm to find an approximate Euclidean minimum spanning tree of P whose weight is at most 1 + ffl times
Results 1  10
of
243