Tools
Sorted by:
Try your query at:
 |
 |
 |
 |
 |
 |
Results 1 - 10
of
1,248
More algorithms for all-pairs shortest paths in weighted graphs
- In Proceedings of 39th Annual ACM Symposium on Theory of Computing
, 2007
"... In the first part of the paper, we reexamine the all-pairs shortest paths (APSP) problem and present a new algorithm with running time O(n 3 log 3 log n / log 2 n), which improves all known algorithms for general real-weighted dense graphs. In the second part of the paper, we use fast matrix multipl ..."
Abstract
-
Cited by 75 (3 self)
- Add to MetaCart
)), where ω < 2.376; in two dimensions, this is O(n 2.922). Our framework greatly extends the previously considered case of small-integer-weighted graphs, and incidentally also yields the first truly subcubic result (near O(n 3−(3−ω)/4) = O(n 2.844) time) for APSP in real-vertex-weighted graphs, as well
The geometry of graphs and some of its algorithmic applications
- COMBINATORICA
, 1995
"... In this paper we explore some implications of viewing graphs as geometric objects. This approach offers a new perspective on a number of graph-theoretic and algorithmic problems. There are several ways to model graphs geometrically and our main concern here is with geometric representations that res ..."
Abstract
-
Cited by 524 (19 self)
- Add to MetaCart
that respect the metric of the (possibly weighted) graph. Given a graph G we map its vertices to a normed space in an attempt to (i) Keep down the dimension of the host space and (ii) Guarantee a small distortion, i.e., make sure that distances between vertices in G closely match the dis-tances between
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 error-correcting codes. The most dramatic instance of this is the near Shannon-limit performanc ..."
Abstract
-
Cited by 676 (15 self)
- Add to MetaCart
the real QMR network to converge if the priors were sampled randomly in the range [0, Small priors are not the only thing that causes oscil lation. Small weights can, too. The effect of both The exact marginals are represented by the circles; the ends of the "error bars" represent the loopy
The Average Distance in a Random Graph with Given Expected Degrees
"... Random graph theory is used to examine the “small-world phenomenon”– any two strangers are connected through a short chain of mutual acquaintances. We will show that for certain families of random graphs with given expected degrees, the average distance is almost surely of order log n / log ˜ d whe ..."
Abstract
-
Cited by 289 (13 self)
- Add to MetaCart
Random graph theory is used to examine the “small-world phenomenon”– any two strangers are connected through a short chain of mutual acquaintances. We will show that for certain families of random graphs with given expected degrees, the average distance is almost surely of order log n / log ˜ d
Approximate distance oracles
, 2004
"... Let G = (V, E) be an undirected weighted graph with |V | = n and |E | = m. Let k ≥ 1 be an integer. We show that G = (V, E) can be preprocessed in O(kmn 1/k) expected time, constructing a data structure of size O(kn 1+1/k), such that any subsequent distance query can be answered, approximately, in ..."
Abstract
-
Cited by 273 (9 self)
- Add to MetaCart
Let G = (V, E) be an undirected weighted graph with |V | = n and |E | = m. Let k ≥ 1 be an integer. We show that G = (V, E) can be preprocessed in O(kmn 1/k) expected time, constructing a data structure of size O(kn 1+1/k), such that any subsequent distance query can be answered, approximately
Bipartite subgraphs of integer weighted graphs
- Discrete Math
, 1998
"... For every integer p> 0 let f(p) be the minimum possible value of the maximum weight of a cut in an integer weighted graph with total weight p. It is shown that for every large n and every m < n, f ( � � n n 2 + m) = ⌊ 2 n 4 ⌋ + min( ⌈ 2 ⌉, f(m)). This supplies the precise value of f(p) for ..."
Abstract
-
Cited by 8 (4 self)
- Add to MetaCart
For every integer p> 0 let f(p) be the minimum possible value of the maximum weight of a cut in an integer weighted graph with total weight p. It is shown that for every large n and every m < n, f ( � � n n 2 + m) = ⌊ 2 n 4 ⌋ + min( ⌈ 2 ⌉, f(m)). This supplies the precise value of f
Turán problems for integer-weighted graphs
- J. GRAPH THEORY
, 2002
"... A multigraph is (k, r)-dense if every k-set spans at most r edges. What is the maximum number of edges exN(n, k, r) in a (k, r)-dense multigraph on n vertices? We determine the maximum possible weight of such graphs for almost all k and r (e.g., for all r> k3) by determining a constant m = m(k, r ..."
Abstract
-
Cited by 6 (1 self)
- Add to MetaCart
A multigraph is (k, r)-dense if every k-set spans at most r edges. What is the maximum number of edges exN(n, k, r) in a (k, r)-dense multigraph on n vertices? We determine the maximum possible weight of such graphs for almost all k and r (e.g., for all r> k3) by determining a constant m = m
Extremal Problems On Integer-Weighted Graphs
, 1999
"... . We consider complete graphs with integer edge weights, including the possibility of negative weights. Let ex(Kn ; Km ; r) denote the maximum weight of an integer-weighted Kn such that no Km subgraph has weight at least r. In 1997, Bondy and Tuza [1] extended Tur'an's theorem for 0=1-weig ..."
Abstract
- Add to MetaCart
. We consider complete graphs with integer edge weights, including the possibility of negative weights. Let ex(Kn ; Km ; r) denote the maximum weight of an integer-weighted Kn such that no Km subgraph has weight at least r. In 1997, Bondy and Tuza [1] extended Tur'an's theorem for 0
All Pairs Shortest Paths in Undirected Graphs with Integer Weights
- In IEEE Symposium on Foundations of Computer Science
, 1999
"... We show that the All Pairs Shortest Paths (APSP) problem for undirected graphs with integer edge weights taken from the range f1; 2; : : : ; Mg can be solved using only a logarithmic number of distance products of matrices with elements in the range f1; 2; : : : ; Mg. As a result, we get an algorith ..."
Abstract
-
Cited by 56 (7 self)
- Add to MetaCart
We show that the All Pairs Shortest Paths (APSP) problem for undirected graphs with integer edge weights taken from the range f1; 2; : : : ; Mg can be solved using only a logarithmic number of distance products of matrices with elements in the range f1; 2; : : : ; Mg. As a result, we get
Polynomial Time Approximation Schemes for Dense Instances of NP-Hard Problems
, 1995
"... We present a unified framework for designing polynomial time approximation schemes (PTASs) for "dense" instances of many NP-hard optimization problems, including maximum cut, graph bisection, graph separation, minimum k-way cut with and without specified terminals, and maximum 3-satisfiabi ..."
Abstract
-
Cited by 189 (35 self)
- Add to MetaCart
: picking a small random set of vertices, guessing where they go on the optimum solution, and then using their placement to determine the placement of everything else. The approach then develops into a PTAS for approximating certain smooth integer programs where the objective function and the constraints
Results 1 - 10
of
1,248
