Results 1  10
of
249
Approximate MaxFlow MinCut Theorems (Course Notes Extension for COMP5703)
, 2014
"... In this report, we discuss two approximate maxflow mincut theorems that first introduced by Tom Leighton and Satish Rao in 1988 [9] and extended in 1999 [10] for uniform multicommodity flow problems. In the theorems they first showed that for any nnode multicommodity flow problem with uniform de ..."
Abstract
 Add to MetaCart
In this report, we discuss two approximate maxflow mincut theorems that first introduced by Tom Leighton and Satish Rao in 1988 [9] and extended in 1999 [10] for uniform multicommodity flow problems. In the theorems they first showed that for any nnode multicommodity flow problem with uniform
An Approximate MaxFlow MinCut Theorem for Uniform Multicommodity Flow Problems with Applications to Approximation Algorithms
, 1989
"... In this paper, we consider a multicommodity flow problem where for each pair of vertices, (u,v), we are required to sendf halfunits of commodity (uv) from u to v and f halfunits of commodity (vu) from v to u without violating capacity constraints. Our main result is an algorithm for performing th9 ..."
Abstract

Cited by 246 (12 self)
 Add to MetaCart
9 task provided that the capacity of each cut exceeds the demand across the cut by a b(log n) factor. The condition on cuts is required in the worst case, and is trivially within a i(log n) factor of optimal for any flow problem. The result is of interest because it can be used to construct
Bounds on the MaxFlow MinCut Ratio for Directed Multicommodity Flows
, 1993
"... The most wellknown theorem in combinatorial optimization is the classical maxflow mincut theorem of Ford and Fulkerson. This theorem serves as the basis for deriving efficient algorithms for finding maxflows and mincuts. Starting with the work of Leighton and Rao, significant effort was directe ..."
Abstract

Cited by 8 (3 self)
 Add to MetaCart
was directed towards finding approximate analogs for the undirected multicommodity flow problem. In this paper we consider an approximate maxflow mincut theorem for directed graphs. We prove a polylogarithmic bound on the worst case ratio between the minimum multicut and the value of the maximum
AN APPROXIMATE MAXFLOW MINCUT RELATION FOR Undirected Multicommodity Flow, . . .
, 1995
"... In this paper, we prove the first approximate maxflow mincut theorem for undirected mult icommodity flow. We show that for a feasible flow to exist in a mult icommodity problem, it is sufficient hat every cut's capacity exceeds its demand by a factor of O(logClogD), where C is the sum of all ..."
Abstract

Cited by 7 (1 self)
 Add to MetaCart
In this paper, we prove the first approximate maxflow mincut theorem for undirected mult icommodity flow. We show that for a feasible flow to exist in a mult icommodity problem, it is sufficient hat every cut's capacity exceeds its demand by a factor of O(logClogD), where C is the sum of all
Multicommodity maxflow mincut theorems and their use in designing approximation algorithms
 J. ACM
, 1999
"... In this paper, we establish maxflow mincut theorems for several important classes of multicommodity flow problems. In particular, we show that for any nnode multicommodity flow problem with uniform demands, the maxflow for the problem is within an O(log n) factor of the upper bound implied by ..."
Abstract

Cited by 357 (6 self)
 Add to MetaCart
by the mincut. The result (which is existentially optimal) establishes an important analogue of the famous 1commodity maxflow mincut theorem for problems with multiple commodities. The result also has substantial applications to the field of approximation algorithms. For example, we use the flow result
Singlesink multicommodity flow with side constraints
"... In recent years, several new models for network flows have been analyzed, inspired by emerging telecommunication technologies. These include models of resilient flow, motivated by the introduction of high capacity optical links, coloured flow, motivated by WavelengthDivisionMultiplexed optical net ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
are destined to a common node (sink) in the network. In such cases, one may seek bounds on the “flowcut gap ” for the model. Such approximate maxflow mincut theorems are a useful measure for bounding the impact of new technology on congestion in networks whose traffic flows obey these side constraints.
Multicommodity Flows and Approximation Algorithms
, 1994
"... This thesis is about multicommodity flows and their use in designing approximation algorithms for problems involving cuts in graphs. In a groundbreaking work Leighton and Rao [34] showed an approximate maxflow mincut theorem for uniform multicommodity flow and used this to obtain an approximation ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
This thesis is about multicommodity flows and their use in designing approximation algorithms for problems involving cuts in graphs. In a groundbreaking work Leighton and Rao [34] showed an approximate maxflow mincut theorem for uniform multicommodity flow and used this to obtain
An O(log k) approximate mincut maxflow theorem and approximation algorithm
 SIAM J. COMPUT
, 1998
"... It is shown that the minimum cut ratio is within a factor of O(log k) of the maximum concurrent flow for kcommodity flow instances with arbitrary capacities and demands. This improves upon the previously bestknown bound of O(log 2 k) and is existentially tight, up to a constant factor. An algori ..."
Abstract

Cited by 129 (6 self)
 Add to MetaCart
. An algorithm for finding a cut with ratio within a factor of O(log k) of the maximum concurrent flow, and thus of the optimal mincut ratio, is presented.
Approximate MaxFlow Min(multi)cut Theorems and Their Applications
 SIAM Journal on Computing
, 1993
"... Consider the multicommodity flow problem in which the object is to maximize the sum of commodities routed. We prove the following approximate maxflow minmulticut theorem: min multicut O(logk) max flow min multicut; where k is the number of commodities. Our proof is constructive; it enables us ..."
Abstract

Cited by 160 (3 self)
 Add to MetaCart
for the latter problem. 1 Introduction Much of flow theory, and the theory of cuts in graphs, is built around a single theorem  the celebrated maxflow mincut theorem of Ford and Fulkerson [FF], and Elias, Feinstein and Shannon [EFS]. The power of this theorem lies in that it relates two fundamental graph
Small distortion and volume preserving embeddings for Planar and Euclidean metrics
, 1999
"... A finite metric space, (S,d) , contains a finite set of points and a distance function on pairs of points. A contraction is an embedding, h, of a finite metric space (S, d) into Rd where for any u, v E S, the Euclidean (&) distance between h(u) and h(v) is no more than d(u, v). The distortion of ..."
Abstract

Cited by 68 (1 self)
 Add to MetaCart
mincut theorem for k commodity flow problems. A generalization of embeddings that preserve distances between pairsof points are embeddings that preserve volumes of larger sets. In particular, A (k, c)volume respecting embedding of npoints in any metric space is a contraction where every subset
Results 1  10
of
249