A Method for Obtaining the Maximum (δ,η)-Balanced Flow in a Network

Kishimoto, Wataru

doi:10.1007/978-3-642-21527-8_28

Cited by 3 publications

(6 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On the basis of the algorithm for the maximum δ-reliable flow [10] and that of the maximum (δ, η)-reliable flow [11], we show a method for evaluating the maximum value of d-balanced flow between a specified pair of vertices. The method consists of calculations of the maximum value of ordinary flows between the pair of vertices.…”

Section: A Methods For Obtaining the Maximum D-balanced Flowmentioning

confidence: 99%

See 1 more Smart Citation

An Extension of a Balanced Flow in a Network

Kishimoto

2013

Electronic Notes in Discrete Mathematics

Self Cite

View full text Add to dashboard Cite

Section: A Methods For Obtaining the Maximum D-balanced Flowmentioning

confidence: 99%

“…A multiroute flow [1,7,8] corresponds to a multiroute communication channel. A δ-reliable flow is an extension of a multiroute flow [9,10] and a (δ, η)-balanced flow is a further extension of a δ-reliable flow [11].…”

Section: Introductionmentioning

confidence: 99%

An Extension of a Balanced Flow in a Network

Kishimoto

2013

Electronic Notes in Discrete Mathematics

Self Cite

View full text Add to dashboard Cite

“…The study of k-route flow and k-route cut problems was initiated by Kishimoto [21], and has since received much attention in the theoretical Computer Science community [7,10,5,23,22,11]. Bruhn et al [7] gave a 2(k − 1)-approximation for single-source k-MC with unit costs, whereas [10,5,23] obtained efficient polylogarithmic approximation results for k-MC with small values of k. Subsequently, Chuzhoy et al [11] obtained the first non-trivial results for k-MC with arbitrary k in the form of bicriteria approximation guarantees.…”

Section: Introductionmentioning

confidence: 99%

“…The study of k-route cut problems can be motivated from various perspectives. One motivation comes from the fact that k-route cuts are dual objects to k-route flows [21], which can be seen as a robust or faulttolerant version of flows where we seek to send traffic along tuples of k edge-disjoint paths. A k-route cut establishes an upper bound on the value (suitably defined) of the maximum k-route flow, and can thus be seen as identifying the bottleneck in a network when we seek a certain level of robustness.…”

Section: Introductionmentioning

confidence: 99%

Improved Region-Growing and Combinatorial Algorithms for k-Route Cut Problems (Extended Abstract)

Guruganesh¹,

Sanità²,

Swamy³

2014

Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms

View full text Add to dashboard Cite

We study the k-route generalizations of various cut problems, the most general of which is k-route multicut (k-MC) problem, wherein we have r source-sink pairs and the goal is to delete a minimum-cost set of edges to reduce the edge-connectivity of every source-sink pair to below k. The k-route extensions of multiway cut (k-MWC), and the minimum s-t cut problem (k-(s, t)-Cut), are similarly defined. We present various approximation and hardness results for k-MC, k-MWC, and k-(s, t)-Cut that improve the state-of-the-art for these problems in several cases. Our contributions are threefold.• For k-route multiway cut, we devise simple, but surprisingly effective, combinatorial algorithms that yield bicriteria approximation guarantees that markedly improve upon the previous-best guarantees. • For k-route multicut, we design algorithms that improve upon the previous-best approximation factors by roughly an O( √ log r)-factor, when k = 2, and for general k and unit costs and any fixed violation of the connectivity threshold k. The main technical innovation is the definition of a new, powerful region growing lemma that allows us to perform region-growing in a recursive fashion even though the LP solution yields a different metric for each source-sink pair, and without incurring an O(log 2 r) blow-up in the cost that is inherent in some previous applications of region growing to k-route cuts. We obtain the same benefits as [15] do in their divide-and-conquer algorithms, and thereby obtain an O(ln r ln ln r)-approximation to the cost. We also obtain some extensions to kroute node-multicut problems.• We complement these results by showing that the k-route s-t cut problem is at least as hard to approximate as the densest-k-subgraph (DkS) problem on uniform hypergraphs. In particular, this implies that one cannot avoid a poly(k)-factor if one seeks a unicriterion approximation, without improving the state-of-the-art for DkS on graphs, and proving the existence of a family of one-way functions. Previously, only NP-hardness of k-(s, t)-Cut was known.

show abstract

“…Multi-route flows were introduced by Kishimoto [9], and have found a number of applications in communication networks [2,3,5]. In a series of papers Kishimoto and others [9,10,1] developed efficient algorithms for finding multi-route flows, as well as explored approximate max-flow min-cut theorems in this setting. For example, Bagchi et al [4] showed a strong duality theorem for multi-route flows and cuts in the single-source single-sink case under a non-standard definition of the cost of a cut.…”

Section: Introductionmentioning

confidence: 99%

Region growing for multi-route cuts

Barman

Chawla

2010

Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms

View full text Add to dashboard Cite

We study a number of multi-route cut problems: given a graph G = (V, E) and connectivity thresholds k (u,v) on pairs of nodes, the goal is to find a minimum cost set of edges or vertices the removal of which reduces the connectivity between every pair (u, v) to strictly below its given threshold. These problems arise in the context of reliability in communication networks; They are natural generalizations of traditional minimum cut problems where the thresholds are either 1 (we want to completely separate the pair) or ∞ (we don't care about the connectivity for the pair). We provide the first non-trivial approximations to a number of variants of the problem including for both node-disjoint and edge-disjoint connectivity thresholds. A main contribution of our work is an extension of the region growing technique for approximating minimum multicuts to the multi-route setting. When the connectivity thresholds are either 2 or ∞ (the "2-route cut" case), we obtain polylogarithmic approximations while satisfying the thresholds exactly. For arbitrary connectivity thresholds this approach leads to bicriteria approximations where we approximately satisfy the thresholds and approximately minimize the cost. We present a number of different algorithms achieving different cost-connectivity tradeoffs.

show abstract

A Method for Obtaining the Maximum (δ,η)-Balanced Flow in a Network

Cited by 3 publications

References 14 publications

An Extension of a Balanced Flow in a Network

An Extension of a Balanced Flow in a Network

Improved Region-Growing and Combinatorial Algorithms for k-Route Cut Problems (Extended Abstract)

Region growing for multi-route cuts

Contact Info

Product

Resources

About