# Approximating Disjoint-Path Problems Using Greedy Algorithms and Packing Integer Programs

@inproceedings{Kolliopoulos1998ApproximatingDP, title={Approximating Disjoint-Path Problems Using Greedy Algorithms and Packing Integer Programs}, author={Stavros G. Kolliopoulos and Clifford Stein}, booktitle={IPCO}, year={1998} }

In the edge(vertex)-disjoint path problem we are given a graph $G$ and a set ${\cal T}$ of connection requests. Every connection request in ${\cal T}$ is a vertex pair $(s_i,t_i),$ $1 \leq i \leq K.$ The objective is to connect a maximum number of the pairs via edge(vertex)-disjoint paths. The edge-disjoint path problem can be generalized to the multiple-source unsplittable flow problem where connection request $i$ has a demand $\rho_i$ and every edge $e$ a capacity $u_e.$ All these problems…

## 104 Citations

### Approximating disjoint-path problems using packing integer programs

- Computer ScienceMath. Program.
- 2004

Improved approximation algorithms for column-restricted packing integer programs are developed that are simple to implement and achieve good performance when the input has a special structure and are motivated by the disjoint paths applications.

### Inapproximability of Edge-Disjoint Paths and low congestion routing on undirected graphs

- Mathematics, Computer ScienceComb.
- 2007

This paper studies the hardness of EDPwC in undirected graphs and shows an Ω(log logV/log log log V) hardness of approximation for EDPWC and an Φ(loglogV/ log log logV) hardness-of- approximation for the Undirected congestion minimization problem.

### Improved Bi-criteria Approximation for the All-or-Nothing Multicommodity Flow Problem in Arbitrary Networks

- Computer ScienceArXiv
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This paper is the first to achieve a constant approximation of the maximum throughput with an edge capacity violation ratio that is at most logarithmic in $n$, with high probability, and presents a derandomization of the algorithm that maintains the same approximation bounds.

### Approximation Algorithms for the Edge-Disjoint Paths Problem via Raecke Decompositions

- Computer Science, Mathematics2010 IEEE 51st Annual Symposium on Foundations of Computer Science
- 2010

This work presents a $(polylog(n), poly(\log\log n))-approximation, which means that if there exists a solution that routes X demands integrally on edge-disjoint paths (i.e. with congestion $1), then the approximation algorithm can route X/polylog (n) demands with congestion.

### Exact and approximation algorithms for network flow and disjoint-path problems

- Computer Science
- 1998

This thesis focuses on efficient exact algorithms for network flow problems in P and on approximation algorithms for NP-hard variants such as disjoint paths and unsplittable flow, and explores the topic of approximating disJoint-path problems using polynomial-size packing integer programs.

### Edge-Disjoint Paths and Unsplittable Flow

- MathematicsHandbook of Approximation Algorithms and Metaheuristics
- 2007

This chapter limits itself mostly to results on offline approximation algorithms for problems on general graphs as influenced from the network flow perspective.

### Near-optimal hardness results and approximation algorithms for edge-disjoint paths and related problems

- Computer Science, MathematicsSTOC '99
- 1999

It is shown that in directed networks, for any e>0, EDP is NP-hard to approximate within m1/2-e even in undirected networks, and design simple approximation algorithms that achieve essentially matching approximation guarantees for some generalizations of EDP.

### Edge Disjoint Paths in Moderately Connected Graphs

- Mathematics, Computer ScienceSIAM J. Comput.
- 2006

This work shows a polylogarithmic approximation algorithm for the undirected EDP problem in general graphs with a moderate restriction on graph connectivity; it requires the global minimum cut of G to be Ω(log5n) and applies to graphs with high diameters and asymptotically large minors.

### New Hardness Results for Undirected Edge Disjoint Paths

- Computer Science, Mathematics
- 2005

The hardness result of Andrews and Zhang as well as the first polylogarithmic integrality gaps and hardness results for undirected EDP when congestion is allowed are improved and it is shown that it is possible to obtain a hardness result that is comparable to the integrality gap.

### Hardness of the undirected edge-disjoint paths problem with congestion

- Computer Science46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05)
- 2005

An improved hardness result for EDP is obtained, and the first polylogarithmic integrality gaps and hardness of approximation results for E DPwC are shown, and similar results can be obtained for the all-or-nothing flow (ANF) problem, a relaxation of EDP.

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