Greedy Edge-Disjoint Paths in Complete Graphs

  title={Greedy Edge-Disjoint Paths in Complete Graphs},
  author={Paz Carmi and Thomas Wilhelm Erlebach and Yoshio Okamoto},
The maximum edge-disjoint paths problem (MEDP) is one of the most classical NP-hard problems. We study the approximation ratio of a simple and practical approximation algorithm, the shortest-path-first greedy algorithm (SGA), for MEDP in complete graphs. Previously, it was known that this ratio is at most 54. Adapting results by Kolman and Scheideler [Proceedings of SODA, 2002, pp. 184–193], we show that SGA achieves approximation ratio 8F+1 for MEDP in undirected graphs with flow number F and… 

The maximum edge-disjoint paths problem in complete graphs

Approximation Strategies for Routing Edge Disjoint Paths in Complete Graphs

It is shown that no on-line algorithm for the considered problem is ever better than a 1.50-approximation, and the proposed approximation techniques are adapted for other routing problems in complete graphs, leading to an off-line 3- approximation (on-line 4-Approximation) for routing with minimum edge load.

Path problems in generalized stars, complete graphs, and brick wall graphs

A nature-inspired algorithm for the disjoint paths problem

  • M. BlesaC. Blum
  • Computer Science
    Proceedings 20th IEEE International Parallel & Distributed Processing Symposium
  • 2006
A more sophisticated ACO algorithm is evolved based on the (basic) approach in Blesa and Blum (2004) and the quality of the solutions they obtain are susceptible to improvement.


  • C. Bentz
  • Mathematics, Computer Science
  • 2005
It is shown that, for a fixed number of source-sink pairs, the minimum multicut problem is polynomial-time solvable in planar graphs and in bounded tree-width graphs.

Disjoint paths in sparse graphs

  • C. Bentz
  • Mathematics
    Discret. Appl. Math.
  • 2009

Analyzing approximation algorithms with the dual-fitting method 1 A greedy algorithm for S ET C OVER

  • Computer Science, Mathematics
  • 2005
One of the best examples of combinatorial approximation algorithms is a greedy algorithm approximating the (weighted) SET COVER problem, where the goal is to find a sub-family of S with minimum total weight such that the union of the sub- family is U.

On Solving the Maximum Disjoint Paths Problem with Ant Colony Optimization

  • M. BlesaC. Blum
  • Computer Science
    Handbook of Approximation Algorithms and Metaheuristics
  • 2007
The efficient use of modern communication networks depends on our capabilities for solving a number of demanding algorithmic problems, some of which are concerned with the allocation of network

A bibliography on multicut and integer multiflow problems

We present a bibliography about the maximum integral multiflow and the minimum multicut problems and their subproblems, such as the multiterminal cut and the unsplittable flow problems. Some

Call admission control and on-line interval coloring

A polynomial-time algorithm that solves the problem optimally provided that the calls are given as pre-specified paths in the ring and can be derandomized by means of Hadamard matrices keeping the same approximation ratio.



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

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.

New Results for Path Problems in Generalized Stars, Complete Graphs, and Brick Wall Graphs

It is shown that maximum path coloring can be solved optimally in polynomial time for bidirected generalized stars, and the maximum edge-disjoint paths problem is proved NP-hard for complete graphs (undirected orbidirected), and a constant-factor approximation algorithm is presented.

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

These techniques lead to the first approximation algorithm and obtain an approximation ratio that matches, to within logarithmic factors, the $O(\sqrt{|E|})$ approximation ratio for the simple edge-disjoint path problem.

Edge disjoint paths revisited

Algorithms for the EDP in directed and undirected graphs obtaining improved approximation ratios and the greedy algorithm has an approximation ratio that is the first sub-linear approximation ratios for EDP.

Approximation Algorithms and Complexity Results for Path Problems in Trees of Rings

The path packing problem can be solved in polynomial time, the path coloring problem with prespecified paths can be approximated within a constant factor, and the maximum (weight) edge-disjoint paths problem is NP-hard and can be approximation within a constants factor.

A Greedy Facility Location Algorithm Analyzed Using Dual Fitting

A natural greedyalgorithm for the metric uncapacitated facilitylo cation problem is presented and the method of dual fitting is used to analyze its approximation ratio, which turns out to be 1.861.

Improved bounds for the unsplittable flow problem

The primal-dual method for approximation algorithms

An overview of a technique used to design and analyze algorithms that provide approximate solutions to NP-hard problems in combinatorial optimization called the primal-dual method for approximation algorithms, which can be used to derive approximation algorithms for a number of different problems.

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques

  • Carnegie
  • Computer Science
    Lecture Notes in Computer Science
  • 2004
The problem of dedicating the least amount of the currently available network capacity for protection, while guaranteeing fast restoration to the existing traffic along with any traffic that may be admitted in the future is interested.

Computers and Intractability: A Guide to the Theory of NP-Completeness

The experiences, understandings, and beliefs that guide the professional practices of teacher educators are explored, and the book paints a picture of a profession that offers huge rewards, alongside challenges and frustrations.