Approximation Algorithms for Survivable Multicommodity Flow Problems with Applications to Network Design

Abstract

Abstract-Multicommodity flow (MF) problems have a wide variety of applications in areas such as VLSI circuit design, network design, etc., and are therefore very well studied. The fractional MF problems are polynomial time solvable while integer versions are N P-complete. However, exact algorithms to solve the fractional MF problems have high computational complexity. Therefore approximation algorithms to solve the fractional MF problems have been explored in the literature to reduce their computational complexity. Using these approximation algorithms and the randomized rounding technique, polynomial time approximation algorithms have been explored in the literature.In the design of high-speed networks, such as optical wavelength division multiplexing (WDM) networks, providing survivability carries great significance. Survivability is the ability of the network to recover from failures.It further increases the complexity of network design and presents network designers with more formidable challenges.In this work we formulate the survivable versions of the MF problems. We build approximation algorithms for the survivable multicommodity flow (SMF) problems based on the framework of the approximation algorithms for the MF problems presented in [1] and [2]. We discuss applications of the SMF problems to solve survivable routing in capacitated networks.

Flow Allocation with Path Protection in Next Generation Internet Networks

“…Particularly, three relevant papers [6], [7] and [8] are similar to our work. First, in [6], the authors introduce algorithms for capacity dimensioning for optical networks.…”

“…The authors provide a ρ-approximation algorithm and the running time depends on the number of disjoint paths. Third, [8] investigated very recently the problem of survivable flow allocation with full sharing between the demands. A preliminary step computes the se of failure disjoint paths and feed the approximation algorithm (note that the corresponding problem for the precomputation step is N P-hard).…”

On Critical Service Recovery After Massive Network Failures

“…Numerous works address the case of sparse, or small scale failures through the provision of alternative paths, provided either proactively, as in the work of Todimala et. al [4], Hansen et al [5], [6], [7], Medard et al [8], or reactively, as in the work of Zheng et al [9]. Suchara et.…”

Progressive damage assessment and network recovery after massive failures

“…Numerous works address the case of sparse failures through the provision of alternative paths, provided either proactively, as in the work of Todimala et. al [6], or reactively, as in the work of Zheng et al [7], whereas Suchara et. al [8] jointly adress recovery and traffic engineering, to minimize congestion after a failure.…”