Faster Approximate Multicommodity Flow Using Quadratically Coupled Flows

The maximum multicommodity flow problem is a natural generalization of the maximum flow problem to route multiple distinct flows. Obtaining a $1-\epsilon$ approximation to the multicommodity flow problem on graphs is a well-studied problem. In this paper we present an adaptation of recent advances in single-commodity flow algorithms to this problem. As the underlying linear systems in the electrical problems of multicommodity flow problems are no longer Laplacians, our approach is tailored to generate specialized systems which can be preconditioned and solved efficiently using Laplacians. Given an undirected graph with m edges and k commodities, we give algorithms that find $1-\epsilon$ approximate solutions to the maximum concurrent flow problem and the maximum weighted multicommodity flow problem in time \tilde{O}(m^{4/3}\poly(k,\epsilon^{-1}))

Network Flow Optimization for Restoration of Images

The network flow optimization approach is offered for restoration of grayscale and color images corrupted by noise. The Ising models are used as a statistical background of the proposed method. The new multiresolution network flow minimum cut algorithm, which is especially efficient in identification of the maximum a posteriori estimates of corrupted images, is presented. The algorithm is able to compute the MAP estimates of large size images and can be used in a concurrent mode. We also describe the efficient solutions of the problem of integer minimization of two energy functions for the Ising models of gray-scale and color images

A polynomial time approximation algorithm for the two-commodity splittable flow problem

We consider a generalization of the unsplittable maximum two-commodity flow problem on undirected graphs where each commodity $${i \in \{1, 2\}}$$ can be split into a bounded number k i of equally-sized chunks that can be routed on different paths. We show that in contrast to the single-commodity case this problem is NP-hard, and hard to approximate to within a factor of α > 1/2. We present a polynomial time 1/2-approximation algorithm for the case of uniform chunk size over both commodities and show that for even k i and a mild cut condition it can be modified to yield an exact method. The uniform case can be used to derive a 1/4-approximation for the maximum concurrent (k 1, k 2)-splittable flow without chunk size restrictions for fixed demand ratio

SCOR: Software-defined Constrained Optimal Routing Platform for SDN

A Software-defined Constrained Optimal Routing (SCOR) platform is introduced as a Northbound interface in SDN architecture. It is based on constraint programming techniques and is implemented in MiniZinc modelling language. Using constraint programming techniques in this Northbound interface has created an efficient tool for implementing complex Quality of Service routing applications in a few lines of code. The code includes only the problem statement and the solution is found by a general solver program. A routing framework is introduced based on SDN's architecture model which uses SCOR as its Northbound interface and an upper layer of applications implemented in SCOR. Performance of a few implemented routing applications are evaluated in different network topologies, network sizes and various number of concurrent flows.Comment: 19 pages, 11 figures, 11 algorithms, 3 table