The edge-disjoint path problem on random graphs by message-passing

We present a message-passing algorithm to solve the edge disjoint path problem (EDP) on graphs incorporating under a unique framework both traffic optimization and path length minimization. The min-sum equations for this problem present an exponential computational cost in the number of paths. To overcome this obstacle we propose an efficient implementation by mapping the equations onto a weighted combinatorial matching problem over an auxiliary graph. We perform extensive numerical simulations on random graphs of various types to test the performance both in terms of path length minimization and maximization of the number of accommodated paths. In addition, we test the performance on benchmark instances on various graphs by comparison with state-of-the-art algorithms and results found in the literature. Our message-passing algorithm always outperforms the others in terms of the number of accommodated paths when considering non trivial instances (otherwise it gives the same trivial results). Remarkably, the largest improvement in performance with respect to the other methods employed is found in the case of benchmarks with meshes, where the validity hypothesis behind message-passing is expected to worsen. In these cases, even though the exact message-passing equations do not converge, by introducing a reinforcement parameter to force convergence towards a sub optimal solution, we were able to always outperform the other algorithms with a peak of 27% performance improvement in terms of accommodated paths. On random graphs, we numerically observe two separated regimes: one in which all paths can be accommodated and one in which this is not possible. We also investigate the behaviour of both the number of paths to be accommodated and their minimum total length.Comment: 14 pages, 8 figure

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

A Quasi-PTAS for Unsplittable Flow on Line Graphs

We study the Unsplittable Flow Problem (UFP) on a line graph, focusing on the long-standing open question of whether the problem is APX-hard. We describe a deterministic quasi-polynomial time approximation scheme for UFP on line graphs, thereby ruling out an APX-hardness result, unless NP is contained in DTIME(2^polylog(n)). Our result requires a quasi-polynomial bound on all edge capacities and demands in the input instance. Earlier results on this problem included a polynomial time (2+epsilon)-approximation under the assumption that no demand exceeds any edge capacity (the no-bottleneck assumption ) and a super-constant integrality gap if this assumption did not hold. Unlike most earlier work on UFP, our results do not require a no-bottleneck assumption

A Quasi-PTAS for Unsplittable Flow on Line Graphs

We study the Unsplittable Flow Problem (UFP) on a line graph, focusing on the long-standing open question of whether the problem is APX-hard. We describe a deterministic quasi-polynomial time approximation scheme for UFP on line graphs, thereby ruling out an APX-hardness result, unless NP is contained in DTIME(2^polylog(n)). Our result requires a quasi-polynomial bound on all edge capacities and demands in the input instance. Earlier results on this problem included a polynomial time (2+epsilon)-approximation under the assumption that no demand exceeds any edge capacity (the no-bottleneck assumption ) and a super-constant integrality gap if this assumption did not hold. Unlike most earlier work on UFP, our results do not require a no-bottleneck assumption

Low-overhead hard real-time aware interconnect network router

The increasing complexity of embedded systems is accelerating the use of multicore processors in these systems. This trend gives rise to new problems such as the sharing of on-chip network resources among hard real-time and normal best effort data traffic. We propose a network-on-chip router that provides predictable and deterministic communication latency for hard real-time data traffic while maintaining high concurrency and throughput for best-effort/general-purpose traffic with minimal hardware overhead. The proposed router requires less area than non-interfering networks, and provides better Quality of Service (QoS) in terms of predictability and determinism to hard real-time traffic than priority-based routers. We present a deadlock-free algorithm for decoupled routing of the two types of traffic. We compare the area and power estimates of three different router architectures with various QoS schemes using the IBM 45-nm SOI CMOS technology cell library. Performance evaluations are done using three realistic benchmark applications: a hybrid electric vehicle application, a utility grid connected photovoltaic converter system, and a variable speed induction motor drive application