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

Routing Games with Progressive Filling

Max-min fairness (MMF) is a widely known approach to a fair allocation of bandwidth to each of the users in a network. This allocation can be computed by uniformly raising the bandwidths of all users without violating capacity constraints. We consider an extension of these allocations by raising the bandwidth with arbitrary and not necessarily uniform time-depending velocities (allocation rates). These allocations are used in a game-theoretic context for routing choices, which we formalize in progressive filling games (PFGs). We present a variety of results for equilibria in PFGs. We show that these games possess pure Nash and strong equilibria. While computation in general is NP-hard, there are polynomial-time algorithms for prominent classes of Max-Min-Fair Games (MMFG), including the case when all users have the same source-destination pair. We characterize prices of anarchy and stability for pure Nash and strong equilibria in PFGs and MMFGs when players have different or the same source-destination pairs. In addition, we show that when a designer can adjust allocation rates, it is possible to design games with optimal strong equilibria. Some initial results on polynomial-time algorithms in this direction are also derived

Multi-capacity bin packing with dependent items and its application to the packing of brokered workloads in virtualized environments

Providing resource allocation with performance predictability guarantees is increasingly important in cloud platforms, especially for data-intensive applications, in which performance depends greatly on the available rates of data transfer between the various computing/storage hosts underlying the virtualized resources assigned to the application. Existing resource allocation solutions either assume that applications manage their data transfer between their virtualized resources, or that cloud providers manage their internal networking resources. With the increased prevalence of brokerage services in cloud platforms, there is a need for resource allocation solutions that provides predictability guarantees in settings, in which neither application scheduling nor cloud provider resources can be managed/controlled by the broker. This paper addresses this problem, as we define the Network-Constrained Packing (NCP) problem of finding the optimal mapping of brokered resources to applications with guaranteed performance predictability. We prove that NCP is NP-hard, and we define two special instances of the problem, for which exact solutions can be found efficiently. We develop a greedy heuristic to solve the general instance of the NCP problem , and we evaluate its efficiency using simulations on various application workloads, and network models.This work was done while author was at Boston University. It was partially supported by NSF CISE awards #1430145, #1414119, #1239021 and #1012798. (1430145 - NSF CISE; 1414119 - NSF CISE; 1239021 - NSF CISE; 1012798 - NSF CISE