35 research outputs found
A note on the data-driven capacity of P2P networks
We consider two capacity problems in P2P networks. In the first one, the
nodes have an infinite amount of data to send and the goal is to optimally
allocate their uplink bandwidths such that the demands of every peer in terms
of receiving data rate are met. We solve this problem through a mapping from a
node-weighted graph featuring two labels per node to a max flow problem on an
edge-weighted bipartite graph. In the second problem under consideration, the
resource allocation is driven by the availability of the data resource that the
peers are interested in sharing. That is a node cannot allocate its uplink
resources unless it has data to transmit first. The problem of uplink bandwidth
allocation is then equivalent to constructing a set of directed trees in the
overlay such that the number of nodes receiving the data is maximized while the
uplink capacities of the peers are not exceeded. We show that the problem is
NP-complete, and provide a linear programming decomposition decoupling it into
a master problem and multiple slave subproblems that can be resolved in
polynomial time. We also design a heuristic algorithm in order to compute a
suboptimal solution in a reasonable time. This algorithm requires only a local
knowledge from nodes, so it should support distributed implementations.
We analyze both problems through a series of simulation experiments featuring
different network sizes and network densities. On large networks, we compare
our heuristic and its variants with a genetic algorithm and show that our
heuristic computes the better resource allocation. On smaller networks, we
contrast these performances to that of the exact algorithm and show that
resource allocation fulfilling a large part of the peer can be found, even for
hard configuration where no resources are in excess.Comment: 10 pages, technical report assisting a submissio
Heuristic for the preemptive asymmetric stacker crane problem
International audienceIn this paper, we deal with the preemptive asymmetric stacker crane problem in an heuristic way. We first present some theoretical results which allow us to turn this problem into a specific tree design problem. We next derive from this new representation a simple, efficient local search heuristic, as well as an original LIP model. We conclude by presenting experimental results which aim at both testing the efficiency of our heuristic and at evaluating the impact of the preemption hypothesis
Connected subgraphs, matching, and partitions
Given an undirected graph G and a real edge-weight vector, the connected subgraph problem consists of finding a maximum-weight subset of edges which induces a connected subgraph of G. In this paper, we establish a link between the complexity of the connected subgraph problem and the matching number. We study the separation problem associated with the Matching-partition inequalities wich are introduced by Didi Biha et al. [4] for the connected subgraph polytope
On superperfection of edge-intersection graphs of paths
International audienceThe Routing and Spectrum Assignment problem in Flexgrid Elastic Optical Networks can be modeled in two phases: a selection of paths in the network and an interval coloring problem in the edge-intersection graph of these paths. The interval chromatic number equals the smallest size of a spectrum such that a proper interval coloring is possible, the weighted clique number is a natural lower bound. Graphs where both parameters coincide for all induced subgraphs and for all possible integral weights are called superperfect. We examine the question which minimal non-superperfect graphs can occur in the edge-intersection graphs of paths in different underlying networks and show that for any possible network (even if it is restricted to a path) the resulting edge-intersection graphs are not necessarily superperfect
An extended formulation for the Constraint Routing and Spectrum Assignment Problem in Elastic Optical Networks *
The emergence of Elastic Optical Networks allowed a more flexible spectrum allocation for routing traffic demands within telecommunication networks. From this context arises the Routing and Spectrum Assignment problem, which consists of routing a given set of origin-destination traffic demands and assigning them to contiguous spectrum frequencies such that no frequency slot is assigned to more than one demand within a network link. This work deals with the variant where each demand route must additionally satisfy a maximal-length constraint. In this paper we propose a compact extended formulation for the Constrained Routing and Spectrum Assignment Problem. We show that our extended formulation is theoretically stronger than formulations known in the literature. Experimental results demonstrate the efficiency of our approach
A novel integer linear programming model for routing and spectrum assignment in optical networks
International audienceThe routing and spectrum assignment problem is an NP-hard problem that receives increasing attention during the last years. Existing integer linear programming models for the problem are either very complex and suer from tractability issues or are simplied and incomplete so that they can optimize only some objective functions. The majority of models uses edge-path formulations where variables are associated with all possible routing paths so that the number of variables grows exponentially with the size of the instance. An alternative is to use edge-node formulations that allow to devise compact models where the number of variables grows only polynomially with the size of the instance. However, all known edge-node formulations are incomplete as their feasible region is a superset of all feasible solutions of the problem and can, thus, handle only some objective functions. Our contribution is to provide the rst complete edge-node formulation for the routing and spectrum assignment problem which leads to a tractable integer linear programming model. Indeed, computational results show that our complete model is competitive with incomplete models as we can solve instances of the RSA problem larger than instances known in the literature to optimality within reasonable time and w.r.t. several objective functions. We further devise some directions of future research
The complexity of the Unit Stop Number Problem and its implications to other related problems
The Stop Number Problem arises in the management of a dial-a-ride system served by a fleet of autonomous electric vehicles. In such a system, clients request for a ride from an origin station to a destination station, and a fleet of capacitated vehicles must satisfy all requests. The goal is to minimize the number of pick-up/drop-off operations. In this paper we focus on a special case of this problem that was recently conjectured to be NP-Hard. In this regard, we show how such special case relates to other problems known in the literature in order to derive some polynomial-time solvable variants. Moreover, we provide a positive answer to the conjecture by showing that the problem is NP-Hard for any fixed capacity greater than or equal to 2, even for the case where the graph of requests is restricted to the class of planar bipartite graphs. Our proof of NP-Hardness also improves the complexity results known in the literature for the related problems identified
Complexity, Algorithmic, and Computational Aspects of a Dial-a-Ride Type Problem
In dial-a-ride systems involving autonomous vehicles circulating along a circuit, a fleet of vehicles must serve clients who request rides between stations of the circuit such that the total number of pickup and drop-off operations is minimized. In this paper, we focus on a unitary variant where each client requests a single place in the vehicles and all the clients must be served within a single tour of the circuit. Such unitary variant induces a combinatorial optimization problem for which we introduce a nontrivial special case that is polynomially solvable when the capacity of each vehicle is at most 2 but it is NP-Hard otherwise. We also study the polytope associated with the solutions to this problem. We introduce new families of valid inequalities and give necessary and sufficient conditions under which they are facet-defining. Based on these inequalities, we devise an efficient branch-and-cut algorithm that outperforms the state-of-the-art commercial solvers
Design of Survivable Networks: A survey
For the past few decades, combinatorial optimization techniques have been shown to be powerful tools for formulating and solving optimization problems arising from practical situations. In particular, many network design problems have been formulated as combinatorial optimization problems. With the advances of optical technologies and the explosive growth of the Internet, telecommunication networks have seen an important evolution and therefore, designing survivable networks has become a major objective for telecommunication operators. Over the past years, a big amount of research has then been done for devising efficient methods for survivable network models, and particularly cutting plane based algorithms. In this paper, we attempt to survey some of these models and the optimization methods used for solving them
A branch-and-cut algorithm for a resource-constrained scheduling problem
This paper is devoted to the exact resolution of a strongly NP-hard resource-constrained scheduling problem, the Process Move Programming problem, which arises in relation to the operability of certain high-availability real-time distributed systems. Based on the study of the polytope defined as the convex hull of the incidence vectors of the admissible process move programs, we present a branch-and-cut algorithm along with extensive computational results demonstrating its practical relevance, in terms of both exact and approximate resolution when the instance size increases