A regret model applied to the maximum capture location problem

This article addresses issues related to location and allocation problems. Herein, we intend to demonstrate the influence of congestion, through the random number generation, of such systems in final solutions. An algorithm is presented which, in addition to the GRASP, incorporates the Regret with the pminmax method to evaluate the heuristic solution obtained with regard to its robustness for different scenarios. Taking as our point of departure the Maximum Capture Location Problem proposed by Church and Revelle [1, 26], an alternative perspective is added in which the choice behavior of the server does not depend only on the elapsed time from the demand point looking to the center, but includes also the service waiting time.N/

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

A regret model applied to the maximum coverage location problem with queue discipline

This article discusses issues related to the location and allocation problems where is intended to demonstrate, through the random number generation, the influence of congestion of such systems in the final solutions. It is presented an algorithm that, in addition to the GRASP, incorporates the Regret with the pminmax method to evaluate the heuristic solution obtained in regard to its robustness for different scenarios. To the well know Maximum Coverage Location Problem from Church and Revelle [1] an alternative perspective is added in which the choice behavior of the server does not only depend on the elapsed time from the demand point looking to the center, but also includes the waiting time for service conditioned by a waiting queue.N/

A regret model applied to the facility location problem with limited capacity facilities

This article addresses issues related to location and allocation problems. Herein, we intend to demonstrate the influence of congestion, through the random number generation, of such systems in final solutions. An algorithm is presented which, in addition to the GRASP, incorporates the Regret with the pminmax method to evaluate the heuristic solution obtained with regard to its robustness for different scenarios. Taking as our point of departure the Facility Location Problem proposed by Balinski [27], an alternative perspective is added associating regret values to particular solutions.N/

A Tutorial on Clique Problems in Communications and Signal Processing

Since its first use by Euler on the problem of the seven bridges of K\"onigsberg, graph theory has shown excellent abilities in solving and unveiling the properties of multiple discrete optimization problems. The study of the structure of some integer programs reveals equivalence with graph theory problems making a large body of the literature readily available for solving and characterizing the complexity of these problems. This tutorial presents a framework for utilizing a particular graph theory problem, known as the clique problem, for solving communications and signal processing problems. In particular, the paper aims to illustrate the structural properties of integer programs that can be formulated as clique problems through multiple examples in communications and signal processing. To that end, the first part of the tutorial provides various optimal and heuristic solutions for the maximum clique, maximum weight clique, and $k$-clique problems. The tutorial, further, illustrates the use of the clique formulation through numerous contemporary examples in communications and signal processing, mainly in maximum access for non-orthogonal multiple access networks, throughput maximization using index and instantly decodable network coding, collision-free radio frequency identification networks, and resource allocation in cloud-radio access networks. Finally, the tutorial sheds light on the recent advances of such applications, and provides technical insights on ways of dealing with mixed discrete-continuous optimization problems

Networking - A Statistical Physics Perspective

Efficient networking has a substantial economic and societal impact in a broad range of areas including transportation systems, wired and wireless communications and a range of Internet applications. As transportation and communication networks become increasingly more complex, the ever increasing demand for congestion control, higher traffic capacity, quality of service, robustness and reduced energy consumption require new tools and methods to meet these conflicting requirements. The new methodology should serve for gaining better understanding of the properties of networking systems at the macroscopic level, as well as for the development of new principled optimization and management algorithms at the microscopic level. Methods of statistical physics seem best placed to provide new approaches as they have been developed specifically to deal with non-linear large scale systems. This paper aims at presenting an overview of tools and methods that have been developed within the statistical physics community and that can be readily applied to address the emerging problems in networking. These include diffusion processes, methods from disordered systems and polymer physics, probabilistic inference, which have direct relevance to network routing, file and frequency distribution, the exploration of network structures and vulnerability, and various other practical networking applications.Comment: (Review article) 71 pages, 14 figure

On Optimal Geographical Caching in Heterogeneous Cellular Networks

In this work we investigate optimal geographical caching in heterogeneous cellular networks where different types of base stations (BSs) have different cache capacities. Users request files from a content library according to a known probability distribution. The performance metric is the total hit probability, which is the probability that a user at an arbitrary location in the plane will find the content that it requires in one of the BSs that it is covered by. We consider the problem of optimally placing content in all BSs jointly. As this problem is not convex, we provide a heuristic scheme by finding the optimal placement policy for one type of base station conditioned on the placement in all other types. We demonstrate that these individual optimization problems are convex and we provide an analytical solution. As an illustration, we find the optimal placement policy of the small base stations (SBSs) depending on the placement policy of the macro base stations (MBSs). We show how the hit probability evolves as the deployment density of the SBSs varies. We show that the heuristic of placing the most popular content in the MBSs is almost optimal after deploying the SBSs with optimal placement policies. Also, for the SBSs no such heuristic can be used; the optimal placement is significantly better than storing the most popular content. Finally, we show that solving the individual problems to find the optimal placement policies for different types of BSs iteratively, namely repeatedly updating the placement policies, does not improve the performance.Comment: The article has 6 pages, 7 figures and is accepted to be presented at IEEE Wireless Communications and Networking Conference (WCNC) 2017, 19 - 22 March 2017, San Francisco, CA, US