Network Connectivity Game

We investigate the cost allocation strategy associated with the problem of providing service /communication between all pairs of network nodes. There is a cost associated with each link and the communication between any pair of nodes can be delivered via paths connecting those nodes. The example of a cost efficient solution which could provide service for all node pairs is a (non-rooted) minimum cost spanning tree. The cost of such a solution should be distributed among users who might have conflicting interests. The objective of this paper is to formulate the above cost allocation problem as a cooperative game, to be referred to as a Network Connectivity (NC) game, and develop a stable and efficient cost allocation scheme. The NC game is related to the Minimum Cost Spanning Tree games and to the Shortest Path games. The profound difference is that in those games the service is delivered from some common source node to the rest of the network, while in the NC game there is no source and the service is established through the two-way interaction among all pairs of participating nodes. We formulate Network Connectivity (NC) game and construct an efficient cost allocation algorithm which finds some points in the core of the NC game. Finally, we discuss the Egalitarian Network Cost Allocation (ENCA) rule and demonstrate that it finds an additional core point

On some cost allocation problems in communication networks

New technologies prompted an explosion in the development of communication networks. Modern network optimization techniques usually lead to a design of the most profitable, or the least cost network that will provide some service to customers. There are various costs and gains associated with building and using a communication network. Moreover, the involved multiple network users and/or owners possibly have conflicting objectives. However, they might cooperate in order to decrease their joint cost or increase their joint profit. Clearly, these individuals or organizations will support a globally \u27attractive\u27 solution(s) only if their expectations for a \u27fair share\u27 of the cost or profit are met. Consequently, providing network developers, users and owners with efficiently computable \u27fair\u27 cost allocation solution procedures is of great importance for strategic management. This work is an overview of some recent results (some already published as well as some new) in the development of cooperative game theory based mechanisms to efficiently compute \u27attractive\u27 cost allocation solutions for several important classes of communication networks

On Cost Allocation in Networks with Threshold Based Discounting

We study network design in which each pair of nodes can communicate via a direct link and the communication flow can be delivered through any path in the network. The cost of flow through each link is discounted if and only if the amount of flow exceeds certain threshold. This exploitation of economies of scale encourages the concentration of flows and use of relatively small number of links. Applications include telecommunications, airline traffic flow, and mail delivery networks. The cost of services delivered through such a network is distributed among its users who may be individuals or organizations with possibly conflicting interests. The cooperation between these users is essential for the exploitation of economies of scale. Consequently, there is a need to ensure a fair distribution of the cost of providing the service among network users. In order to describe this cost allocation problem we formulate the associated cooperative game, to be referred to as the threshold game. We then demonstrate that certain cost allocation solution (the core of the threshold game) can be efficiently applied to relatively ’large’ networks with threshold-based discounting

On strongly polynomial algorithms for some classes of quadratic programming problems

In this paper we survey some results concerning polynomial and/or strongly polynomial solvability of some classes of quadratic programming problems. The discussion on polynomial solvability of continuous convex quadratic programming is followed by a couple of models for quadratic integer programming which, due to their special structure, allow polynomial (or even strongly polynomial) solvability. The theoretical merit of those results stems from the fact that a running time (i.e. the number of elementary arithmetic operations) of a strongly polynomial algorithm is independent of the input size of the problem

Network cost allocation games based on threshold discounting

Consider networks in which each pair of nodes needs to communicate. The communication flow between any pair of nodes can be delivered through a direct link or via some connecting path in the network. By discounting the cost of flow through links for which the high flow volume is anticipated, network designers exploit economies of scale. This approach encourages the concentration of flows and use of relatively small number of links. This led to the design of well known hub networks and more recently hub-like networks. Applications include telecommunications, airline traffic flow, and mail delivery networks. The cost of services delivered through such networks is distributed among its users who may be individuals or organizations with possibly conflicting interests. The cooperation of these users is essential for the exploitation of economies of scale. Consequently, there is a need to find a fair distribution of the cost of providing the service among network users. In this paper, we present a survey of some recent results in the development of cooperative game theory based mechanisms to efficiently characterize cost allocation solutions for hub and hub-like networks. Specifically, we formulate the associated hub and hub-like network cost allocation games. Then, while paying special attention to users\u27 contribution to economies of scale, we demonstrate that some attractive cost allocation solutions, which provide users with the incentive to cooperate, can be efficiently computed

An application of a genetic algorithm for throughput optimization in non-broadcast WDM optical networks with regular topologies

We apply a genetic algorithm from Podnar and Skorin-Kapov [5] to a virtual topology design of a Wide-Area WDM Optical Network with regular topologies. Based on a given physical topology a virtual topology consisting of optical lightpaths is constructed. The objective is to minimize the maximal throughput, which implies balancing link loads and accommodating on-growing traffic requirements in a timely fashion. The genetic algorithm is applied to benchmark instances of regular topologies

On polynomial solvability of the high multiplicity total weighted tardiness problem

AbstractIn a recent paper Hochbaum developed a polynomial algorithm for solving a scheduling problem of minimizing the total weighted tardiness for a large number of unit length jobs which can be partitioned into few sets of jobs with identical due dates and penalty weights. The number of unit jobs in a set is called the multiplicity of that set. The problem was formulated in Hochbaum as an integer quadratic nonseparable transportation problem and solved, in polynomial time, independent of the size of the multiplicities and the due dates but depending on the penalty weights. In this paper we show how to solve the above problem in polynomial time which is independent of the sizes of the weights. The running time of the algorithm depends on the dimension of the problem and only the size of the maximal difference between two consecutive due dates. In the case where the due dates are large, but the size of the maximal difference between two consecutive due dates is polynomially bounded by the dimension of the problem, the algorithm runs in strongly polynomial time

On Delay versus Congestion in Designing Rearrangeable Multihop Lightwave Networks

We investigate design issues of optical networks in light of two conflicting criteria: throughput maximization (or, equivalently, congestion minimization) versus delay minimization. We assume the network has an arbitrary topology, the flow can be split and sent via different routes, and it can be transferred via intermediate nodes. Tabu search heuristic is used to compare solutions with different weights assigned to each of the two criteria. The approach is tested on a benchmark data set, the 14-dimensional NSFNET T1 network with traffic from 1993. The results suggest that (1) some connectivity matrices are quite robust and desirable regarding both criteria simultaneously; (2) forcing minimization of total delay unconditionally can result with significantly inferior throughput. Some decisions strategies are outlined