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 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

Training Artificial Neural Networks: Backpropagation via Nonlinear Optimization

In this paper we explore different strategies to guide backpropagation algorithm used for training artificial neural networks. Two different variants of steepest descent-based backpropagation algorithm, and four different variants of conjugate gradient algorithm are tested. The variants differ whether or not the time component is used, and whether or not additional gradient information is utilized during one-dimensional optimization. Testing is performed on randomly generated data as well as on some benchmark data regarding energy prediction. Based on our test results, it appears that the most promissing backpropagation strategy is to initially use steepest descent algorithm, and then continue with conjugate gradient algorithm. The backpropagation through time strategy combined with conjugate gradients appears to be promissing as well

Connection Machine Implementation of a Tabu Search Algorithm for the Traveling Salesman Problem

A tabu search algorithm for the traveling salesman problem (TSP) is developed. The algorithm is based on the well known 2-opt move which is implemented in parallel on the connection machine CM-2. This involves decomposing the evaluation of the whole 2-opt neighborhood into small independent steps that can be executed in parallel by different processors. The implementation is efficient and highly scalable. Implementation details and results of computation for some TSPs from the literature are presented

On Hub Location Models

The study of hub location models involves designing communication networks where some of the nodes serve as focal points (i.e. hubs) and other nodes are connected to those hubs. Possible applications include airline traffic flow, telecommunications, and mail delivery networks. In this paper we present an overview of recent results on solvability of some hub location models. The overview includes a heuristic approach based on tabu search, lower bounds for cases where distances satisfy triangular inequality, tight linear programming relaxations, and a linkage between optimal and heuristic solutions. As a result of those studies the range of optimally solvable instances of NP-hard hub location problems was extended. In particular, well known and heavily used bench-mark data set of real world problems (Civil Aeronautics Board (CAB) data set), that has resisted efficient solutions for more than a decade, has been solved to optimality. The paper concludes with the discussion of some avenues for future research

Beyond anticipation: Exceeding of expectation and aesthetics

In this work I analyze the significance of irreducibly exceeded expectation in encounters with the environment (including nature proper and artworks). It is argued that the significance is properly aesthetic, independently of culture and taste. Because of one's inability to represent it, the encounter with irreducible newness creates a break since prior to it one was active in creating representations. Recuperation from such a break results in gaining one's sensibility and reflection, i.e. one's representational powers. This is experienced as the phenomenon of surprise. I propose a phenomenology of surprise as a complex process in which one first regains sensibility, then reflection, leading from astonishment to wonderment and further to admiration and responsibility. The consideration of the "expectation of the irreducible exceeding of expectation" provides a depiction of desire for encountering irreducible alterity. The irreducibility of the properly aesthetic is denoted as desire\\surprise to indicate a break (excess, immediacy, the unrepresentable) separating desire stemming from one's past experiencing and surprise that acknowledges the birth of one's sensibility and reflection, enriching each in the process. Following this thematic and a preliminary characterization of the properly aesthetic experience, it is argued that the properly aesthetic can happen in our interaction with nature as well as in our experience of artworks. Arguments are presented for carrying over Kant's theory of sublimity from nature to art. The concept of experience as related to the aesthetic is analyzed. In discussing expectations, it is argued that the seemingly opposing views of Heidegger and Blanchot on death can be brought together by considering death as the negation of the irreducible exceeding of expectation. The notion of excess is analyzed as it relates to desire and the impossibility of immediacy. A phenomenology of the irreducible exceeding of expectation as surprise is viewed as a series of announcements starting with the announcement of sensibility, proceeding with astonishment announcing reflection, then wonderment engendered in sublimity, and subsequently branching into admiration (characterizing art evaluation) and responsibility (characterizing moral judgments). The unfolding of surprise is contrasted with the becoming of knowledge and in particular Hegel's absolute knowledge