We investigate the complexity of shortest paths in timedependent graphs, in which the costs of edges vary as a function of time, and as a result the shortest path between two nodes s and d can change over time. Our main result is that when the edge cost functions are (polynomial-size) piecewise

. The success (or failure) to select the best available path depends on the statistics of the wireless channel, and a methodology to evaluate performance for any kind of wireless channel statistics, is provided. Information theoretic analysis of outage probability shows that our scheme achieves the same

We consider in this paper the shortest-path problem in networks in which the delay (or weight) of the edges changes with time according to arbitrary functions. We present algorithms for finding the shortest-path and minimum-delay under various waiting constraints and investigate the properties

problems fit in this framework, including the shortest path, minimum-cost spanning tree, minimum-weight perfect matching, traveling salesman, and Steiner tree problems. Our technique produces approximation algorithms that run in O(n log n) time and come within a factor of 2 of optimal for most

. As an application, we provide an optimal time algorithm for computing the geodesic distances and thereby extracting shortest paths on triangulated manifolds. 1 Introduction Sethian`s Fast Marching Method [8], is a numerical algorithm for solving the Eikonal equation on a rectangular orthogonal mesh in O(M log M

are considered, a key difficulty is how to transfer local timing functions among the participating nodes. To that end it is necessary to characterize the parameterization of the functions and accommodate this parameterization in the computation. In particular, we consider the shortest-path problem in networks

In recent years there has been a growing interest in using stochastic time-dependent (STD) networks as a modelling tool for a number of ap-plications within such areas as transportation and telecommunications. It is known that an optimal routing policy does not necessarily correspond to a path

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property, which makes the time-dependent shortest path problem solvable in polynomial-time. Using the β-synchronizer, we propose a fast distributed algorithm to build all-to-one shortest paths with polynomial message complexity and time complexity. The algorithm determines the shortest paths for all

Abstract: In this study, we analyzed the complexity of the Time-Dependent Shortest Paths Problem (TD-2SP) and its variants, and developed model and algorithm to solve this problem as well as more general versions of it in which the pair of paths is required to be only partially disjoint