We address the problem identifying the K best point-to-point simple paths connecting a given pair of nodes in a directed network with arbitrary lengths. The main result in this paper is the proof that a path tree containing the kth point-to-point shortest simple path can be obtained by using one of the previous (k-1) path trees containing each one of the previous (k-1) best point-to-point short...

The shortest path problem in which the (s, t)-paths P of a given digraph G = (V,E) are compared with respect to the sum of their edge costs is one of the best known problems in combinatorial optimization. The paper is concerned with a number of variations of this problem having different objective functions like bottleneck, balanced, minimum deviation, algebraic sum, k-sum and k-max objectives,...

We study the following problem k-constrained shortest path problem: given an acyclic directed graph D = (V,E) with arc weights ci,j , (i, j) ∈ E, two nodes s and t and an integer k, nd a shortest st-path containing at most k arcs. An important application of the problem in linear curve approximation is discussed. Vertices and edges of associated polytopes are determined, and integrality of thes...

Communication on interconnection networks is a fundamental problem that has to be solved optimally in order to optimize the usage of a parallel computer. One of the basic communication problems is k-k routing, in which every processing unit, PU, sends and receives exactly k packets. If the distribution of the destinations is homogeneous, then generally it is quite easy to perform the routing ef...

The shortest path problem is solved and applied to the calculations of half lives with respect to spontaneous fission of heavy nuclei. The dynamical programming method of Bellman and Kalaba is used to find the fission path in the d-dimensional space of deformation parameters. Fission half lives of heavy isotopes (100<Z<110) are shown and compared to the experimental data. 1. Introductory remark...

The Shortest Path Problem with Resource Constraints is a common subproblem in many Branch-Cut-and-Price algorithms (BCP), e.g., routing and scheduling problems. This paper presents a general label-setting algorithm for solving various shortest path problems. An integration of the ‘Shortest Path Problem with Resource Constraints and k-cycle elimination’ with the ‘Partial Elementarity’ is introdu...

The bandwidth problem is one of the most serious problems for multi-hop wireless mesh networks (WMNs) due to the influence of link interference. In this paper, we study joint problem of interference-aware bandwidth guaranteed scheduling and shortest path routing in IEEE 802.11-based multi-channel wireless mesh networks with dynamic traffic. We present distributed bandwidth guaranteed TDMA sched...

The shortest hyperpath problem is an extension of the classical shortest path problem and has applications in many different areas. Recently, algorithms for finding the K shortest hyperpaths in a directed hypergraph have been developed by Andersen, Nielsen and Pretolani. In this paper we improve the worst-case computational complexity of an algorithm for finding the K shortest hyperpaths in an ...

a shortest path problem is a practical issue in networks for real-world situations. this paper addresses the fuzzy shortest path (fsp) problem to obtain the best fuzzy path among fuzzy paths sets. for this purpose, a new efficient algorithm is introduced based on a new definition of ideal fuzzy sets (ifss) in order to determine the fuzzy shortest path. moreover, this algorithm is developed for ...