Proof: (by induction). We want to show that one SAP doesn’t introduce negative cycles in Gf . Initially there are no negative cost cycles. Feasible prices can be computed by using shortest path distances from s. After finding the shortest s-t path, it has reduced cost 0. Every arc on the path has reduced length 0. This demonstrates that the triangle inequality property is tight on shortest path...

Use of path expressions is a common feature in most XML query languages, and many evaluation methods for path expression queries have been proposed recently. However, there are few researches on the issue of optimizing regular path expression queries. In this paper, two kinds of path expression optimization principles are proposed, named path shortening and path complementing, respectively. The...

The problem of finding a minimal cost-reliability ratio path is considered. The optimal solution to this problem is shown to map into an extreme supported non-dominated objective point in the objective space of the biobjective shortest path problem. Different forms of reliability are presented. We assume that this reliability does not change over time. We employ a parametric network simplex alg...

We explore a symmetry-based reformulation technique which can speed up optimal pathfinding on undirected uniform-cost grid maps by over 30 times. Our offline approach decomposes grid maps into a set of empty rectangles, removing from each all interior nodes and possibly some from along the perimeter. We then add macro-edges between selected pairs of remaining perimeter nodes to facilitate prova...

With the growing volumes of vehicle trajectory data, it becomes increasingly possible to capture time-varying and uncertain travel costs in a road network, including travel time and fuel consumption. The current paradigm represents a road network as a weighted graph; it blasts trajectories into small fragments that fit the underlying edges to assign weights to edges; and it then applies a routi...

A class of cooperative games arising from shortest path problems is deened. These shortest path games are shown to be totally balanced and allow a population-monotonic allocation scheme. Possible methods for obtaining core elements are indicated; rst, by relating to the allocation rules in taxation and bankruptcy problems, second, by constructing an explicit rule that takes opportunity costs in...

The Minimum Cost Path Problem with Relays (MCPPR) consists of finding a minimum cost path from a source to a destination, along which relay nodes are located at a certain cost, subject to a weight constraint. This paper first models the MCPPR as a particular bicriteria path problem involving an aggregated function of the path and relay costs, as well as a weight function. A variant of this prob...

Recent developments in plan recognition have established a method of identifying an agent’s most probable plan or goal by use of a classical planner and an appeal to the principle of rational action. We examine this technique in the strict context of path-planning. We show that a simpler formula provides an identical result in less than half the time under all but one set of conditions, which w...

This paper studies the path planning problem for mobile robots to move smoothly and safely along a shorter curvature-constrained path in completely known dynamic environments. The cost of travel is defined by an obstacle-avoidance cost, which is designed as a weighted penetration depth to vertices of obstacles, and a length cost. The path is composed of a pre-specified number of cubic spiral se...