the problem of navigation among movable obstacles (namo) is to find a collision free path for a robot while the robot is able to manipulate and transfer some objects (if possible or needed) to clear its path toward the goal. namo is a np-complete problem and is in a class of motion planning problems that have dynamic environments. in this domain, an optimal plan for the robot can be defined wit...

We consider generalized shortest path problems with cost and weight functions for the arcs of a graph. According to their weight arcs may generate or consume ow. Weights may be additive or multiplicative on a path. More precisely, if x units enter an arc a = (u; v) then x + w(a) resp. x w(a) leave it. The cost is charged per unit and summed over the edges of a path. If the weights multiply, the...

Numerous algorithms have been proposed to solve the shortest-pathproblem; many of them consider a single-mode network and crispcosts. Other attempts have addressed the problem of fuzzy costs ina single-mode network, the so-called fuzzy shortest-path problem(FSPP). The main contribution of the present work is to solve theoptimum path problem in a multimodal transportation network, inwhich the co...

We consider biobjective shortest path problems in networks with fuzzy arc lengths. Considering the available studies for single objective shortest path problems in fuzzy networks, using a distance function for comparison of fuzzy numbers, we propose three approaches for solving the biobjective prob- lems. The rst and second approaches are extensions of the labeling method to solve the sing...

We consider bicriteria optimization problems and investigate the relationship between two standard approaches to solving them: (i) computing the Pareto curve and (ii) the so-called decision maker’s approach in which both criteria are combined into a single (usually non-linear) objective function. Previous work by Papadimitriou and Yannakakis showed how to efficiently approximate the Pareto curv...

In this paper, we formulate a novel problem called Which-Edge question on shortest path queries. Specifically, this problem aims to find k edges that minimize the total distance for a given set of shortest path queries on a graph. This problem has important applications in logistics, urban planning, and network planning. We show the NP-hardness of the problem, as well as present efficient algor...

In this paper, we study dynamic shortest path problems, which is to determine a shortest path from a specified source node to every other node in the network where arc travel times change dynamically. We consider two problems: the minimum time walk problem (which is to find a walk with the minimum travel time) and the minimum cost walk problem (which is to find a walk with the minimum travel co...

We present the rst lower bounds for shortest path problems (including euclidean shortest path) in three dimensions, and for some constrained motion planning problems in two and three dimensions. Our proofs are based a technique called free path encoding and use homotopy equivalence classes of paths to encode state. We rst apply the method to the shortest path problem in three dimensions. The pr...