In this paper, we reduce the logspace shortest path problem to biconnected graphs; in particular, we present a logspace shortest path algorithm for general graphs which uses a logspace shortest path oracle for biconnected graphs. We also present a linear time logspace shortest path algorithm for graphs with bounded vertex degree and biconnected component size, which does not rely on an oracle. ...

In this article, we study the problem of finding the next-to-shortest path in circular-arc graph. A next-to-shortest path between any pair of vertices in a shortest path amongst all paths between those vertices with length strictly greater than the length of the shortest path. The next-to-shortest path problem in a directed graph in NP-hard. Here we deigned a polynomial time algorithm to solve ...

The quickest path problem, a version of the shortest path problem, is to find a single quickest path which sends a given amount of data from the source to the sink with minimum transmission time. More specifically, the capacity of each arc in the network is assumed to be deterministic. However, in many real-life networks such as computer systems, telecommunication systems, etc., the capacity of...

Motivated by what is required for real-time path planning, the paper starts out by presenting RMPD, a new recursive “local” planner founded on the key notion that, unless made necessary by an obstacle, there must be no deviation from the shortest path between any two points, which would normally be a straight line path in the configuration space. Subsequently, we increase the power of RMPD by i...

A shortest-path algorithm finds a path containing the minimal cost between two vertices in a graph. A plethora of shortest-path algorithms is studied in the literature that span across multiple disciplines. This paper presents a survey of shortest-path algorithms based on a taxonomy that is introduced in the paper. One dimension of this taxonomy is the various flavors of the shortest-path probl...

We study two-stage, finite-scenario stochastic versions of several combinatorial optimization problems, and provide nearly tight approximation algorithms for them. Our problems range from the graph-theoretic (shortest path, vertex cover, facility location) to set-theoretic (set cover, bin packing), and contain representatives with different approximation ratios. The approximation ratio of the s...

Stochastic Shortest Path problems (SSPs), a subclass of Markov Decision Problems (MDPs), can be efficiently dealt with using Real-Time Dynamic Programming (RTDP). Yet, MDP models are often uncertain (obtained through statistics or guessing). The usual approach is robust planning: searching for the best policy under the worst model. This paper shows how RTDP can be made robust in the common case...