Curve approximation and constrained shortest path problems Geir Dahl and Bjørnar Realfsen Preprint

Curve approximation and constrained shortest path problems

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...

Large-Scale Integer Programs in Image Analysis

An important problem in image analysis is to segment an image into regions with di erent class-labels. This is releveant in applications in medicine and cartography. In a proper statistical framework this problem may be viewed as a discrete optimization problem. We present two integer linear programming formulations of the problem and study some properties of these models and associated polytop...

Approximation Solutions for Time-Varying Shortest Path Problem

Abstract. Time-varying network optimization problems have tradition-ally been solved by specialized algorithms. These algorithms have NP-complement time complexity. This paper considers the time-varying short-est path problem, in which can be optimally solved in O(T(m + n)) time,where T is a given integer. For this problem with arbitrary waiting times,we propose an approximation algorithm, whic...

Notes on polyhedra associated with hop - constrained paths Geir Dahl

Routing of Electric Vehicles: Constrained Shortest Path Problems with Resource Recovering Nodes

We consider a constrained shortest path problem with the possibility to refill the resource at certain nodes. This problem is motivated by routing electric vehicles with a comparatively short cruising range due to the limited battery capacity. Thus, for longer distances the battery has to be recharged on the way. Furthermore, electric vehicles can recuperate energy during downhill drive. We ext...