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We consider a generalization of the capacitated vehicle routing problem known as the cumulative vehicle routing problem in the literature. Cumulative VRPs are known be a simple model for fuel consumption in VRPs. We examine four variants of the problem, and give constant factor approximation algorithms. Our results are based on a well-known heuristic of… (More)

D * is a greedy heuristic planning method that is widely used in robotics, including several Nomad class robots and the Mars rover prototype, to reach a destination in unknown terrain. We obtain nearly sharp lower and upper bounds of Ω(n log n/ log log n) and O(n log n), respectively, on the worst-case total distance traveled by the robot, for the grid… (More)

Robots often have to navigate robustly despite incomplete information about the terrain or their location in the terrain. In this case, they often use greedy methods to make planning tractable. In this paper, we analyze two such robot-navigation methods. The first method is Greedy Localization, which determines the location of a robot in known terrain by… (More)

Localization is a fundamental problem in robotics. The " kidnapped robot " possesses a compass and map of its environment; it must determine its location at a minimum cost of travel distance. The problem is NP-hard [G. where n is the map size. No approximation algorithm has been known. We give an O(log 3 n)-factor algorithm. The key idea is to plan travel… (More)

Localization is a fundamental problem in robotics. The 'kidnapped robot' possesses a compass and map of its environment; it must determine its location at a minimum cost of travel distance. The problem is NP-hard [6] even to minimize within factor <i>c</i> log <i>n</i>[21], where <i>n</i> is the number of vertices. No approximation algorithm has been known.… (More)

We show that hitting set and set cover problems with half-strips oriented in two opposite directions are NP-complete.

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