Apurva Mudgal

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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)
Localization is a fundamental problem in robotics. The robot possesses line-of-sight sensors, a compass, and a map of its polygonal environment; it must determine its location at a minimum cost of travel distance. Localization is NP-hard [3], even to minimize within a c log n factor [15], where n is the number of polygon vertices. No approximation algorithm(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)
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 logn/ log logn) and O(n logn), respectively, on the worst-case total distance traveled by the robot, for the grid graphs(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. Dudek, K. Romanik, and S. Whitesides, SIAM J. Comput., 27 (1998), pp. 583–604] even to minimize within factor c logn [C. Tovey and S. Koenig,(More)