Efficient solutions to some transportation problems with applications to minimizing robot arm travel
SIAM Journal on Computing
Preemptive ensemble motion planning on a tree
SIAM Journal on Computing
Nonpreemptive ensemble motion planning on a tree
Journal of Algorithms
Approximating Capacitated Routing and Delivery Problems
SIAM Journal on Computing
The Swapping Problem on a Line
SIAM Journal on Computing
Computer-Aided Complexity Classification of Dial-a-Ride Problems
INFORMS Journal on Computing
An approximation algorithm for the pickup and delivery vehicle routing problem on trees
Discrete Applied Mathematics - Special issue: Discrete algorithms and optimization, in honor of professor Toshihide Ibaraki at his retirement from Kyoto University
Heuristics for the mixed swapping problem
Computers and Operations Research
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The uncapacitated swapping problem is defined by a graph consisting of n vertices, and m object types. Each vertex of the graph is associated with two object types: the one that it currently holds, and the one it demands. Each vertex holds or demands at most one unit of an object. The problem is balanced in the sense that for each object type, its total supply equals its total demand. A vehicle of unlimited capacity is assumed to transport the objects in order to fulfill the requirements of all vertices. The objective is to find a shortest route along which the vehicle can accomplish the rearrangement of the objects, given designated initial and terminal vertices. The uncapacitated swapping problem on a general graph, including a tree graph, is known to be NP-Hard. In this paper we show that for the line and circle graphs, the problem is polynomially solvable: we propose an O(n)-time algorithm for a line and an O(n^3)-time algorithm for a circle.