Shortest path in complete bipartite digraph problem and it applications
- State Univ. of New York, Buffalo, NY (United States)
- Tokyo Denki Univ., Saitama (Japan)
We introduce the shortest path in complete bipartite digraph (SPCB) problem: Given a weighted complete bipartite digraph G = (X, Y, E) with X = (x{sub 0},{hor_ellipsis}, Xn) and Y = (y{sub 0},{hor_ellipsis},y{sub m}), find a shortest path from x{sub 0} to x{sub n} in G. For arbitrary weights, the problem needs at least {Omega}(nm) time to solve. We show if the weight matrices are concave, the problem can be solved in O(n + m log n) time. As applications, we discuss the traveling salesman problem for points on a convex polygon and the minimum latency tour problem for points on a straight line. The known algorithms for both problems require {Theta}(n{sup 2}) time. Using our SPCB algorithm, we show they can be solved in O(n log n) time. These results solve two open questions.
- OSTI ID:
- 471678
- Report Number(s):
- CONF-970142--; CNN: Grant CCR-9205982
- Country of Publication:
- United States
- Language:
- English
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