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|標題:||An Optimal Algorithm for Shortest Paths on Weighted Interval and Circular-arc Graphs with Applications||作者:||M.J.Atallah
|關鍵字:||Shortest paths;Interval graphs;Circular-arc graphs;Union-find algorithms;Minimum circle cover||出版社:||Springer-Verlag||Project:||Algorithmica, Volume�14, Issue�5, Page(s) �429-441.||摘要:||
We give the first linear-time algorithm for computing single-source shortest paths in a weighted interval or circular-arc graph, when we are given the model of that graph, i.e., the actual weighted intervals or circular-arcsand the sorted list of the interval endpoints. Our algorithm solves this problem optimally inO(n) time, wheren is the number of intervals or circular-arcs in a graph. An immediate consequence of our result is anO(qn + n logn)-time algorithm for the minimum-weight circle-cover problem, whereq is the minimum number of arcs crossing any point on the circle; then logn term in this time complexity is from a preprocessing sorting step when the sorted list of endpoints is not given as part of the input. The previously best time bounds were0(n logn) for this shortest paths problem, andO(qn logn) for the minimum-weight circle-cover problem. Thus we improve the bounds of both problems. More importantly, the techniques we give hold the promise of achieving similar (logn)-factor improvements in other problems on such graphs.
|Appears in Collections:||資訊科學與工程學系所|
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