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The Ferry Cover Problem
National Technical University of Athens.
2009 (English)In: Theory of Computing Systems, ISSN 1432-4350, E-ISSN 1433-0490, Vol. 44, no 2, 215-229 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we define and study a family of optimization problems called FERRY problems, which may be viewed as generalizations of the classical wolf-goat-cabbage puzzle. We present the FERRY COVER problem (FC), where the objective is to determine the minimum required boat size to safely transport n items represented by a graph G and demonstrate a close connection with VERTEX COVER which leads to hardness and approximation results. We also completely solve the problem on trees. Then we focus on a variation of the same problem with the added constraint that only 1 round-trip is allowed (FC(1)). We present a reduction from MAX-NAE{3}-SAT which shows that this problem is NP-hard and APX-hard. We also provide an approximation algorithm for bipartite graphs with a factor asymptotically equal to 4/3 and a 1.56-approximation algorithm for planar graphs. Finally, we generalize the above problem to define FC(m), where at most m round-trips are allowed, and MFT(k), which is the problem of minimizing the number of round-trips when the boat capacity is k. We present some preliminary lemmata for both, which provide bounds on the value of the optimal solution, and relate them to FC.

Place, publisher, year, edition, pages
2009. Vol. 44, no 2, 215-229 p.
Keyword [en]
Approximation algorithms, Graph algorithms, Vertex cover, Transportation problems, Wolf-goat-cabbage puzzle
National Category
Computer and Information Science
URN: urn:nbn:se:kth:diva-58605DOI: 10.1007/s00224-008-9107-0ISI: 000263099400007OAI: diva2:473415
QC 20120109Available from: 2012-01-05 Created: 2012-01-05 Last updated: 2012-01-09Bibliographically approved

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Lampis, Michael
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