The ferry cover problem

Lampis, M; Mitsou, V

dc.contributor.author	Lampis, M	en
dc.contributor.author	Mitsou, V	en
dc.date.accessioned	2014-03-01T02:44:58Z
dc.date.available	2014-03-01T02:44:58Z
dc.date.issued	2007	en
dc.identifier.issn	03029743	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/32065
dc.subject	Approximation algorithms	en
dc.subject	Graph algorithms	en
dc.subject	Transportation problems	en
dc.subject	Vertex cover	en
dc.subject	Wolf-goat-cabbage puzzle	en
dc.subject.other	Approximation algorithms	en
dc.subject.other	Constraint theory	en
dc.subject.other	Graph theory	en
dc.subject.other	Problem solving	en
dc.subject.other	Set theory	en
dc.subject.other	Graph algorithms	en
dc.subject.other	Preliminary lemmata	en
dc.subject.other	Transportation problems	en
dc.subject.other	Wolf goat cabbage puzzles	en
dc.subject.other	Game theory	en
dc.title	The ferry cover problem	en
heal.type	conferenceItem	en
heal.identifier.primary	10.1007/978-3-540-72914-3_20	en
heal.identifier.secondary	http://dx.doi.org/10.1007/978-3-540-72914-3_20	en
heal.publicationDate	2007	en
heal.abstract	In the classical wolf-goat-cabbage puzzle, a ferry boat man must ferry three items across a river using a boat that has room for only one, without leaving two incompatible items on the same bank alone. In this paper we define and study a family of optimization problems called FERRY problems, which may be viewed as generalizations of this familiar puzzle. In all FERRY problems we are given a set of items and a graph with edges connecting items that must not be left together unattended. We present the FERRY COVER problem (FC), where the objective is to determine the minimum required boat size 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 (FC1). 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 trees with a factor asymptotically equal to 4/3. Finally, we generalize the above problem to define FCm, where at most m round-trips are allowed, and MFTk, 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. © Springer-Verlag Berlin Heidelberg 2007.	en
heal.journalName	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)	en
dc.identifier.doi	10.1007/978-3-540-72914-3_20	en
dc.identifier.volume	4475 LNCS	en
dc.identifier.spage	227	en
dc.identifier.epage	239	en