The ferry cover problem

Lampis, M; Mitsou, V

dc.contributor.author	Lampis, M	en
dc.contributor.author	Mitsou, V	en
dc.date.accessioned	2014-03-01T01:32:10Z
dc.date.available	2014-03-01T01:32:10Z
dc.date.issued	2009	en
dc.identifier.issn	1432-4350	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20051
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.classification	Computer Science, Theory & Methods	en
dc.subject.classification	Mathematics	en
dc.subject.other	APPROXIMATION	en
dc.subject.other	COMPLEXITY	en
dc.title	The ferry cover problem	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s00224-008-9107-0	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s00224-008-9107-0	en
heal.language	English	en
heal.publicationDate	2009	en
heal.abstract	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 (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 bipartite graphs with a factor asymptotically equal to \frac{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. © 2008 Springer Science+Business Media, LLC.	en
heal.publisher	SPRINGER	en
heal.journalName	Theory of Computing Systems	en
dc.identifier.doi	10.1007/s00224-008-9107-0	en
dc.identifier.isi	ISI:000263099400007	en
dc.identifier.volume	44	en
dc.identifier.issue	2	en
dc.identifier.spage	215	en
dc.identifier.epage	229	en