Showing papers presented at "Fun with Algorithms in 2001"
Proceedings Article•
1 Jan 2001
TL;DR: The theme of this paper, and the main motivation for writing it, was presented by Professor Chew Becca, from the Tattooine University, who was vis Department a few months ago, with a problem that seem — to him — of the greatest practical importance.
Abstract: 1 Prologue The theme of this paper, and the main motivation for writing it, was pro us by Professor Chew Becca, from the Tattooine University, who was vis Department a few months ago. He presented us with a problem that seem — to him — of the greatest practical importance. His stay at our Departm too brief for us to completely solve the problem, but we are reporting her progress that we have made after his visit. Prof. Becca's problem was apparently simple. As is, by now, well kn Rebels had infiltrated an important Imperial base with one of their best a call him Lucky Skywalker. Due to the chronic shortage of vessels that the Rebel's fleet at the time, Lucky's mission was to " appropriate " the possible number of Imperial ships and send them, without them being inte through a large extension of Empire-controlled space. The ultimate destin the ships was to be a secret Rebel base, where the ships were to be rewor were to become part of the Rebel fleet. However, Lucky's mission was placed under a few other constraints. T would have to escape unnoticed by the Imperials, always proceeding in fleet formation, and they could have no crew on board, since no other age available. Furthermore, the ships could not communicate with each other, the risk of their radio communication being intercepted. Worst of all, to further strengthen his grip on the entire universe, the Dark Emperor had had his latest operating system, Windows 3000, installed on the navi computers of all the ships in the Imperial fleet. This left no available me the computers to use as storage for an auto-pilot algorithm. Finally, the Re not want to provide the coordinates of their secret base to the auto-pilot Empire then could have traced them and attacked the base in force.
7 citations
Proceedings Article•
1 Jan 2001
TL;DR: This paper addresses the problem of allocating rooms among people in a suitable topology of corridor with some contraints of undesired neighborhood with polynomial time algorithms for several cases of increasing difficulty, including the one where k people have to fit into one room.
Abstract: In this paper we address the problem of allocating rooms among people in a suitable topology of corridor with some contraints of undesired neighborhood. People are partitioned into families, and we consider both internal crashes (sharing a room with someone belonging to a different family), and external crashes (being in a room next to, or in front of someone belonging to a different family). The goal is to minimize a suitably defined weight of such crashes. We give polynomial time algorithms for several cases of increasing difficulty, including the one where k people (with k any given constant) have to fit into one room. Finally, we give a 4 3 approximation for the case with both double and triple rooms.
2 citations
Proceedings Article•
1 Jan 2001
TL;DR: Some new topological properties of the Sprouts Game are studied and their effectiveness is shown by giving a complete analysis of the case x0 = 7, for which no formal proof is, to the best of the authors' knowledge, known.
Abstract: Sprouts is a two players game that was first introduced by M.S. Patterson and J.H. Conway in 1967. There are two players A and B that starting from a set of x0 vertices draw a plane graph by alternatively connecting any pair of two vertices with degree less than three with an edge, and by inserting a new vertex in the new edge. The move is possible if and only if the new connection maintains the planarity of the graph. The player that executes the last possible move is the winner. We study some new topological properties of the Sprouts Game and we show their effectiveness by giving a complete analysis of the case x0 = 7, for which no formal proof is, to the best of our knowledge, known.
2 citations