TY - GEN

T1 - Group search on the line

AU - Chrobak, Marek

AU - Gąsieniec, Leszek

AU - Gorry, Thomas

AU - Martin, Russell

PY - 2015/1/1

Y1 - 2015/1/1

N2 - In this paper we consider the group search problem, or evacuation problem, in which k mobile entities (Mεs) located on the line perform search for a specific destination. The Mεs are initially placed at the same origin on the line L and the target is located at an unknown distance d, either to the left or to the right from the origin. All Mεs must simultaneously occupy the destination, and the goal is to minimize the time necessary for this to happen. The problem with k = 1 is known as the cow-path problem, and the time required for this problem is known to be 9d - o(d) in the worst case (when the cow moves at unit speed); it is also known that this is the case for k ≥ 1 unit-speed Mεs. In this paper we present a clear argument for this claim by showing a rather counter-intuitive result. Namely, independent of the number of Mεs, group search cannot be performed faster than in time 9d - o(d). We also examine the case of k = 2 Mεs with different speeds, showing a surprising result that the bound of 9d can be achieved when one Mε has unit speed, and the other Mε moves with speed at least 1/3.

AB - In this paper we consider the group search problem, or evacuation problem, in which k mobile entities (Mεs) located on the line perform search for a specific destination. The Mεs are initially placed at the same origin on the line L and the target is located at an unknown distance d, either to the left or to the right from the origin. All Mεs must simultaneously occupy the destination, and the goal is to minimize the time necessary for this to happen. The problem with k = 1 is known as the cow-path problem, and the time required for this problem is known to be 9d - o(d) in the worst case (when the cow moves at unit speed); it is also known that this is the case for k ≥ 1 unit-speed Mεs. In this paper we present a clear argument for this claim by showing a rather counter-intuitive result. Namely, independent of the number of Mεs, group search cannot be performed faster than in time 9d - o(d). We also examine the case of k = 2 Mεs with different speeds, showing a surprising result that the bound of 9d can be achieved when one Mε has unit speed, and the other Mε moves with speed at least 1/3.

KW - Evacuation

KW - Group search

KW - Mobile entity

UR - http://www.scopus.com/inward/record.url?scp=84922022460&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84922022460&partnerID=8YFLogxK

U2 - 10.1007/978-3-662-46078-8_14

DO - 10.1007/978-3-662-46078-8_14

M3 - Conference contribution

AN - SCOPUS:84922022460

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 164

EP - 176

BT - SOFSEM 2015

A2 - Italiano, Giuseppe F.

A2 - Margaria-Steffen, Tiziana

A2 - Pokorný, Jaroslav

A2 - Quisquater, Jean-Jacques

A2 - Wattenhofer, Roger

PB - Springer Verlag

T2 - 41st International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2015

Y2 - 24 January 2015 through 29 January 2015

ER -