TY - GEN
T1 - Group search on the line
AU - Chrobak, Marek
AU - Gąsieniec, Leszek
AU - Gorry, Thomas
AU - Martin, Russell
N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2015.
PY - 2015
Y1 - 2015
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
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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 -