TY - GEN

T1 - On minimum and maximum spanning trees of linearly moving points

AU - Katoh, Naoki

AU - Tokuyama, Takeshi

AU - Iwano, Kazuo

PY - 1992

Y1 - 1992

N2 - The authors investigate the upper bounds on the numbers of transitions of minimum and maximum spanning trees (MinST and MaxST for short) for linearly moving points. Suppose that one is given a set of n points in general d-dimensional space, S=(p1,p2,..., pn), and that all points move along different straight lines at different but fixed speeds, i.e., the position of pi is a linear function of a real parameter. They investigate the numbers of transitions of MinST and MaxST when t increases from - infinity to + infinity. They assume that the dimension d is a fixed constant. Since there are O(n2) distances among n points, there are naively O(n4) transitions of MinST and MaxST. They improve these trivial upper bounds for L1 and L/sub infinity / distance metrics. Let cp(n, min) (resp. cp(n, max)) be the number of maximum possible transitions of MinST (resp. MaxST) in Lp metric for n linearly moving points. They give the following results; c1(n, min)=O(n5/2a(n)), c/sub infinity /(n, min)=O(n5/2a(n)), c1(n, max)=O(nn) and c/sub infinity /(n, max)=O(n2) where O(n) is the inverse Ackermann function. They also investigate two restricted cases.

AB - The authors investigate the upper bounds on the numbers of transitions of minimum and maximum spanning trees (MinST and MaxST for short) for linearly moving points. Suppose that one is given a set of n points in general d-dimensional space, S=(p1,p2,..., pn), and that all points move along different straight lines at different but fixed speeds, i.e., the position of pi is a linear function of a real parameter. They investigate the numbers of transitions of MinST and MaxST when t increases from - infinity to + infinity. They assume that the dimension d is a fixed constant. Since there are O(n2) distances among n points, there are naively O(n4) transitions of MinST and MaxST. They improve these trivial upper bounds for L1 and L/sub infinity / distance metrics. Let cp(n, min) (resp. cp(n, max)) be the number of maximum possible transitions of MinST (resp. MaxST) in Lp metric for n linearly moving points. They give the following results; c1(n, min)=O(n5/2a(n)), c/sub infinity /(n, min)=O(n5/2a(n)), c1(n, max)=O(nn) and c/sub infinity /(n, max)=O(n2) where O(n) is the inverse Ackermann function. They also investigate two restricted cases.

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U2 - 10.1109/SFCS.1992.267750

DO - 10.1109/SFCS.1992.267750

M3 - Conference contribution

AN - SCOPUS:0040128395

T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

SP - 396

EP - 405

BT - Proceedings - 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992

PB - IEEE Computer Society

T2 - 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992

Y2 - 24 October 1992 through 27 October 1992

ER -