TY - JOUR

T1 - Efficient algorithms for centers and medians in interval and circular-arc graphs

AU - Bespamyatnikh, S.

AU - Bhattacharya, B.

AU - Keil, J. Mark

AU - Kirkpatrick, D.

AU - Segal, M.

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2000.

PY - 2000/1/1

Y1 - 2000/1/1

N2 - The p-center problem is to locate p facilities on a network so as to minimize the largest distance from a demand point to its nearest facility. The p-median problem is to locate p facilities on a network so as to minimize the average distance from one of the n demand points to one of the p facilities. We provide, given the interval model of an n vertex interval graph, an Ofn) time algorithm for the 1-median problem on the interval graph. We also show how to solve the p-median problem, for arbitrary p, on an interval graph in 0(pn log n) time and on an circular-arc graph in 0(pn2 logn) time. Other than for trees, no polynomial time algorithm for p-median problem has been reported for any large class of graphs. We introduce a spring model of computation and show how to solve the p-center problem on an circular-arc graph in 0(pn) time, assuming that the arc endpoints are sorted.

AB - The p-center problem is to locate p facilities on a network so as to minimize the largest distance from a demand point to its nearest facility. The p-median problem is to locate p facilities on a network so as to minimize the average distance from one of the n demand points to one of the p facilities. We provide, given the interval model of an n vertex interval graph, an Ofn) time algorithm for the 1-median problem on the interval graph. We also show how to solve the p-median problem, for arbitrary p, on an interval graph in 0(pn log n) time and on an circular-arc graph in 0(pn2 logn) time. Other than for trees, no polynomial time algorithm for p-median problem has been reported for any large class of graphs. We introduce a spring model of computation and show how to solve the p-center problem on an circular-arc graph in 0(pn) time, assuming that the arc endpoints are sorted.

UR - http://www.scopus.com/inward/record.url?scp=84927145711&partnerID=8YFLogxK

U2 - 10.1007/3-540-45253-2_10

DO - 10.1007/3-540-45253-2_10

M3 - Article

AN - SCOPUS:84927145711

SN - 0302-9743

VL - 1879

SP - 100

EP - 112

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

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

ER -