A Dynamic Separator Algorithm
نویسندگان
چکیده
Our work is based on the pioneering work in sphere separators done by Miller, Teng, Vavasis et al, [8, 12], who gave efficient static (fixed input) algorithms for finding sphere separators of size s(n) = O(n d−1 d ) for a set of points in R. We present dynamic algorithms which maintain separators for a dynamically changing graph. Our algorithms answer queries and process insertions and deletions to the input set, If the total input size and number of queries is n, our algorithm is polylog, that is, it takes (logn) expected sequential time per request to process worst case queries and worst case changes to the input set. This is the first known polylog randomized dynamic algorithm for separators of a large class of graphs known as overlap graphs [12], which include planar graphs and k-neighborhood graphs. We maintain a separator in expected time O(logn) and we maintain a separator tree in expected time O(log n). Moreover, our algorithm uses only linear space. ∗Supported by National Science Foundation Grant Number NSF-IRI-91-00681 and Army Research Office contract DAAH-04-96-1-0448. A preliminary version of this paper appeared as A Dynamic Separator Algorithm, in the proceedings of the 3rd Annual WADS, Montreal, Quebec, August 1993, pp 107-118.
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