A Dynamic Separator Algorithm

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 Rd . 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)O(1) 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(log n) and we maintain a separator tree in expected time O(log3 n). Moreover, our algorithm uses only linear space. ∗ Supported ...

• Type: Conference
• Year: 1993
• Where: WADS
• Authors: Deganit Armon, John H. Reif
• Keywords: Algorithm, Algorithms, Dynamic Algorithm, Sphere Separators, WADS 1993