Predecessor Queries in Dynamic Integer Sets

We consider the problem of maintaining a set of n integers in the range 0::2w ? 1 under the operations of insertion, deletion, predecessor queries, minimum queries and maximum queries on a unit cost RAM with word size w bits. Let f(n) be an arbitrary nondecreasing smooth function satisfying loglogn f(n) plogn. A data structure is presented supporting insertions and deletions in worst case O(f(n)) time, predecessor queries in worst case O((logn)=f(n)) time and minimum and maximum queries in worst case constant time. The required space is O(n2 w ) for an arbitrary constant > 0. The RAM operations used are addition, arbitrary left and right bit shifts and bit-wise boolean operations. The data structure is the rst supporting predecessor queries in worst case O(logn= loglogn) time while having worst case O(loglogn) update time.

• Type: Conference
• Year: 1997
• Where: STACS
• Authors: Gerth Stølting Brodal
• Keywords: Maximum Queries, Predecessor Queries, STACS 1997, Theoretical Computer Science, Worst Case