Integer priority queues with decrease key in constant time and the single source shortest paths problem

  • Authors:

  • Mikkel Thorup

  • Affiliations:

  • AT&T Labs, Florham Park, NJ

  • Venue:
  • Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
  • Year:
  • 2003

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Abstract

We consider Fibonacci heap style integer priority queues supporting insert and decrease key operations in constant time. We present a deterministic linear space solution that with n integer keys support delete in O(log log n) time. If the integers are in the range [0,N), we can also support delete in O(log log N) time.Even for the special case of monotone priority queues, where the minimum has to be non-decreasing, the best previous bounds on delete were O((log n)1/(3-ε)) and O((log N)1/(4-ε)). These previous bounds used both randomization and amortization. Our new bounds a deterministic, worst-case, with no restriction to monotonicity, and exponentially faster.As a classical application, for a directed graph with n nodes and m edges with non-negative integer weights, we get single source shortest paths in O(m+n log log n) time, or O(m+n log log C) if C is the maximal edge weight. The later solves an open problem of Ahuja, Mehlhorn, Orlin, and Tarjan from 1990.