Improved Bounds and New Trade-Offs for Dynamic All Pairs Shortest Paths

  • Authors:

  • Camil Demetrescu;Giuseppe F. Italiano

  • Affiliations:

  • -;-

  • Venue:
  • ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
  • Year:
  • 2002

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Abstract

Let G be a directed graph with n vertices, subject to dynamic updates, and such that each edge weight can assume at most S different arbitrary real values throughout the sequence of updates. We present a new algorithm for maintaining all pairs shortest paths in G in O(S0.5 驴 n2.5 log1.5 n) amortized time per update and in O(1) worst-case time per distance query. This improves over previous bounds.We also show how to obtain query/update trade-offs for this problem, by introducing two new families of algorithms. Algorithms in the first family achieve an update bound of 脮(S 驴 k 驴 n2) and a query bound of 脮(n/k), and improve over the best known update bounds for k in the range (n/S)1/3 驴 k n/S)1/2. Algorithms in the second family achieve an update bound of 脮(S 驴 k 驴 n2) and a query bound of 脮(n2/k2), and are competitive with the best known update bounds (first family included) for k in the range (n/S)1/6 驴 k n/S)1/3.