Approximate Distance Oracles with Improved Query Time [chapter]

Christian Wulff-Nilsen
2016 Encyclopedia of Algorithms  
Given an undirected graph G with m edges, n vertices, and non-negative edge weights, and given an integer k ≥ 2, we show that a (2k − 1)-approximate distance oracle for G of size O(kn 1+1/k ) and with O(log k) query time can be constructed in This improves the O(k) query time of Thorup and Zwick. Furthermore, for any 0 < ǫ ≤ 1, we give an oracle of size O(kn 1+1/k ) that answers ((2 + ǫ)k)-approximate distance queries in O(1/ǫ) time. At the cost of a k-factor in size, this improves the 128k
more » ... oximation achieved by the constant query time oracle of Mendel and Naor and approaches the best possible tradeoff between size and stretch, implied by a widely believed girth conjecture of Erdős. We can match the O(n 1+1/k ) size bound of Mendel and Naor for any constant ǫ > 0 and k = O(log n/ log log n).
doi:10.1007/978-1-4939-2864-4_568 fatcat:adaclkt7trefbokrjcxaccz3g4