Distance Oracles for Sparse Graphs

Abstract— Thorup and Zwick, in their seminal work, introduced the approximate distance oracle, which is a data structure that answers distance queries in a graph. For any integer k, they showed an efficient algorithm to construct an approximate distance oracle using space O(kn1+1/k ) that can answer queries in time O(k) with a distance estimate that is at most α = 2k − 1 times larger than the actual shortest distance (α is called the stretch). They proved that, under a combinatorial conjecture, their data structure is optimal in terms of space: if a stretch of at most 2k−1 is desired, then the space complexity is at least n1+1/k . Their proof holds even if infinite query time is allowed: it is essentially an “incompressibility” result. Also, the proof only holds for dense graphs, and the best bound it can prove only implies that the size of the data structure is lower bounded by the number of edges of the graph. Naturally, the following question arises: what happens for s...

• Type: Conference
• Year: 2009
• Where: FOCS
• Authors: Christian Sommer 0002, Elad Verbin, Wei Yu
• Keywords: Approximate Distance Oracle, Data Structures, FOCS 2009, Lower Bounds, Theoretical Computer Science