Succinct Representations of Arbitrary Graphs

Abstract. We consider the problem of encoding a graph with n vertices and m edges compactly supporting adjacency, neighborhood and degree queries in constant time in the log n-bit word RAM model. The adjacency query asks whether there is an edge between two vertices, the neighborhood query reports the neighbors of a given vertex in constant time per neighbor, and the degree query reports the number of incident edges to a given vertex. We study the problem in the context of succinctness, where the goal is to achieve the optimal space requirement as a function of n and m, to within lower order terms. We prove a lower bound in the cell probe model that it is impossible to achieve the information-theory lower bound within lower order terms unless the graph is too sparse (namely m = o n for any constant > 0) or too dense (namely m = n2for any constant > 0). Furthermore, we present a succinct encoding for graphs for all values of n, m supporting queries in constant time. The space re...

• Type: Conference
• Year: 2008
• Where: ESA
• Authors: Arash Farzan, J. Ian Munro
• Keywords: Algorithms, Constant Time, ESA 2008, Lower Bound, Lower Order Terms