Adjacency queries in dynamic sparse graphs

Adjacency queries in dynamic sparse graphs

We deal with the problem of maintaining a dynamic graph so that queries of the form “is there an edge between u and v?” are processed fast. We consider graphs of bounded arboricity, i.e., graphs with no dense subgraphs, like for example planar graphs. Brodal and Fagerberg [WADS’99] described a very simple linear-size data structure which processes queries in constant worst-case time and perform...

Orienting Dynamic Graphs, with Applications to Maximal Matchings and Adjacency Queries

We consider the problem of edge orientation, whose goal is to orient the edges of an undirected dynamic graph with n vertices such that vertex out-degrees are bounded, typically by a function of the graph’s arboricity. Our main result is to show that an O(βα)-orientation can be maintained in O( lg(n/(βα)) β ) amortized edge insertion time and O(βα) worst-case edge deletion time, for any β ≥ 1, ...

Dynamic Skyline Queries in Large Graphs

Abstract. Given a set of query points, a dynamic skyline query reports all data points that are not dominated by other data points according to the distances between data points and query points. In this paper, we study dynamic skyline queries in a large graph (DSG-query for short). Although dynamic skylines have been studied in Euclidean space [16], road network [6], and metric space [4, 7], t...

Dynamic Representation of Sparse Graphs

Faster Approximate Distance Queries and Compact Routing in Sparse Graphs

A distance oracle is a compact representation of the shortest distance matrix of a graph. It can be queried to retrieve approximate distances and corresponding paths between any pair of vertices. A lower bound, due to Thorup and Zwick, shows that a distance oracle that returns paths of worst-case stretch (2k − 1) must require space Ω(n) for graphs over n nodes. The hard cases that enforce this ...