TRANSIT Ultrafast Shortest-Path Queries with Linear-Time Preprocessing

Ultrafast Shortest-Path Queries via Transit Nodes

PReaCH: A Fast Lightweight Reachability Index Using Pruning and Contraction Hierarchies

We develop the data structure PReaCH (for Pruned Reachability Contraction Hierarchies) which supports reachability queries in a directed graph, i.e., it supports queries that ask whether two nodes in the graph are connected by a directed path. PReaCH adapts the contraction hierarchy speedup techniques for shortest path queries to the reachability setting. The resulting approach is surprisingly ...

Round-Based Public Transit Routing (Extended Abstract)

We study the problem of computing best connections in public transit networks. A common approach models the network as a graph (Pyrga et al. 2008) on which it runs a shortest path algorithm (Dijkstra 1959). To enable interactive queries, a variety of speedup techniques exist that use a preprocessing stage to accelerate queries (Delling et al. 2009; Bast et al. 2010). Unfortunately, developed wi...

Shortest Path Queries in Digraphs of Small Treewidth

We consider the problem of preprocessing an n-vertex digraph with real edge weights so that subsequent queries for the shortest path or distance between any two vertices can be efficiently answered. We give algorithms that depend on the treewidth of the input graph. When the treewidth is a constant, our algorithms can answer distance queries in O(α(n)) time after O(n) preprocessing. This improv...

Optimal Shortest Path and Minimum-Link Path Queries Between Two Convex Polygons Inside a Simple Polygonal Obstacle

We present e cient algorithms for shortest path and minimum link path queries between two convex polygons inside a simple polygon P which acts as an obstacle to be avoided Let n be the number of vertices of P and h the total number of vertices of the query polygons We show that shortest path queries can be performed optimally in time O logh logn plus O k time for reporting the k edges of the pa...