Related papers: Lower Bounds in the Preprocessing and Query Phases…
The NP-hard maximum value preordering problem is both a joint relaxation and a hybrid of the clique partition problem (a clustering problem) and the partial ordering problem. Toward approximate solutions and lower bounds, we introduce a…
We propose a new exact method for shortest-path distance queries on large-scale networks. Our method precomputes distance labels for vertices by performing a breadth-first search from every vertex. Seemingly too obvious and too inefficient…
Contraction Hierarchies (CH) (Geisberger et al., 2008) is one of the most widely used algorithms for shortest-path queries on road networks. Compared to Dijkstra's algorithm, CH enables orders of magnitude faster query performance through a…
A long series of recent results and breakthroughs have led to faster and better distributed approximation algorithms for single source shortest paths (SSSP) and related problems in the CONGEST model. The runtime of all these algorithms,…
The 3SUM conjecture has proven to be a valuable tool for proving conditional lower bounds on dynamic data structures and graph problems. This line of work was initiated by P\v{a}tra\c{s}cu (STOC 2010) who reduced 3SUM to an offline…
Fastest-path queries between two points in a very large road map is an increasingly important primitive in modern transportation and navigation systems, thus very efficient computation of these paths is critical for system performance and…
A drawback of the classic approach for complexity analysis of distributed graph problems is that it mostly informs about the complexity of notorious classes of ``worst case'' graphs. Algorithms that are used to prove a tight (existential)…
The min-rank of a digraph was shown by Bar-Yossef et al. (2006) to represent the length of an optimal scalar linear solution of the corresponding instance of the Index Coding with Side Information (ICSI) problem. In this work, the graphs…
Many path-finding algorithms on graphs such as A* are sped up by using a heuristic function that gives lower bounds on the cost to reach the goal. Aiming to apply similar techniques to speed up sampling-based motion-planning algorithms, we…
MapReduce (and its open source implementation Hadoop) has become the de facto platform for processing large data sets. MapReduce offers a streamlined computational framework by interleaving sequential and parallel computation while hiding…
All parallel algorithms for directed reachability and shortest paths crucially rely on efficient shortcut constructions. These constructions find directed paths and shortcut them by adding edges, with the goal to reduce the diameter of the…
Modern route planners such as Google Maps and Apple Maps serve millions of users worldwide, optmizing routes in large-scale road networks where fast responses are required under diverse cost metrics including travel time, fuel consumption,…
The \emph{maximal $k$-edge-connected subgraphs} problem is a classical graph clustering problem studied since the 70's. Surprisingly, no non-trivial technique for this problem in weighted graphs is known: a very straightforward…
Distributed network optimization algorithms, such as minimum spanning tree, minimum cut, and shortest path, are an active research area in distributed computing. This paper presents a fast distributed algorithm for such problems in the…
Using Dijkstra's algorithm to compute the shortest paths in a graph from a single source node to all other nodes is common practice in industry and academia. Although the original description of the algorithm advises using a Fibonacci Heap…
Transit Node Routing (TNR) is a fast and exact distance oracle for road networks. We show several new results for TNR. First, we give a surprisingly simple implementation fully based on Contraction Hierarchies that speeds up preprocessing…
We consider the problem of computing compact routing tables for a (weighted) planar graph $G:= (V, E,w)$ in the PRAM, CONGEST, and the novel HYBRID communication model. We present algorithms with polylogarithmic work and communication that…
In several important routing contexts it is required to identify a set of routes, each of which optimizes a different criterion. For instance, in the context of vehicle routing, one route would minimize the total distance traveled, while…
Modern graph or network datasets often contain rich structure that goes beyond simple pairwise connections between nodes. This calls for complex representations that can capture, for instance, edges of different types as well as so-called…
In this work, we present the first algorithm to compute expander decompositions in an m-edge directed graph with near-optimal time \~O(m). Further, our algorithm can maintain such a decomposition in a dynamic graph and again obtains…