Engineering Nearly Linear-Time Algorithms for Small Vertex Connectivity

by   Max Franck, et al.

Vertex connectivity is a well-studied concept in graph theory with numerous applications. A graph is k-connected if it remains connected after removing any k-1 vertices. The vertex connectivity of a graph is the maximum k such that the graph is k-connected. There is a long history of algorithmic development for efficiently computing vertex connectivity. Recently, two near linear-time algorithms for small k were introduced by [Forster et al. SODA 2020]. Prior to that, the best known algorithm was one by [Henzinger et al. FOCS'96] with quadratic running time when k is small. In this paper, we study the practical performance of the algorithms by Forster et al. In addition, we introduce a new heuristic on a key subroutine called local cut detection, which we call degree counting. We prove that the new heuristic improves space-efficiency (which can be good for caching purposes) and allows the subroutine to terminate earlier. According to experimental results on random graphs with planted vertex cuts, random hyperbolic graphs, and real world graphs with vertex connectivity between 4 and 15, the degree counting heuristic offers a factor of 2-4 speedup over the original non-degree counting version for most of our data. It also outperforms the previous state-of-the-art algorithm by Henzinger et al. even on relatively small graphs.



There are no comments yet.


page 1

page 2

page 3

page 4


Computing and Testing Small Vertex Connectivity in Near-Linear Time and Queries

We present a new, simple, algorithm for the local vertex connectivity pr...

Efficient Computation of Optimal Temporal Walks under Waiting-Time Constraints

Node connectivity plays a central role in temporal network analysis. We ...

Sparsifying Disk Intersection Graphs for Reliable Connectivity

The intersection graph induced by a set of n disks can be dense. It is ...

Computing and Testing Small Connectivity in Near-Linear Time and Queries via Fast Local Cut Algorithms

Consider the following "local" cut-detection problem in a directed graph...

Deterministic Graph Cuts in Subquadratic Time: Sparse, Balanced, and k-Vertex

We study deterministic algorithms for computing graph cuts, with focus o...

Optimal In-place Algorithms for Basic Graph Problems

We present linear time in-place algorithms for several basic and fundam...

Theoretically and Practically Efficient Parallel Nucleus Decomposition

This paper studies the nucleus decomposition problem, which has been sho...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.