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arXiv · 1810.03491

An Improved Algorithm for Incremental Cycle Detection and Topological Ordering in Sparse Graphs

Sayan Bhattacharya·Janardhan Kulkarni
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Abstract

We consider the problem of incremental cycle detection and topological ordering in a directed graph $G = (V, E)$ with $|V| = n$ nodes. In this setting, initially the edge-set $E$ of the graph is empty. Subsequently, at each time-step an edge gets inserted into $G$. After every edge-insertion, we have to report if the current graph contains a cycle, and as long as the graph remains acyclic, we have to maintain a topological ordering of the node-set $V$. Let $m$ be the total number of edges that get inserted into $G$. We present a randomized algorithm for this problem with $\tilde{O}(m^{4/3})$ total expected update time.

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Sayan Bhattacharya, Janardhan Kulkarni. 2018-10-08. An Improved Algorithm for Incremental Cycle Detection and Topological Ordering in Sparse Graphs. https://arxiv.org/abs/1810.03491

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