**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**32586

##### All-Pairs Shortest-Paths Problem for Unweighted Graphs in O(n2 log n) Time

**Authors:**
Udaya Kumar Reddy K. R,
K. Viswanathan Iyer

**Abstract:**

Given a simple connected unweighted undirected graph G = (V (G), E(G)) with |V (G)| = n and |E(G)| = m, we present a new algorithm for the all-pairs shortest-path (APSP) problem. The running time of our algorithm is in O(n2 log n). This bound is an improvement over previous best known O(n2.376) time bound of Raimund Seidel (1995) for general graphs. The algorithm presented does not rely on fast matrix multiplication. Our algorithm with slight modifications, enables us to compute the APSP problem for unweighted directed graph in time O(n2 log n), improving a previous best known O(n2.575) time bound of Uri Zwick (2002).

**Keywords:**
Distance in graphs,
Dynamic programming,
Graphalgorithms,
Shortest paths.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1334732

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