Algebraic techniques have had an important impact on graph algorithms so far. Porting
them, eg, the matrix inverse, into the dynamic regime improved best-known bounds for …

We continue the study of distance sensitivity oracles (DSOs). Given a directed graph $ G $
with $ n $ vertices and edge weights in $\{1, 2,\dots, M\} $, we want to build a data structure …

A k-spanner of a graph G is a sparse subgraph H whose shortest path distances match
those of G up to a multiplicative error k. In this paper we study spanners that are resistant to …

We consider the problem of building distance sensitivity oracles (DSOs). Given a directed
graph G=(V, E) with edge weights in {1, 2,…, M}, we need to preprocess it into a data …

We present the first compact distance oracle that tolerates multiple failures and maintains*
exact* distances. Given an undirected weighted graph G=(V, E) and an arbitrarily large …

We design $ f $-edge fault-tolerant diameter oracles ($ f $-FDOs). We preprocess a given
graph $ G $ on $ n $ vertices and $ m $ edges, and a positive integer $ f $, to construct a …

Given an undirected graph G=(V, E) of n vertices and m edges with weights in [1, W], we
construct vertex sensitive distance oracles (VSDO), which are data structures that …

We construct data structures for extremal and pairwise distances in directed graphs in the
presence of transient edge failures. Henzinger et al.[ITCS 2017] initiated the study of fault …

Given a graph with a source vertex $ s $, the Single Source Replacement Paths (SSRP)
problem is to compute, for every vertex $ t $ and edge $ e $, the length $ d (s, t, e) $ of a …

Depth first search (DFS) tree is one of the most well-known data structures for designing
efficient graph algorithms. Given an undirected graph $ G=(V, E) $ with $ n $ vertices and …