{"ID":5935897,"CreatedAt":"2026-07-07T01:22:02.77346169Z","UpdatedAt":"2026-07-07T02:10:06.972658124Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.02999","arxiv_id":"2607.02999","title":"Approximate Single Source Dual Fault Tolerant Distance Oracle","abstract":"We are given an undirected weighted graph $G$ with $n$ vertices and $m$ edges, edge weights in $[1, W]$, and a designated source vertex $s$. We design a single source dual fault tolerant distance oracle for $G$. Given a destination vertex $t$ and a set $F$ of at most two faulty edges, the oracle returns a $(1 + O(ε))$-approximation of the weight of the shortest path from the source $s$ to $t$ avoiding $F$. Our oracle uses $\\tilde{O}(n\\sqrt{n})$ space and has $\\tilde{O}(1)$ query time. Prior to our result, single source single fault tolerant oracles were known to return a $(1+ε)$ approximation of the weight of the shortest path using $\\tilde{O}(n)$ space and $O(1)$ query time. However, extending these approaches to multiple faults remained an open problem. Indeed, all $(1+ε)$-approximate distance oracles that handle multiple faults require $Ω(n^2)$ space. We break this bound by presenting the first dual fault tolerant distance oracle with $o(n^2)$ space.","short_abstract":"We are given an undirected weighted graph $G$ with $n$ vertices and $m$ edges, edge weights in $[1, W]$, and a designated source vertex $s$. We design a single source dual fault tolerant distance oracle for $G$. Given a destination vertex $t$ and a set $F$ of at most two faulty edges, the oracle returns a $(1 + O(ε))$-...","url_abs":"https://arxiv.org/abs/2607.02999","url_pdf":"https://arxiv.org/pdf/2607.02999v1","authors":"[\"Koustav Das\",\"Manoj Gupta\"]","published":"2026-07-03T06:33:14Z","proceeding":"cs.DS","tasks":"[\"cs.DS\"]","methods":"[]","has_code":false}