{"ID":2846032,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.02214","arxiv_id":"2511.02214","title":"Disjoint Paths in Expanders in Deterministic Almost-Linear Time via Hypergraph Perfect Matching","abstract":"We design efficient deterministic algorithms for finding short edge-disjoint paths in expanders. Specifically, given an $n$-vertex $m$-edge expander $G$ of conductance $φ$ and minimum degree $δ$, and a set of pairs $\\{(s_i,t_i)\\}_i$ such that each vertex appears in at most $k$ pairs, our algorithm deterministically computes a set of edge-disjoint paths from $s_i$ to $t_i$, one for every $i$: (1) each of length at most $18 \\log (n)/φ$ and in $mn^{1+o(1)}\\min\\{k, φ^{-1}\\}$ total time, assuming $φ^3δ\\ge (35\\log n)^3 k$, or (2) each of length at most $n^{o(1)}/φ$ and in total $m^{1+o(1)}$ time, assuming $φ^3 δ\\ge n^{o(1)} k$. Before our work, deterministic polynomial-time algorithms were known only for expanders with constant conductance and were significantly slower. To obtain our result, we give an almost-linear time algorithm for \\emph{hypergraph perfect matching} under generalizations of Hall-type conditions (Haxell 1995), a powerful framework with applications in various settings, which until now has only admitted large polynomial-time algorithms (Annamalai 2018).","short_abstract":"We design efficient deterministic algorithms for finding short edge-disjoint paths in expanders. Specifically, given an $n$-vertex $m$-edge expander $G$ of conductance $φ$ and minimum degree $δ$, and a set of pairs $\\{(s_i,t_i)\\}_i$ such that each vertex appears in at most $k$ pairs, our algorithm deterministically com...","url_abs":"https://arxiv.org/abs/2511.02214","url_pdf":"https://arxiv.org/pdf/2511.02214v1","authors":"[\"Matija Bucić\",\"Zhongtian He\",\"Shang-En Huang\",\"Thatchaphol Saranurak\"]","published":"2025-11-04T03:06:16Z","proceeding":"cs.DS","tasks":"[\"cs.DS\"]","methods":"[]","has_code":false}