Disjoint Paths in Expanders in Deterministic Almost-Linear Time via Hypergraph Perfect Matching
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912686800896000 |
|---|---|
| author | Bucić, Matija He, Zhongtian Huang, Shang-En Saranurak, Thatchaphol |
| author_facet | Bucić, Matija He, Zhongtian Huang, Shang-En Saranurak, Thatchaphol |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_02214 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Disjoint Paths in Expanders in Deterministic Almost-Linear Time via Hypergraph Perfect Matching Bucić, Matija He, Zhongtian Huang, Shang-En Saranurak, Thatchaphol Data Structures and Algorithms 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). |
| title | Disjoint Paths in Expanders in Deterministic Almost-Linear Time via Hypergraph Perfect Matching |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2511.02214 |