Parameterized Shortest Path Reconfiguration
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914839171956736 |
|---|---|
| author | Bousquet, Nicolas Gajjar, Kshitij Lahiri, Abhiruk Mouawad, Amer E. |
| author_facet | Bousquet, Nicolas Gajjar, Kshitij Lahiri, Abhiruk Mouawad, Amer E. |
| contents | An st-shortest path, or st-path for short, in a graph G is a shortest (induced) path from s to t in G. Two st-paths are said to be adjacent if they differ on exactly one vertex. A reconfiguration sequence between two st-paths P and Q is a sequence of adjacent st-paths starting from P and ending at Q. Deciding whether there exists a reconfiguration sequence between two given $st$-paths is known to be PSPACE-complete, even on restricted classes of graphs such as graphs of bounded bandwidth (hence pathwidth). On the positive side, and rather surprisingly, the problem is polynomial-time solvable on planar graphs. In this paper, we study the parameterized complexity of the Shortest Path Reconfiguration (SPR) problem. We show that SPR is W[1]-hard parameterized by k + \ell, even when restricted to graphs of bounded (constant) degeneracy; here k denotes the number of edges on an st-path, and \ell denotes the length of a reconfiguration sequence from P to Q. We complement our hardness result by establishing the fixed-parameter tractability of SPR parameterized by \ell and restricted to nowhere-dense classes of graphs. Additionally, we establish fixed-parameter tractability of SPR when parameterized by the treedepth, by the cluster-deletion number, or by the modular-width of the input graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_12717 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Parameterized Shortest Path Reconfiguration Bousquet, Nicolas Gajjar, Kshitij Lahiri, Abhiruk Mouawad, Amer E. Computational Complexity Data Structures and Algorithms Combinatorics An st-shortest path, or st-path for short, in a graph G is a shortest (induced) path from s to t in G. Two st-paths are said to be adjacent if they differ on exactly one vertex. A reconfiguration sequence between two st-paths P and Q is a sequence of adjacent st-paths starting from P and ending at Q. Deciding whether there exists a reconfiguration sequence between two given $st$-paths is known to be PSPACE-complete, even on restricted classes of graphs such as graphs of bounded bandwidth (hence pathwidth). On the positive side, and rather surprisingly, the problem is polynomial-time solvable on planar graphs. In this paper, we study the parameterized complexity of the Shortest Path Reconfiguration (SPR) problem. We show that SPR is W[1]-hard parameterized by k + \ell, even when restricted to graphs of bounded (constant) degeneracy; here k denotes the number of edges on an st-path, and \ell denotes the length of a reconfiguration sequence from P to Q. We complement our hardness result by establishing the fixed-parameter tractability of SPR parameterized by \ell and restricted to nowhere-dense classes of graphs. Additionally, we establish fixed-parameter tractability of SPR when parameterized by the treedepth, by the cluster-deletion number, or by the modular-width of the input graph. |
| title | Parameterized Shortest Path Reconfiguration |
| topic | Computational Complexity Data Structures and Algorithms Combinatorics |
| url | https://arxiv.org/abs/2406.12717 |