Polynomial kernels for tracking shortest paths

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F23%3A00359993" target="_blank" >RIV/68407700:21240/23:00359993 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.ipl.2022.106315" target="_blank" >https://doi.org/10.1016/j.ipl.2022.106315</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.ipl.2022.106315" target="_blank" >10.1016/j.ipl.2022.106315</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Polynomial kernels for tracking shortest paths

Popis výsledku v původním jazyce

Given an undirected graph G = (V , E), vertices s,t element V , and an integer k, Tracking Shortest Paths requires deciding whether there exists a set of k vertices T ? V such that for any two distinct shortest paths between s and t, say P1 and P2, we have T ∩ V (P1) != T ∩ V (P2). In this paper, we give the first polynomial size kernel for the problem. Specifically we show the existence of a kernel with O(k2) vertices and edges in general graphs and a kernel with O(k) vertices and edges in planar graphs for the Tracking Paths in DAG problem. This problem admits a polynomial parameter transformation to Tracking Shortest Paths, and this implies a kernel with O(k4) vertices and edges for Tracking Shortest Paths in general graphs and a kernel with O(k2) vertices and edges in planar graphs. Based on the above we also give a single exponential algorithm for Tracking Shortest Paths in planar graphs.

Název v anglickém jazyce

Polynomial kernels for tracking shortest paths

Popis výsledku anglicky

Given an undirected graph G = (V , E), vertices s,t element V , and an integer k, Tracking Shortest Paths requires deciding whether there exists a set of k vertices T ? V such that for any two distinct shortest paths between s and t, say P1 and P2, we have T ∩ V (P1) != T ∩ V (P2). In this paper, we give the first polynomial size kernel for the problem. Specifically we show the existence of a kernel with O(k2) vertices and edges in general graphs and a kernel with O(k) vertices and edges in planar graphs for the Tracking Paths in DAG problem. This problem admits a polynomial parameter transformation to Tracking Shortest Paths, and this implies a kernel with O(k4) vertices and edges for Tracking Shortest Paths in general graphs and a kernel with O(k2) vertices and edges in planar graphs. Based on the above we also give a single exponential algorithm for Tracking Shortest Paths in planar graphs.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/EF16_019%2F0000765" target="_blank" >EF16_019/0000765: Výzkumné centrum informatiky</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Information Processing Letters

ISSN

0020-0190

e-ISSN

1872-6119

Svazek periodika

179

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

6

Strana od-do

—

Kód UT WoS článku

000860990000003

EID výsledku v databázi Scopus

2-s2.0-85138122026