Polynomial kernels for tracking shortest paths

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

Polynomial kernels for tracking shortest paths

Original language description

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.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

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

Project

<a href="/en/project/EF16_019%2F0000765" target="_blank" >EF16_019/0000765: Research Center for Informatics</a><br>

Continuities

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

Publication year

2023

Confidentiality

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

Name of the periodical

Information Processing Letters

ISSN

0020-0190

e-ISSN

1872-6119

Volume of the periodical

179

Issue of the periodical within the volume

1

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

6

Pages from-to

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UT code for WoS article

000860990000003

EID of the result in the Scopus database

2-s2.0-85138122026