Improved kernels for tracking paths

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F23%3A00363316" target="_blank" >RIV/68407700:21240/23:00363316 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.ipl.2023.106360" target="_blank" >https://doi.org/10.1016/j.ipl.2023.106360</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.ipl.2023.106360" target="_blank" >10.1016/j.ipl.2023.106360</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Improved kernels for tracking paths

Popis výsledku v původním jazyce

Tracking of moving objects is crucial to security systems and networks. Given a graph G, terminal vertices s and t, and an integer k, the Tracking Paths problem asks whether there exists at most k vertices, which if marked as trackers, would ensure that the sequence of trackers encountered in each s-t path is unique. It is known that the problem is NP-hard and admits a kernel (reducible to an equivalent instance) with O(k6) vertices and O(k7) edges, when parameterized by the size of the output (tracking set) k [4]. In this paper we improve the size of the kernel substantially by providing a kernel with O (k2) vertices and edges for general graphs and a kernel with O (k) vertices and edges for planar graphs. We do this via a new concept, namely a tree-sink structure. We also show that finding a tracking set of size at most n - k for a graph on n vertices is hard for the parameterized complexity class W[1], when parameterized by k

Název v anglickém jazyce

Improved kernels for tracking paths

Popis výsledku anglicky

Tracking of moving objects is crucial to security systems and networks. Given a graph G, terminal vertices s and t, and an integer k, the Tracking Paths problem asks whether there exists at most k vertices, which if marked as trackers, would ensure that the sequence of trackers encountered in each s-t path is unique. It is known that the problem is NP-hard and admits a kernel (reducible to an equivalent instance) with O(k6) vertices and O(k7) edges, when parameterized by the size of the output (tracking set) k [4]. In this paper we improve the size of the kernel substantially by providing a kernel with O (k2) vertices and edges for general graphs and a kernel with O (k) vertices and edges for planar graphs. We do this via a new concept, namely a tree-sink structure. We also show that finding a tracking set of size at most n - k for a graph on n vertices is hard for the parameterized complexity class W[1], when parameterized by k

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

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

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

181

Číslo periodika v rámci svazku

March

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

11

Strana od-do

—

Kód UT WoS článku

000926373100001

EID výsledku v databázi Scopus

2-s2.0-85146593384