Improved kernels for tracking paths
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Improved kernels for tracking paths
Original language description
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
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - 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)
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Information Processing Letters
ISSN
0020-0190
e-ISSN
1872-6119
Volume of the periodical
181
Issue of the periodical within the volume
March
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
11
Pages from-to
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UT code for WoS article
000926373100001
EID of the result in the Scopus database
2-s2.0-85146593384