Polynomial Time Algorithms for Tracking Path Problems

Given a graph G , and terminal vertices s and t , the Tracking Paths problem asks to compute a set of minimum number of vertices to be marked as trackers, such that the sequence of trackers encountered in each s - t path is unique. Tracking Paths is NP -hard in both directed and undirected graphs in...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:Algorithmica Ročník 84; číslo 6; s. 1548 - 1570
Hlavný autor: Choudhary, Pratibha
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Springer US 01.06.2022
Springer Nature B.V
Predmet:
Algorithm Analysis and Problem Complexity
Algorithms
Apexes
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Graph theory
Graphs
Mathematics of Computing
Polynomials
Special Issue on Combinatorial Algorithms (IWOCA 2020)
Theory of Computation
Tracking
Approximation
Bounded degree graphs
Tournaments
Graphs
Paths
Tracking paths
Chordal graphs
ISSN:0178-4617, 1432-0541
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Popis
Shrnutí:Given a graph G , and terminal vertices s and t , the Tracking Paths problem asks to compute a set of minimum number of vertices to be marked as trackers, such that the sequence of trackers encountered in each s - t path is unique. Tracking Paths is NP -hard in both directed and undirected graphs in general. In this paper we give a collection of polynomial time algorithms for some restricted versions of Tracking Paths . We prove that Tracking Paths is polynomial time solvable for undirected chordal graphs and tournament graphs. We also show that Tracking Paths is NP -hard in graphs with bounded maximum degree Δ ≥ 6 , and give a 2 ( Δ + 1 ) -approximate algorithm for this case. Further, we give a polynomial time algorithm which, given an undirected graph G , a tracking set T ⊆ V ( G ) , and a sequence of trackers π , returns the unique s - t path in G that corresponds to π , if one exists. Finally we analyze the version of tracking s - t paths where paths are tracked using edges instead of vertices, and we give a polynomial time algorithm for the same.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-022-00931-1