TY - GEN
T1 - Parameterized Results on Acyclic Matchings with Implications for Related Problems
AU - Chaudhary, Juhi
AU - Zehavi, Meirav
N1 - Publisher Copyright: © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
PY - 2023/1/1
Y1 - 2023/1/1
N2 - A matching M in a graph G is an acyclic matching if the subgraph of G induced by the endpoints of the edges of M is a forest. Given a graph G and a positive integer l, Acyclic Matching asks whether G has an acyclic matching of size (i.e., the number of edges) at least l. In this paper, we first prove that assuming (Formula presented), there does not exist any FPT-approximation algorithm for Acyclic Matching that approximates it within a constant factor when parameterized by l. Our reduction is general in the sense that it also asserts FPT-inapproximability for Induced Matching and Uniquely Restricted Matching. We also consider three below-guarantee parameters for Acyclic Matching, viz. (Formula presented), where n is the number of vertices in G, MM(G) is the matching number of G, and IS(G) is the independence number of G. We note that the result concerning the below-guarantee parameter n/2-l is the most technical part of our paper. Also, we show that Acyclic Matching does not exhibit a polynomial kernel with respect to vertex cover number (or vertex deletion distance to clique) plus the size of the matching unless (Formula presented).
AB - A matching M in a graph G is an acyclic matching if the subgraph of G induced by the endpoints of the edges of M is a forest. Given a graph G and a positive integer l, Acyclic Matching asks whether G has an acyclic matching of size (i.e., the number of edges) at least l. In this paper, we first prove that assuming (Formula presented), there does not exist any FPT-approximation algorithm for Acyclic Matching that approximates it within a constant factor when parameterized by l. Our reduction is general in the sense that it also asserts FPT-inapproximability for Induced Matching and Uniquely Restricted Matching. We also consider three below-guarantee parameters for Acyclic Matching, viz. (Formula presented), where n is the number of vertices in G, MM(G) is the matching number of G, and IS(G) is the independence number of G. We note that the result concerning the below-guarantee parameter n/2-l is the most technical part of our paper. Also, we show that Acyclic Matching does not exhibit a polynomial kernel with respect to vertex cover number (or vertex deletion distance to clique) plus the size of the matching unless (Formula presented).
KW - Acyclic Matching
KW - Induced Matching
KW - Kernelization Lower Bounds
KW - Parameterized Algorithms
KW - Uniquely Restricted Matching
UR - http://www.scopus.com/inward/record.url?scp=85174525904&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-43380-1_15
DO - 10.1007/978-3-031-43380-1_15
M3 - Conference contribution
SN - 9783031433795
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 201
EP - 216
BT - Graph-Theoretic Concepts in Computer Science - 49th International Workshop, WG 2023, Revised Selected Papers
A2 - Paulusma, Daniël
A2 - Ries, Bernard
PB - Springer Science and Business Media Deutschland GmbH
T2 - 49th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2023
Y2 - 28 June 2023 through 30 June 2023
ER -