TY - GEN
T1 - An EPTAS for Budgeted Matching and Budgeted Matroid Intersection via Representative Sets
AU - Doron-Arad, Ilan
AU - Kulik, Ariel
AU - Shachnai, Hadas
N1 - Publisher Copyright:
© Ilan Doron-Arad, Ariel Kulik, and Hadas Shachnai.
PY - 2023/7/1
Y1 - 2023/7/1
N2 - We study the budgeted versions of the well known matching and matroid intersection problems. While both problems admit a polynomial-time approximation scheme (PTAS) [Berger et al. (Math. Programming, 2011), Chekuri, Vondrák and Zenklusen (SODA 2011)], it has been an intriguing open question whether these problems admit a fully PTAS (FPTAS), or even an efficient PTAS (EPTAS). In this paper we answer the second part of this question affirmatively, by presenting an EPTAS for budgeted matching and budgeted matroid intersection. A main component of our scheme is a construction of representative sets for desired solutions, whose cardinality depends only on ε, the accuracy parameter. Thus, enumerating over solutions within a representative set leads to an EPTAS. This crucially distinguishes our algorithms from previous approaches, which rely on exhaustive enumeration over the solution set.
AB - We study the budgeted versions of the well known matching and matroid intersection problems. While both problems admit a polynomial-time approximation scheme (PTAS) [Berger et al. (Math. Programming, 2011), Chekuri, Vondrák and Zenklusen (SODA 2011)], it has been an intriguing open question whether these problems admit a fully PTAS (FPTAS), or even an efficient PTAS (EPTAS). In this paper we answer the second part of this question affirmatively, by presenting an EPTAS for budgeted matching and budgeted matroid intersection. A main component of our scheme is a construction of representative sets for desired solutions, whose cardinality depends only on ε, the accuracy parameter. Thus, enumerating over solutions within a representative set leads to an EPTAS. This crucially distinguishes our algorithms from previous approaches, which rely on exhaustive enumeration over the solution set.
KW - budgeted matching
KW - budgeted matroid intersection
KW - efficient polynomial-time approximation scheme
UR - http://www.scopus.com/inward/record.url?scp=85166542556&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.ICALP.2023.49
DO - 10.4230/LIPIcs.ICALP.2023.49
M3 - Conference contribution
AN - SCOPUS:85166542556
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 50th International Colloquium on Automata, Languages, and Programming, ICALP 2023
A2 - Etessami, Kousha
A2 - Feige, Uriel
A2 - Puppis, Gabriele
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 50th International Colloquium on Automata, Languages, and Programming, ICALP 2023
Y2 - 10 July 2023 through 14 July 2023
ER -