TY - GEN
T1 - Reducing CMSO model checking to highly connected graphs
AU - Lokshtanov, Daniel
AU - Ramanujan, M. S.
AU - Saurabh, Saket
AU - Zehavi, Meirav
N1 - Publisher Copyright:
© 2018 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.
PY - 2018/7/1
Y1 - 2018/7/1
N2 - Given a Counting Monadic Second Order (CMSO) sentence ψ, the CMSO[ψ] problem is defined as follows. The input to CMSO[ψ] is a graph G, and the objective is to determine whether G |= ψ. Our main theorem states that for every CMSO sentence ψ, if CMSO[ψ] is solvable in polynomial time on “globally highly connected graphs”, then CMSO[ψ] is solvable in polynomial time (on general graphs). We demonstrate the utility of our theorem in the design of parameterized algorithms. Specifically we show that technical problem-specific ingredients of a powerful method for designing parameterized algorithms, recursive understanding, can be replaced by a black-box invocation of our main theorem. We also show that our theorem can be easily deployed to show fixed parameterized tractability of a wide range of problems, where the input is a graph G and the task is to find a connected induced subgraph of G such that “few” vertices in this subgraph have neighbors outside the subgraph, and additionally the subgraph has a CMSO-definable property.
AB - Given a Counting Monadic Second Order (CMSO) sentence ψ, the CMSO[ψ] problem is defined as follows. The input to CMSO[ψ] is a graph G, and the objective is to determine whether G |= ψ. Our main theorem states that for every CMSO sentence ψ, if CMSO[ψ] is solvable in polynomial time on “globally highly connected graphs”, then CMSO[ψ] is solvable in polynomial time (on general graphs). We demonstrate the utility of our theorem in the design of parameterized algorithms. Specifically we show that technical problem-specific ingredients of a powerful method for designing parameterized algorithms, recursive understanding, can be replaced by a black-box invocation of our main theorem. We also show that our theorem can be easily deployed to show fixed parameterized tractability of a wide range of problems, where the input is a graph G and the task is to find a connected induced subgraph of G such that “few” vertices in this subgraph have neighbors outside the subgraph, and additionally the subgraph has a CMSO-definable property.
KW - Checking recursive understanding
KW - Fixed parameter
KW - Tractability model
UR - https://www.scopus.com/pages/publications/85049811261
U2 - 10.4230/LIPIcs.ICALP.2018.135
DO - 10.4230/LIPIcs.ICALP.2018.135
M3 - Conference contribution
AN - SCOPUS:85049811261
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018
A2 - Kaklamanis, Christos
A2 - Marx, Daniel
A2 - Chatzigiannakis, Ioannis
A2 - Sannella, Donald
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018
Y2 - 9 July 2018 through 13 July 2018
ER -