TY - GEN
T1 - Classification of OBDD size for monotone 2-CNFs
AU - Razgon, Igor
N1 - Publisher Copyright:
© Igor Razgon; licensed under Creative Commons License CC-BY 4.0
PY - 2021/11/1
Y1 - 2021/11/1
N2 - We introduce a new graph parameter called linear upper maximum induced matching width lu-mim width, denoted for a graph G by lu(G). We prove that the smallest size of the obdd for φ, the monotone 2-cnf corresponding to G, is sandwiched between 2lu(G) and nO(lu(G)). The upper bound is based on a combinatorial statement that might be of an independent interest. We show that the bounds in terms of this parameter are best possible. The new parameter is closely related to two existing parameters: linear maximum induced matching width (lmim width) and linear special induced matching width (lsim width). We prove that lu-mim width lies strictly in between these two parameters, being dominated by lsim width and dominating lmim width. We conclude that neither of the two existing parameters can be used instead of lu-mim width to characterize the size of obdds for monotone 2-cnfs and this justifies introduction of the new parameter.
AB - We introduce a new graph parameter called linear upper maximum induced matching width lu-mim width, denoted for a graph G by lu(G). We prove that the smallest size of the obdd for φ, the monotone 2-cnf corresponding to G, is sandwiched between 2lu(G) and nO(lu(G)). The upper bound is based on a combinatorial statement that might be of an independent interest. We show that the bounds in terms of this parameter are best possible. The new parameter is closely related to two existing parameters: linear maximum induced matching width (lmim width) and linear special induced matching width (lsim width). We prove that lu-mim width lies strictly in between these two parameters, being dominated by lsim width and dominating lmim width. We conclude that neither of the two existing parameters can be used instead of lu-mim width to characterize the size of obdds for monotone 2-cnfs and this justifies introduction of the new parameter.
KW - Lower bounds
KW - Monotone 2-CNFs
KW - Ordered Binary Decision Diagrams
KW - Upper
KW - Width parameters of graphs
UR - http://www.scopus.com/inward/record.url?scp=85121148517&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.IPEC.2021.25
DO - 10.4230/LIPIcs.IPEC.2021.25
M3 - Conference contribution
AN - SCOPUS:85121148517
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 16th International Symposium on Parameterized and Exact Computation, IPEC 2021
A2 - Golovach, Petr A.
A2 - Zehavi, Meirav
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 16th International Symposium on Parameterized and Exact Computation, IPEC 2021
Y2 - 8 September 2021 through 10 September 2021
ER -