TY - GEN
T1 - Parameterized complexity of sparse linear complementarity problems
AU - Sumita, Hanna
AU - Kakimura, Naonori
AU - Makino, Kazuhisa
N1 - Funding Information:
The first author is supported by Grant-in-Aid for JSPS Fellows, and by JST, ERATO, Kawarabayashi Large Graph Project. The second author is supported by JSPS KAKENHI Grant Numbers 25730001 and 24106002, and by JST, ERATO, Kawarabayashi Large Graph Project. The third author is supported by JSPS KAKENHI Grant Numbers 24106002 and 26280001.
Publisher Copyright:
© Hanna Sumita, Naonori Kakimura, and Kazuhisa Makino;.
PY - 2015/11/1
Y1 - 2015/11/1
N2 - In this paper, we study the parameterized complexity of the linear complementarity problem (LCP), which is one of the most fundamental mathematical optimization problems. The parameters we focus on are the sparsities of the input and the output of the LCP: the maximum numbers of nonzero entries per row/column in the coefficient matrix and the number of nonzero entries in a solution. Our main result is to present a fixed-parameter algorithm for the LCP with all the parameters. We also show that if we drop any of the three parameters, then the LCP is fixed-parameter intractable. In addition, we discuss the nonexistence of a polynomial kernel for the LCP.
AB - In this paper, we study the parameterized complexity of the linear complementarity problem (LCP), which is one of the most fundamental mathematical optimization problems. The parameters we focus on are the sparsities of the input and the output of the LCP: the maximum numbers of nonzero entries per row/column in the coefficient matrix and the number of nonzero entries in a solution. Our main result is to present a fixed-parameter algorithm for the LCP with all the parameters. We also show that if we drop any of the three parameters, then the LCP is fixed-parameter intractable. In addition, we discuss the nonexistence of a polynomial kernel for the LCP.
KW - Linear complementarity problem
KW - Parameterized complexity
KW - Sparsity
UR - http://www.scopus.com/inward/record.url?scp=84958257443&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84958257443&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.IPEC.2015.355
DO - 10.4230/LIPIcs.IPEC.2015.355
M3 - Conference contribution
AN - SCOPUS:84958257443
T3 - Leibniz International Proceedings in Informatics, LIPIcs
SP - 355
EP - 364
BT - 10th International Symposium on Parameterized and Exact Computation, IPEC 2015
A2 - Husfeldt, Thore
A2 - Husfeldt, Thore
A2 - Kanj, Iyad
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 10th International Symposium on Parameterized and Exact Computation, IPEC 2015
Y2 - 16 September 2015 through 18 September 2015
ER -