TY - JOUR
T1 - Grid recognition
T2 - Classical and parameterized computational perspectives
AU - Gupta, Siddharth
AU - Sa'ar, Guy
AU - Zehavi, Meirav
N1 - Funding Information:
Supported in part by the Engineering and Physical Sciences Research Council (EPSRC) grant EP/V007793/1.Supported in part by the Israeli Smart Transportation Research Center (ISTRC).The project was supported by Israel Science Foundation grant no. 1176/18, and the European Research Council (ERC) Starting grant titled PARAPATH.
Publisher Copyright:
© 2023 Elsevier Inc.
PY - 2023/9/1
Y1 - 2023/9/1
N2 - Over the past few decades, a large body of works studied the (in)tractability of various computational problems on grid graphs, which often yield substantially faster algorithms than general graphs. Unfortunately, the recognition of a grid graph is hard—it was shown to be NP-hard already in 1987. In this paper, we provide several positive results in this regard in the framework of parameterized complexity. Specifically, our contribution is threefold. First, we show that the problem is FPT parameterized by k+mcc where mcc is the maximum size of a connected component of G. Second, we present a new parameterization, denoted aG, relating graph distance to geometric distance. We show that the problem is para-NP-hard parameterized by aG, but FPT parameterized by aG on trees, as well as FPT parameterized by k+aG. Third, we show that the recognition of k×r grid graphs is NP-hard on graphs of pathwidth 2 where k=3.
AB - Over the past few decades, a large body of works studied the (in)tractability of various computational problems on grid graphs, which often yield substantially faster algorithms than general graphs. Unfortunately, the recognition of a grid graph is hard—it was shown to be NP-hard already in 1987. In this paper, we provide several positive results in this regard in the framework of parameterized complexity. Specifically, our contribution is threefold. First, we show that the problem is FPT parameterized by k+mcc where mcc is the maximum size of a connected component of G. Second, we present a new parameterization, denoted aG, relating graph distance to geometric distance. We show that the problem is para-NP-hard parameterized by aG, but FPT parameterized by aG on trees, as well as FPT parameterized by k+aG. Third, we show that the recognition of k×r grid graphs is NP-hard on graphs of pathwidth 2 where k=3.
KW - Grid graph
KW - Grid recognition
KW - Parameterized complexity
UR - http://www.scopus.com/inward/record.url?scp=85151298940&partnerID=8YFLogxK
U2 - 10.1016/j.jcss.2023.02.008
DO - 10.1016/j.jcss.2023.02.008
M3 - Article
AN - SCOPUS:85151298940
SN - 0022-0000
VL - 136
SP - 17
EP - 62
JO - Journal of Computer and System Sciences
JF - Journal of Computer and System Sciences
ER -