Grid recognition: Classical and parameterized computational perspectives

Siddharth Gupta, Guy Sa'ar, Meirav Zehavi

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)17-62
Number of pages46
JournalJournal of Computer and System Sciences
StatePublished - 1 Sep 2023


  • Grid graph
  • Grid recognition
  • Parameterized complexity

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)
  • Computer Networks and Communications
  • Computational Theory and Mathematics
  • Applied Mathematics


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