A binary matrix M has the consecutive ones property (C1P) for rows (resp. columns) if there exists a permutation of its columns (resp. rows) that arranges the ones consecutively in all the rows (resp. columns). If M has the C1P for rows and the C1P for columns, then M is said to have the simultaneous consecutive ones property (SC1P). In this article, we consider the classical complexity and fixed-parameter tractability of a few variants of decision problems related to the SC1P. Given a binary matrix M and a positive integer d, we focus on problems that decide whether there exists a set of rows, columns, and rows as well as columns, respectively, of size at most d in M, whose deletion results in a matrix with the SC1P. We also consider problems that decide whether there exists a set of 0-entries, 1-entries and 0-entries as well as 1-entries, respectively, of size at most d in M, whose flipping results in a matrix with the SC1P. In this paper, we show that all the above mentioned problems are NP-complete. We could also prove that all these problems are fixed-parameter tractable with respect to solution size as the parameter, except for two variants (flipping 1-entries and flipping 0/1-entries). We also give improved FPT algorithms for certain problems on restricted binary matrices.

如果存在二进制列矩阵（列）的排列（在所有行（列）中连续排列），则二进制矩阵M的行（列）具有连续的（C1P）属性。如果M具有用于行的C1P和具有列的C1P，则称M具有同时连续的1属性（SC1P）。在本文中，我们考虑了与SC1P相关的决策问题的一些变体的经典复杂性和固定参数易处理性。给定一个二进制矩阵M和一个正整数d，我们关注于确定是否存在一组行，列，行和列的集合，分别在M中最大为d的问题。，其删除会导致与SC1P形成矩阵。我们还考虑了一些问题，这些问题决定了是否存在一组0个条目，1个条目和0个条目以及1个条目，它们的大小最大为d在M中，其翻转会导致与SC1P形成矩阵。在本文中，我们证明上述所有问题都是NP完全的。我们还可以证明，除了两个变量（翻转1项和翻转0/1项）以外，所有这些问题对于解决方案大小作为参数都是固定参数易处理的。对于受限二进制矩阵上的某些问题，我们还提供了改进的FPT算法。