# Reconstructing binary matrices under window constraints from their row and column sums

## TL;DR

This paper investigates the complexity of reconstructing binary matrices from row and column sums with additional window constraints, revealing surprising shifts between polynomial-time solvability and NP-hardness.

## Contribution

It introduces a new class of constraints in binary matrix reconstruction problems and analyzes their impact on computational complexity.

## Key findings

- Window constraints cause complexity shifts between polynomial and NP-hard.
- Classical reconstruction problems are polynomial, but added constraints increase difficulty.
- The paper characterizes conditions under which the problem becomes computationally hard.

## Abstract

The present paper deals with the discrete inverse problem of reconstructing binary matrices from their row and column sums under additional constraints on the number and pattern of entries in specified minors. While the classical consistency and reconstruction problems for two directions in discrete tomography can be solved in polynomial time, it turns out that these window constraints cause various unexpected complexity jumps back and forth from polynomial-time solvability to $\mathbb{N}\mathbb{P}$-hardness.