# Inferring protein-protein interaction and protein-DNA interaction directions based on cause-effect pairs in undirected and mixed networks

## TL;DR

This paper addresses the maximum graph orientation problem in undirected and mixed networks, proposing algorithms and complexity results to infer interaction directions in biological networks like protein-protein and protein-DNA interactions.

## Contribution

It provides the first parameterized complexity analysis and efficient algorithms for the problem, including exact, approximation, and polynomial-time solutions for special cases.

## Key findings

- Determined the parameterized complexity for non-fixed and fixed path cases.
- Developed an exact algorithm outperforming previous methods on trees with few leaves.
- Presented polynomial-time algorithms for paths and cycles, and an FPT-algorithm for general graphs.

## Abstract

We consider the following problem: Given an undirected (mixed) network and a set of ordered source-target, or cause-effect pairs, direct all edges so as to maximize the number of pairs that admit a directed source-target path. This is called maximum graph orientation problem, and has applications in understanding interactions in protein-protein interaction networks and protein-DNA interaction networks. We have studied the problem on both undirected and mixed networks. In the undirected case, we determine the parameterized complexity of the problem (for non-fixed and fixed paths) with respect to the number of satisfied pairs, which has been an open problem. Also, we present an exact algorithm which outperforms the previous algorithms on trees with bounded number of leaves. In addition, we present a parameterized-approximation algorithm with respect to a parameter named the number of backbones of a tree. In the mixed case, we present polynomial-time algorithms for the problem on paths and cycles, and an FPT-algorithm based on the combined parameter the number of arcs and the number of pairs on general graphs.

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Source: https://tomesphere.com/paper/1706.00911