Exploiting bounded signal flow for graph orientation based on cause-effect pairs.

Britta Dorn,Dominikus Krüger,Johannes Uhlmann,Falk Hüffner,Rolf Niedermeier

doi:10.1186/1748-7188-6-21

Britta Dorn, Dominikus Krüger + Show 3 more

Open Access

https://doi.org/10.1186/1748-7188-6-21

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Abstract

BackgroundWe consider the following problem: Given an undirected network and a set of sender-receiver pairs, direct all edges such that the maximum number of "signal flows" defined by the pairs can be routed respecting edge directions. This problem has applications in understanding protein interaction based cell regulation mechanisms. Since this problem is NP-hard, research so far concentrated on polynomial-time approximation algorithms and tractable special cases.ResultsWe take the viewpoint of parameterized algorithmics and examine several parameters related to the maximum signal flow over vertices or edges. We provide several fixed-parameter tractability results, and in one case a sharp complexity dichotomy between a linear-time solvable case and a slightly more general NP-hard case. We examine the value of these parameters for several real-world network instances.ConclusionsSeveral biologically relevant special cases of the NP-hard problem can be solved to optimality. In this way, parameterized analysis yields both deeper insight into the computational complexity and practical solving strategies.

Highlights

We consider the following problem: Given an undirected network and a set of sender–receiver pairs, direct all edges such that the maximum number of “signal flows” defined by the pairs can be routed respecting edge directions
Given a list of so-called cause–effect pairs, the challenge consists in deducing an orientation of the protein-protein interaction (PPI) network which takes into account the causal relations of as many of these pairs as possible
We show that W-Maximum Tree Orientation (MTO) can be solved in O(2mv · |P| + n4) time on an n-vertex tree, where mv denotes the maximum number of connecting paths over any tree vertex

Summary

Results

We take the viewpoint of parameterized algorithmics and examine several parameters related to the maximum signal flow over vertices or edges. We provide several fixed-parameter tractability results, and in one case a sharp complexity dichotomy between a linear-time solvable case and a slightly more general NP-hard case. We examine the value of these parameters for several real-world network instances

Background

Methods and Results

Conclusions