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Exploiting bounded signal flow for graph orientation based on causeeffect pairs
 In Proceedings of the 1st International ICST Conference on Theory and Practice of Algorithms in (Computer) Systems (TAPAS 2011
"... Background: 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. This problem has applications in understanding protein intera ..."
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Background: 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. This problem has applications in understanding protein interaction based cell regulation mechanisms. Since this problem is NPhard, research so far concentrated on polynomialtime approximation algorithms and tractable special cases. 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 fixedparameter tractability results, and in one case a sharp complexity dichotomy between a lineartime solvable case and a slightly more general NPhard case. We examine the value of these parameters for several realworld network instances. Conclusions: Several biologically relevant special cases of the NPhard problem can be solved to optimality. In this way, parameterized analysis yields both deeper insight into the computational complexity and practical solving strategies. Background Current technologies [1] like twohybrid screening can
Network orientation via shortest paths
 BIOINFORMATICS
, 2014
"... The graph orientation problem calls for orienting the edges of a graph so as to maximize the number of prespecified source–target vertex pairs that admit a directed path from the source to the target. Most algorithmic approaches to this problem share a common preprocessing step, in which the input ..."
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The graph orientation problem calls for orienting the edges of a graph so as to maximize the number of prespecified source–target vertex pairs that admit a directed path from the source to the target. Most algorithmic approaches to this problem share a common preprocessing step, in which the input graph is reduced to a tree by repeatedly contracting its cycles. Although this reduction is valid from an algorithmic perspective, the assignment of directions to the edges of the contracted cycles becomes arbitrary, and the connecting source–target paths may be arbitrarily long. In the context of biological networks, the connection of vertex pairs via shortest paths is highly motivated, leading to the following problem variant: given a graph and a collection of source–target vertex pairs, assign directions to the edges so as to maximize the number of pairs that are connected by a shortest (in the original graph) directed path. This problem is NPcomplete and hard to approximate to within subpolynomial factors. Here we provide a first polynomialsize integer linear program formulation for this problem, which allows its exact solution in seconds on current networks. We apply our algorithm to orient protein–protein interaction networks in yeast and compare it with two stateoftheart algorithms. We find that our algorithm outperforms previous approaches and can orient considerable parts of the network, thus revealing its structure and function. Availability and implementation: The source code is available at www.cs.tau.ac.il/*roded/shortest.zip.
Approximation Algorithms and Hardness Results for Shortest Path Based Graph Orientations
"... The graph orientation problem calls for orienting the edges of an undirected graph so as to maximize the number of prespecified sourcetarget vertex pairs that admit a directed path from the source to the target. Most algorithmic approaches to this problem share a common preprocessing step, in whi ..."
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The graph orientation problem calls for orienting the edges of an undirected graph so as to maximize the number of prespecified sourcetarget vertex pairs that admit a directed path from the source to the target. Most algorithmic approaches to this problem share a common preprocessing step, in which the input graph is reduced to a tree by repeatedly contracting its cycles. While this reduction is valid from an algorithmic perspective, the assignment of directions to the edges of the contracted cycles becomes arbitrary, and the connecting sourcetarget paths may be arbitrarily long. In the context of biological networks, the connection of vertex pairs via shortest paths is highly motivated, leading to the following variant: Given an undirected graph and a collection of sourcetarget vertex pairs, assign directions to the edges so as to maximize the number of pairs that are connected by a shortest (in the original graph) directed path. Here we study this variant, provide strong inapproximability results for it and propose an approximation algorithm for the problem, as well as for relaxations of it where the connecting paths need only be approximately shortest.
On the Complexity of two Problems on Orientations of Mixed Graphs
"... Abstract Interactions between biomolecules within the cell can be modeled by biological networks, i.e. graphs whose vertices are the biomolecules (proteins, genes, metabolites etc.) and whose edges represent their functional relationships. Depending on their nature, the interactions can be undirecte ..."
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Abstract Interactions between biomolecules within the cell can be modeled by biological networks, i.e. graphs whose vertices are the biomolecules (proteins, genes, metabolites etc.) and whose edges represent their functional relationships. Depending on their nature, the interactions can be undirected (e.g. proteinprotein interactions, PPIs) or directed (e.g. proteinDNA interactions, PDIs). A physical network is a network formed by both PPIs and PDIs, and is thus modeled by a mixed graph. External cellular events are transmitted into the nucleus via cascades of activation/deactivation of proteins, that correspond to paths (called signaling pathways) in the physical network from a source protein (cause) to a target protein (effect). There exists experimental methods to identify the causeeffect pairs, but such methods do not provide the signaling pathways. A key challenge is to infer such pathways based on the causeeffect informations. In terms of graph theory, this problem, called MAXIMUM GRAPH ORIENTATION (MGO), is defined as follows: given a mixed graph G and a set P of sourcetarget pairs, find an orientation of G that replaces each (undirected) edge by a single (directed) arc in such a way that there exists a directed path, from s to t, for a maximum number of pairs (s, t) ∈ P. In this work, we consider a variant of MGO, called SGO, in which we ask whether all the pairs in P can be connected by a
Orienting edges to get a directed Steiner forest of low cost
, 2011
"... The input to Maximum pairs Directed Steiner network (MDS) problem is an undirected graph G(V, E) and a collection of pairs {si, ti}. The goal is to direct all edges of E, namely, give them one of the possible directions so that the maximum possible number of pairs is covered. In our second problem w ..."
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The input to Maximum pairs Directed Steiner network (MDS) problem is an undirected graph G(V, E) and a collection of pairs {si, ti}. The goal is to direct all edges of E, namely, give them one of the possible directions so that the maximum possible number of pairs is covered. In our second problem we assume all pairs can be covered but edges have costs. We assume that exist an orientation of part of the edges covering of all pairs. We want to select a mincost set E ′ ⊆ E and orient it to a directed graph G(V, A) such that all pairs are covered and the cost is minimum. This problem is called the Minimum cost all pairs directed Steiner (MADS) problem. We give a ratio 4 approximation, namely, a solution covering all pairs and having cost at most 4·opt where opt is the minimum cost to cover all pairs. In the generalized MADS we have a (possibly zero) demand du,v for every u, v ∈ V × V and the goal is to orient subset of the edges so that there are duv pairs between every u, v and the cost is minimum. We show some small inherent advantage of the uniform costs assumption in one aspect. We show that since the c(u, v) = c(v, u) there always exists a solution covering at least du,v/2 paths from u to v at cost at most 2opt. If the demands and costs are symmetric as well, namely, d (u,v) = d (v,u) for every u, v, we are able to cover all pairs in full demand, and get a ratio 2 for the cost. The demand d, s, t cover problem is given an edge weighted graph G(V, E) a demand d and two vertices s, t to orient part of the edges into a set A so that in G(V, A) there are k vertexdisjoint directed paths from s to t and k vertex disjoint paths from t, s and the cost is minimum. We give a polynomial time solution for this problem. We also discuss several additional observations. 1
A Note on the Parameterized Complexity of Unordered Maximum Tree Orientation
, 2012
"... In the Unordered Maximum Tree Orientation problem, a set P of paths in a tree and a parameter k is given, and we want to orient the edges in the tree such that all but at most k paths in P become directed paths. This is a more difficult variant of a wellstudied problem in computational biology wher ..."
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In the Unordered Maximum Tree Orientation problem, a set P of paths in a tree and a parameter k is given, and we want to orient the edges in the tree such that all but at most k paths in P become directed paths. This is a more difficult variant of a wellstudied problem in computational biology where the directions of paths in P are already given. We show that the parameterized complexity of the unordered version is between Edge Bipartization and Vertex Bipartization, and we give a characterization of orientable path sets in trees by forbidden substructures, which are cycles of a certain kind.
On the Approximability of Reachability Preserving Network Orientations
"... We introduce a graph orientation problem arising in the study of biological networks. Given an undirected graph and a list of ordered sourcetarget vertex pairs, the goal is to orient the graph such that a maximum number of pairs admit a directed sourcetotarget path. We study the complexity and ap ..."
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We introduce a graph orientation problem arising in the study of biological networks. Given an undirected graph and a list of ordered sourcetarget vertex pairs, the goal is to orient the graph such that a maximum number of pairs admit a directed sourcetotarget path. We study the complexity and approximability of this problem. We show that the problem is NPhard even on star graphs and hard to approximate to within some constant factor. On the positive side, we provide an Ω(loglogn/logn)factor approximation algorithm for the problem on nvertex graphs. We further show that for any instance of the problem there exists an orientation of the input graph that satisfies a logarithmic fraction of all pairs and that this bound is tight up to a constant factor. Our techniques also lead to constant factor approximation algorithms for some restricted variants of the problem.