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Optimally orienting physical networks
 In Proceedings of the 15th Annual International Conference on Research in Computational Molecular Biology (RECOMB 2011), volume 6577 of LNCS
, 2011
"... Abstract. In a network orientation problem one is given a mixed graph, consisting of directed and undirected edges, and a set of sourcetarget vertex pairs. The goal is to orient the undirected edges so that a maximum number of pairs admit a directed path from the source to the target. This problem ..."
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Abstract. In a network orientation problem one is given a mixed graph, consisting of directed and undirected edges, and a set of sourcetarget vertex pairs. The goal is to orient the undirected edges so that a maximum number of pairs admit a directed path from the source to the target. This problem is NPcomplete and no approximation algorithms are known for it. It arises in the context of analyzing physical networks of proteinprotein and proteindna interactions. While the latter are naturally directed from a transcription factor to a gene, the direction of signal flow in proteinprotein interactions is often unknown or cannot be measured en masse. One then tries to infer this information by using causality data on pairs of genes such that the perturbation of one gene changes the expression level of the other gene. Here we provide a first polynomialsize ilp formulation for this problem, which can be efficiently solved on current networks. We apply our algorithm to orient proteinprotein interactions in yeast and measure our performance using edges with known orientations. We find that our algorithm achieves high accuracy and coverage in the orientation, outperforming simplified algorithmic variants that do not use information on edge directions. The obtained orientations can lead to better understanding of the structure and function of the network. Key words: network orientation, proteinprotein interaction, proteindna interaction, integer linear program, mixed graph 1
Approximation Algorithms for Orienting Mixed Graphs
"... Abstract. Graph orientation is a fundamental problem in graph theory that has recently arisen in the study of signalingregulatory pathways in protein networks. Given a graph and a list of ordered sourcetarget vertex pairs, it calls for assigning directions to the edges of the graph so as to maximi ..."
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Abstract. Graph orientation is a fundamental problem in graph theory that has recently arisen in the study of signalingregulatory pathways in protein networks. Given a graph and a list of ordered sourcetarget vertex pairs, it calls for assigning directions to the edges of the graph so as to maximize the number of pairs that admit a directed sourcetotarget path. When the input graph is undirected, a sublogarithmic approximation is known for the problem. However, the approximability of the biologicallyrelevant variant, in which the input graph has both directed and undirected edges, was left open. Here we give the first approximation algorithm to this problem. Our algorithm provides a sublinear guarantee in the general case, and logarithmic guarantees for structured instances. Key words: proteinprotein interaction network, mixed graph, graph orientation, approximation algorithm 1
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
Algorithmic Aspects of Heterogeneous Biological Networks Comparison
, 2011
"... Biological networks are commonly used to model molecular activity within the cell. Recent experimental studies have shown that the detection of conserved subnetworks across several networks, coming from different organisms, may allow the discovery of disease pathways and prediction of protein funct ..."
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Biological networks are commonly used to model molecular activity within the cell. Recent experimental studies have shown that the detection of conserved subnetworks across several networks, coming from different organisms, may allow the discovery of disease pathways and prediction of protein functions. There already exist automatic methods that allow to search for conserved subnetworks using networks alignment; unfortunately, these methods are limited to networks of same type, thus having the same graph representation. Towards overcoming this limitation, a unified framework for pairwise comparison and analysis of networks with different graph representations (in particular, a directed acyclic graph D and an undirected graph G over the same set of vertices) is presented in [4]. We consider here a related problem called kDAGCC: given a directed graph D and an undirected graph G on the same set V of vertices, and an integer k, does there exist sets of vertices V1, V2,... Vk ′, k ′ ≤ k such that, for each 1 ≤ i ≤ k ′ , (i) D[Vi] is a DAG and (ii) G[Vi] is connected? Two variants of kDAGCC are of interest: (a) the Vis must form a partition of V, or (b) the Vis must form a cover of V. We study the computational complexity of both variants of kDAGCC and, depending on the constraints imposed on the input, provide several polynomialtime algorithms, hardness and inapproximability results.
Steiner Forest Orientation Problems
, 2012
"... We consider connectivity problems with orientation constraints. Given a directed graph D and a collection of ordered node pairs P let P[D] = {(u,v) ∈ P: D contains a uvpath}. In the Steiner Forest Orientation problem we are given an undirected graph G = (V,E) with edgecosts and a set P ⊆ V × V ..."
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We consider connectivity problems with orientation constraints. Given a directed graph D and a collection of ordered node pairs P let P[D] = {(u,v) ∈ P: D contains a uvpath}. In the Steiner Forest Orientation problem we are given an undirected graph G = (V,E) with edgecosts and a set P ⊆ V × V of ordered node pairs. The goal is to find a minimumcost subgraph H of G and an orientation D of H such that P[D] = P. We give a 4approximation algorithm for this problem. In the Maximum Pairs Orientation problem we are given a graph G and a multicollection of ordered node pairs P on V. The goal is to find an orientation D of G such that P[D]  is maximum. Generalizing the result of Arkin and Hassin [DAM’02] for P  = 2, we will show that for a mixed graph G (that may have both directed and undirected edges), one can decide in n O(P) time whether G has an orientation D with P[D] = P (for undirected graphs this problem admits a polynomial time algorithm for any P, but it is NPcomplete on mixed graphs). For undirected graphs, we will show that one can decide whether G admits an orientation D with P[D]  ≥ k in O(n + m) + 2 O(k·log log k) time; hence this decision problem is fixedparameter tractable, which answers an open question from Dorn et al. [AMB’11]. We also show that Maximum Pairs Orientation admits ratio O(logP/log logP), which is better than the ratio O(log n/log log n) of Gamzu et al. [WABI’10] when P  < n.
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.
Identifying the Signaling Cascades and Regulatory Mechanisms that Control Stress Responses
, 2012
"... not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution, the U.S. government, or any other entity. Keywords: Transcriptional regulation, time series gene expression, proteinprotein Adaptation to diverse and everchanging environmental con ..."
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not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution, the U.S. government, or any other entity. Keywords: Transcriptional regulation, time series gene expression, proteinprotein Adaptation to diverse and everchanging environmental conditions is vital to the survival of all organisms. From singlecelled organisms reacting to changes in the chemical makeup of their surroundings to human cells fighting off infection, there are many global similarities across stress responses. In general, sensory proteins detect environmental perturbations and, via signaling cascades, alert specific transcription factors to adjust gene regulation and counteract negative effects of the stress. In this thesis, we present the challenges that arise when trying to understand such responses and propose computational methods for developing endtoend models of stress response. One primary goal when modeling the reaction to environmental perturbations is to determine the sensory proteins (sources) and transcription factors
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
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.