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Algorithm Engineering for Optimal Graph Bipartization
, 2009
"... We examine exact algorithms for the NPhard Graph Bipartization problem. The task is, given a graph, to find a minimum set of vertices to delete to make it bipartite. Based on the “iterative compression ” method introduced by Reed, Smith, and Vetta in 2004, we present new algorithms and experimental ..."
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Cited by 14 (3 self)
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We examine exact algorithms for the NPhard Graph Bipartization problem. The task is, given a graph, to find a minimum set of vertices to delete to make it bipartite. Based on the “iterative compression ” method introduced by Reed, Smith, and Vetta in 2004, we present new algorithms and experimental results. The worstcase time complexity is improved. Based on new structural insights, we give a simplified correctness proof. This also allows us to establish a heuristic improvement that in particular speeds up the search on dense graphs. Our best algorithm can solve all instances from a testbed from computational biology within minutes, whereas established methods are only able to solve about half of the instances within reasonable time.
The Effect of Negative Feedback Loops on the Dynamics of Boolean Networks
, 2008
"... Feedback loops play an important role in determining the dynamics of biological networks. To study the role of negative feedback loops, this article introduces the notion of distancetopositivefeedback which, in essence, captures the number of independent negative feedback loops in the network, a ..."
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Cited by 12 (2 self)
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Feedback loops play an important role in determining the dynamics of biological networks. To study the role of negative feedback loops, this article introduces the notion of distancetopositivefeedback which, in essence, captures the number of independent negative feedback loops in the network, a property inherent in the network topology. Through a computational study using Boolean networks, it is shown that distancetopositivefeedback has a strong influence on network dynamics and correlates very well with the number and length of limit cycles in the phase space of the network. To be precise, it is shown that, as the number of independent negative feedback loops increases, the number (length) of limit cycles tends to decrease (increase). These conclusions are consistent with the fact that certain natural biological networks exhibit generally regular behavior and have fewer negative feedback loops than randomized networks with the same number of nodes and same connectivity.
Iterative compression for exactly solving nphard minimization problems
 in Algorithmics of Large and Complex Networks, Lecture Notes in Computer Science
"... Abstract. We survey the conceptual framework and several applications of the iterative compression technique introduced in 2004 by Reed, Smith, and Vetta. This technique has proven very useful for achieving a number of recent breakthroughs in the development of fixedparameter algorithms for NPhard ..."
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Cited by 10 (9 self)
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Abstract. We survey the conceptual framework and several applications of the iterative compression technique introduced in 2004 by Reed, Smith, and Vetta. This technique has proven very useful for achieving a number of recent breakthroughs in the development of fixedparameter algorithms for NPhard minimization problems. There is a clear potential for further applications as well as a further development of the technique itself. We describe several algorithmic results based on iterative compression and point out some challenges for future research. 1
FixedParameter Algorithms in Analysis of Heuristics for Extracting Networks in Linear Programs
"... Abstract. A parameterized problem Π can be considered as a set of pairs (I, k) where I is the main part and k (usually an integer) is the parameter. Π is called fixedparameter tractable (FPT) if membership of (I, k) in Π can be decided in time O(f(k)I  c), where I  denotes the size of I, f(k) i ..."
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Abstract. A parameterized problem Π can be considered as a set of pairs (I, k) where I is the main part and k (usually an integer) is the parameter. Π is called fixedparameter tractable (FPT) if membership of (I, k) in Π can be decided in time O(f(k)I  c), where I  denotes the size of I, f(k) is a computable function, and c is a constant independent of k and I. An algorithm of complexity O(f(k)I  c) is called a fixedparameter algorithm. It often happens that although a problem is FPT, the practitioners prefer to use imprecise heuristic methods to solve the problem in the realworld situation simply because of the fact that the heuristic methods are faster. In this paper we argue that in this situation a fixedparameter algorithm for the given problem may be still of a considerable practical use. In particular, the fixedparameter algorithm can be used to evaluate the approximation quality of heuristic approaches. To demonstrate this way of application of fixedparameter algorithms, we consider the problem of extracting a maximumsize reflected network in a linear program. We evaluate a stateoftheart heuristic SGA and two variations of it with a new heuristic and with an exact algorithm. The new heuristic and algorithm use fixedparameter tractable procedures. The new heuristic turned out to be of little practical interest, but the exact algorithm is of interest when the network size is close to that of the linear program especially if the exact algorithm is used in conjunction with SGA. Another conclusion which has a large practical interest is that some variant of SGA can be the best choice because in most cases it returns optimal solutions; previously it was disregarded because comparing to the other heuristics it improved the solution insignificantly at the cost of much larger running times.
The 29th Workshop on Combinatorial Mathematics and Computation Theory Finding the Maximum Balanced Vertex Set on Complete Graphs
"... A signed graph is a simple graph in which each edge is labeled by a sign either + or. A signed graph is balanced if every cycle has even numbers of negative edges. In this paper, we study the problem how to find a maximum vertex subset of a complete signed graph such that the induced subgraph is ba ..."
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A signed graph is a simple graph in which each edge is labeled by a sign either + or. A signed graph is balanced if every cycle has even numbers of negative edges. In this paper, we study the problem how to find a maximum vertex subset of a complete signed graph such that the induced subgraph is balanced. We show that the problem can be reduced to a series of vertex cover problems and therefore admits a 2approximation and a fixedparameter algorithms. We also tested the practical performances of these algorithms on random graphs. Our algorithm can find optimal solution within ten seconds with 100 vertices which is much better than a trivial algorithm. 1
A LocalSearch 2Approximation for
"... Abstract. CorrelationClustering is now an established problem in the algorithms and constrained clustering communities. With the requirement that at most two clusters be formed, the minimisation problem is related to the study of signed graphs in the social psychology community, and has applications ..."
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Abstract. CorrelationClustering is now an established problem in the algorithms and constrained clustering communities. With the requirement that at most two clusters be formed, the minimisation problem is related to the study of signed graphs in the social psychology community, and has applications in statistical mechanics and biological networks. Although a PTAS exists for this problem, its running time is impractical. We therefore introduce a number of new algorithms for 2CC, including two that incorporate some notion of local search. In particular, we show that the algorithm we call PASTAtoss is a 2approximation on complete graphs. Experiments confirm the strong performance of the local search approaches, even on noncomplete graphs, with running time significantly lower than rival approaches. 1