Exact Algorithms for the Quadratic Linear Ordering Problem

The quadratic linear ordering problem naturally generalizes various optimization problems, such as bipartite crossing minimization or the betweenness problem, which includes linear arrangement. These problems have important applications in, e.g., automatic graph drawing and computational biology. We present a new polyhedral approach to the quadratic linear ordering problem that is based on a linearization of the quadratic objective function. Our main result is a reformulation of the 3-dicycle inequalities using quadratic terms, the resulting constraints are shown to be face-inducing for the polytope corresponding to the unconstrained quadratic problem. We exploit this result both within a branch-and-cut algorithm and within an SDP-based branch-and-bound algorithm. Experimental results for bipartite crossing minimization show that this approach clearly outperforms other methods

Exact Algorithms for the Quadratic Linear Ordering Problem

The quadratic linear ordering problem naturally generalizes various optimization problems, such as bipartite crossing minimization or the betweenness problem, which includes linear arrangement. These problems have important applications in, e.g., automatic graph drawing and computational biology. We present a new polyhedral approach to the quadratic linear ordering problem that is based on a linearization of the quadratic objective function. Our main result is a reformulation of the 3-dicycle inequalities using quadratic terms, the resulting constraints are shown to be face-inducing for the polytope corresponding to the unconstrained quadratic problem. We exploit this result both within a branch-and-cut algorithm and within an SDP-based branch-and-bound algorithm. Experimental results for bipartite crossing minimization show that this approach clearly outperforms other methods

Down-Regulation of EBV-LMP1 Radio-Sensitizes Nasal Pharyngeal Carcinoma Cells via NF-κB Regulated ATM Expression

BACKGROUND:The latent membrane protein 1 (LMP1) encoded by EBV is expressed in the majority of EBV-associated human malignancies and has been suggested to be one of the major oncogenic factors in EBV-mediated carcinogenesis. In previous studies we experimentally demonstrated that down-regulation of LMP1 expression by DNAzymes could increase radiosensitivity both in cells and in a xenograft NPC model in mice. RESULTS:In this study we explored the molecular mechanisms underlying the radiosensitization caused by the down-regulation of LMP1 in nasopharyngeal carcinoma. It was confirmed that LMP1 could up-regulate ATM expression in NPCs. Bioinformatic analysis of the ATM ptomoter region revealed three tentative binding sites for NF-κB. By using a specific inhibitor of NF-κB signaling and the dominant negative mutant of IkappaB, it was shown that the ATM expression in CNE1-LMP1 cells could be efficiently suppressed. Inhibition of LMP1 expression by the DNAzyme led to attenuation of the NF-κB DNA binding activity. We further showed that the silence of ATM expression by ATM-targeted siRNA could enhance the radiosensitivity in LMP1 positive NPC cells. CONCLUSIONS:Together, our results indicate that ATM expression can be regulated by LMP1 via the NF-κB pathways through direct promoter binding, which resulted in the change of radiosensitivity in NPCs

A New Exact Algorithm for the Two-Sided Crossing Minimization Problem

The Two-Sided Crossing Minimization (TSCM) problem calls for minimizing the number of edge crossings of a bipartite graph where the two sets of vertices are drawn on two parallel layers and edges are drawn as straight lines. This well-known problem has important applications in VLSI design and automatic graph drawing. In this paper, we present a new branch-and-cut algorithm for the TSCM problem by modeling it directly to a binary quadratic programming problem. We show that a large number of effective cutting planes can be derived based on a reformulation of the TSCM problem. We compare our algorithm with a previous exact algorithm by testing both implementations with the same set of instances. Experimental evaluation demonstrates the effectiveness of our approach

Crossing minimization problems of drawing bipartite graphs in two clusters

Abstract. Crossing minimization problem is a classic and very important problem in graph drawing [1]; the results directly affect the effectiveness of the layout, especially for very large scale graphs. But in many cases crossings cannot be avoided. In this paper we present two models for bipartite graph drawing, aiming to reduce crossings that cannot be avoided in the traditional bilayer drawings. We characterize crossing minimization problems in these models, and prove that they are N Pcomplete.

Crossing Minimization Problems of Drawing Bipartite Graphs in Two Clusters

The crossing minimization problem is a classic and very important problem in graph drawing (Pach, Toth 1997); the results directly a#ect the e#ectiveness of the layout, especially for very large scale graphs. But in many cases crossings cannot be avoided. In this paper we present two models for bipartite graph drawing, aiming to reduce crossings that cannot be avoided in the traditional bilayer drawings. We characterize crossing minimization problems in these models, and prove that they are NP-complete

Mixed integer programming based maintenance scheduling for the Hunter Valley coal chain

We consider the scheduling of the annual maintenance for the Hunter Valley Coal Chain. The coal chain is a system comprising load points, railway track and different types of terminal equipment, interacting in a complex way. A variety of maintenance tasks have to be performed on all parts of the infrastructure on a regular basis in order to assure the operation of the system as a whole. The main objective in the planning of these maintenance jobs is to maximize the total annual throughput. Based on a network flow model of the system, we propose a mixed integer programming formulation for this planning task. In order to deal with the resulting large scale model which cannot be solved directly by a general purpose solver, we propose two steps. The number of binary variables is reduced by choosing a representative subset of the variables of the original problem, and a rolling horizon approach enables the approximation of the long term (i.e. annual) problem by a sequence of shorter problems (for instance, monthly)

Scheduling arc maintenance jobs in a network to maximize total flow over time

We consider the problem of scheduling a set of maintenance jobs on the arcs of a network so that the total flow over the planning time horizon is maximized. A maintenance job causes an arc outage for its duration, potentially reducing the capacity of the network. The problem can be expected to have applications across a range of network infrastructures critical to modern life. For example, utilities such as water, sewerage and electricity all flow over networks. Products are manufactured and transported via supply chain networks. Such networks need regular, planned maintenance in order to continue to function. However the coordinated timing of maintenance jobs can have a major impact on the network capacity lost due to maintenance. Here we describe the background to the problem, define it, prove it is strongly NP-hard, and derive four local search-based heuristic methods. These methods integrate exact maximum flow solutions within a local search framework. The availability of both primal and dual solvers, and dual information from the maximum flow solver, is exploited to gain efficiency in the algorithms. The performance of the heuristics is evaluated on both randomly generated instances, and on instances derived from real-world data. These are compared with a state-of-the-art integer programming solver