The distance-based critical node detection problem : models and algorithms

In the wake of terrorism and natural disasters, assessing networked systems for vulnerability to failures that arise from these events is essential to maintaining the operations of the systems. This is very crucial given the heavy dependence of daily social and economic activities on networked systems such as transport, telecommunication and energy networks as well as the interdependence of these networks. In this thesis, we explore methods to assess the vulnerability of networked systems to element failures which employ connectivity as the performance measure for vulnerability. The associated optimisation problem termed the critical node (edge) detection problem seeks to identify a subset of nodes (edges) of a network whose deletion (failure) optimises a network connectivity objective. Traditional connectivity measures employed in most studies of the critical node detection problem overlook internal cohesiveness of networks and the extent of connectivity in the network. This limits the effectiveness of the developed methods in uncovering vulnerability with regards to network connectivity. Our work therefore focuses on distance-based connectivity which is a fairly new class of connectivity introduced for studying the critical node detection problem to overcome the limitations of traditional connectivity measures. In Chapter 1, we provide an introduction outlining the motivations and the methods related to our study. In Chapter 2, we review the literature on the critical node detection problem as well as its application areas and related problems. Following this, we formally introduce the distance-based critical node detection problem in Chapter 3 where we propose new integer programming models for the case of hop-based distances and an efficient algorithm for the separation problems associated with the models. We also propose two families of valid inequalities. In Chapter 4, we consider the distance-based critical node detection problem using a heuristic approach in which we propose a centrality-based heuristic that employs a backbone crossover and a centrality-based neighbourhood search. In Chapter 5, we present generalisations of the methods proposed in Chapter 3 to edge-weighted graphs. We also introduce the edge-deletion version of the problem which we term the distance based critical edge detection problem. Throughout Chapters 3, 4 and 5, we provide computational experiments. Finally, in Chapter 6 we present conclusions as well future research directions. Keywords: Network Vulnerability, Critical Node Detection Problem, Distance-based Connectivity, Integer Programming, Lazy Constraints, Branch-and-cut, Heuristics.In the wake of terrorism and natural disasters, assessing networked systems for vulnerability to failures that arise from these events is essential to maintaining the operations of the systems. This is very crucial given the heavy dependence of daily social and economic activities on networked systems such as transport, telecommunication and energy networks as well as the interdependence of these networks. In this thesis, we explore methods to assess the vulnerability of networked systems to element failures which employ connectivity as the performance measure for vulnerability. The associated optimisation problem termed the critical node (edge) detection problem seeks to identify a subset of nodes (edges) of a network whose deletion (failure) optimises a network connectivity objective. Traditional connectivity measures employed in most studies of the critical node detection problem overlook internal cohesiveness of networks and the extent of connectivity in the network. This limits the effectiveness of the developed methods in uncovering vulnerability with regards to network connectivity. Our work therefore focuses on distance-based connectivity which is a fairly new class of connectivity introduced for studying the critical node detection problem to overcome the limitations of traditional connectivity measures. In Chapter 1, we provide an introduction outlining the motivations and the methods related to our study. In Chapter 2, we review the literature on the critical node detection problem as well as its application areas and related problems. Following this, we formally introduce the distance-based critical node detection problem in Chapter 3 where we propose new integer programming models for the case of hop-based distances and an efficient algorithm for the separation problems associated with the models. We also propose two families of valid inequalities. In Chapter 4, we consider the distance-based critical node detection problem using a heuristic approach in which we propose a centrality-based heuristic that employs a backbone crossover and a centrality-based neighbourhood search. In Chapter 5, we present generalisations of the methods proposed in Chapter 3 to edge-weighted graphs. We also introduce the edge-deletion version of the problem which we term the distance based critical edge detection problem. Throughout Chapters 3, 4 and 5, we provide computational experiments. Finally, in Chapter 6 we present conclusions as well future research directions. Keywords: Network Vulnerability, Critical Node Detection Problem, Distance-based Connectivity, Integer Programming, Lazy Constraints, Branch-and-cut, Heuristics

Breaking Instance-Independent Symmetries In Exact Graph Coloring

Code optimization and high level synthesis can be posed as constraint satisfaction and optimization problems, such as graph coloring used in register allocation. Graph coloring is also used to model more traditional CSPs relevant to AI, such as planning, time-tabling and scheduling. Provably optimal solutions may be desirable for commercial and defense applications. Additionally, for applications such as register allocation and code optimization, naturally-occurring instances of graph coloring are often small and can be solved optimally. A recent wave of improvements in algorithms for Boolean satisfiability (SAT) and 0-1 Integer Linear Programming (ILP) suggests generic problem-reduction methods, rather than problem-specific heuristics, because (1) heuristics may be upset by new constraints, (2) heuristics tend to ignore structure, and (3) many relevant problems are provably inapproximable. Problem reductions often lead to highly symmetric SAT instances, and symmetries are known to slow down SAT solvers. In this work, we compare several avenues for symmetry breaking, in particular when certain kinds of symmetry are present in all generated instances. Our focus on reducing CSPs to SAT allows us to leverage recent dramatic improvement in SAT solvers and automatically benefit from future progress. We can use a variety of black-box SAT solvers without modifying their source code because our symmetry-breaking techniques are static, i.e., we detect symmetries and add symmetry breaking predicates (SBPs) during pre-processing. An important result of our work is that among the types of instance-independent SBPs we studied and their combinations, the simplest and least complete constructions are the most effective. Our experiments also clearly indicate that instance-independent symmetries should mostly be processed together with instance-specific symmetries rather than at the specification level, contrary to what has been suggested in the literature

The detection and classification of blast cell in Leukaemia Acute Promyelocytic Leukaemia (AML M3) blood using simulated annealing and neural networks

This paper was delivered at AIME 2011: 13th Conference on Artifical Intelligence in Medicine.This paper presents a method for the detection and classification of blast cells in M3 with others sub-types using simulated annealing and neural networks. In this paper, we increased our test result from 10 images to 20 images. We performed Hill Climbing, Simulated Annealing and Genetic Algorithms for detecting the blast cells. As a result, simulated annealing is the “best” heuristic search for detecting the leukaemia cells. From the detection, we performed features extraction on the blast cells and we classifying based on M3 and other sub-types using neural networks. We received convincing result which has targeting around 97% in classifying of M3 with other sub-types. Our results are based on real world image data from a Haematology Department.Universiti Sains Islam Malaysia and the Ministry of Higher Education, Malaysi

Approximate Closest Community Search in Networks

Recently, there has been significant interest in the study of the community search problem in social and information networks: given one or more query nodes, find densely connected communities containing the query nodes. However, most existing studies do not address the "free rider" issue, that is, nodes far away from query nodes and irrelevant to them are included in the detected community. Some state-of-the-art models have attempted to address this issue, but not only are their formulated problems NP-hard, they do not admit any approximations without restrictive assumptions, which may not always hold in practice. In this paper, given an undirected graph G and a set of query nodes Q, we study community search using the k-truss based community model. We formulate our problem of finding a closest truss community (CTC), as finding a connected k-truss subgraph with the largest k that contains Q, and has the minimum diameter among such subgraphs. We prove this problem is NP-hard. Furthermore, it is NP-hard to approximate the problem within a factor $(2-\varepsilon)$, for any $\varepsilon >0$. However, we develop a greedy algorithmic framework, which first finds a CTC containing Q, and then iteratively removes the furthest nodes from Q, from the graph. The method achieves 2-approximation to the optimal solution. To further improve the efficiency, we make use of a compact truss index and develop efficient algorithms for k-truss identification and maintenance as nodes get eliminated. In addition, using bulk deletion optimization and local exploration strategies, we propose two more efficient algorithms. One of them trades some approximation quality for efficiency while the other is a very efficient heuristic. Extensive experiments on 6 real-world networks show the effectiveness and efficiency of our community model and search algorithms

RASCAL: calculation of graph similarity using maximum common edge subgraphs

A new graph similarity calculation procedure is introduced for comparing labeled graphs. Given a minimum similarity threshold, the procedure consists of an initial screening process to determine whether it is possible for the measure of similarity between the two graphs to exceed the minimum threshold, followed by a rigorous maximum common edge subgraph (MCES) detection algorithm to compute the exact degree and composition of similarity. The proposed MCES algorithm is based on a maximum clique formulation of the problem and is a significant improvement over other published algorithms. It presents new approaches to both lower and upper bounding as well as vertex selection