Bounded Decentralised Coordination over Multiple Objectives

We propose the bounded multi-objective max-sum algorithm (B-MOMS), the first decentralised coordination algorithm for multi-objective optimisation problems. B-MOMS extends the max-sum message-passing algorithm for decentralised coordination to compute bounded approximate solutions to multi-objective decentralised constraint optimisation problems (MO-DCOPs). Specifically, we prove the optimality of B-MOMS in acyclic constraint graphs, and derive problem dependent bounds on its approximation ratio when these graphs contain cycles. Furthermore, we empirically evaluate its performance on a multi-objective extension of the canonical graph colouring problem. In so doing, we demonstrate that, for the settings we consider, the approximation ratio never exceeds 2, and is typically less than 1.5 for less-constrained graphs. Moreover, the runtime required by B-MOMS on the problem instances we considered never exceeds 30 minutes, even for maximally constrained graphs with $100$ agents. Thus, B-MOMS brings the problem of multi-objective optimisation well within the boundaries of the limited capabilities of embedded agents

Theory and Techniques for Synthesizing a Family of Graph Algorithms

Although Breadth-First Search (BFS) has several advantages over Depth-First Search (DFS) its prohibitive space requirements have meant that algorithm designers often pass it over in favor of DFS. To address this shortcoming, we introduce a theory of Efficient BFS (EBFS) along with a simple recursive program schema for carrying out the search. The theory is based on dominance relations, a long standing technique from the field of search algorithms. We show how the theory can be used to systematically derive solutions to two graph algorithms, namely the Single Source Shortest Path problem and the Minimum Spanning Tree problem. The solutions are found by making small systematic changes to the derivation, revealing the connections between the two problems which are often obscured in textbook presentations of them.Comment: In Proceedings SYNT 2012, arXiv:1207.055

Complexity of Model Testing for Dynamical Systems with Toric Steady States

In this paper we investigate the complexity of model selection and model testing for dynamical systems with toric steady states. Such systems frequently arise in the study of chemical reaction networks. We do this by formulating these tasks as a constrained optimization problem in Euclidean space. This optimization problem is known as a Euclidean distance problem; the complexity of solving this problem is measured by an invariant called the Euclidean distance (ED) degree. We determine closed-form expressions for the ED degree of the steady states of several families of chemical reaction networks with toric steady states and arbitrarily many reactions. To illustrate the utility of this work we show how the ED degree can be used as a tool for estimating the computational cost of solving the model testing and model selection problems

An Algebraic Framework for Compositional Program Analysis

The purpose of a program analysis is to compute an abstract meaning for a program which approximates its dynamic behaviour. A compositional program analysis accomplishes this task with a divide-and-conquer strategy: the meaning of a program is computed by dividing it into sub-programs, computing their meaning, and then combining the results. Compositional program analyses are desirable because they can yield scalable (and easily parallelizable) program analyses. This paper presents algebraic framework for designing, implementing, and proving the correctness of compositional program analyses. A program analysis in our framework defined by an algebraic structure equipped with sequencing, choice, and iteration operations. From the analysis design perspective, a particularly interesting consequence of this is that the meaning of a loop is computed by applying the iteration operator to the loop body. This style of compositional loop analysis can yield interesting ways of computing loop invariants that cannot be defined iteratively. We identify a class of algorithms, the so-called path-expression algorithms [Tarjan1981,Scholz2007], which can be used to efficiently implement analyses in our framework. Lastly, we develop a theory for proving the correctness of an analysis by establishing an approximation relationship between an algebra defining a concrete semantics and an algebra defining an analysis.Comment: 15 page

Distributive Network Utility Maximization (NUM) over Time-Varying Fading Channels

Distributed network utility maximization (NUM) has received an increasing intensity of interest over the past few years. Distributed solutions (e.g., the primal-dual gradient method) have been intensively investigated under fading channels. As such distributed solutions involve iterative updating and explicit message passing, it is unrealistic to assume that the wireless channel remains unchanged during the iterations. Unfortunately, the behavior of those distributed solutions under time-varying channels is in general unknown. In this paper, we shall investigate the convergence behavior and tracking errors of the iterative primal-dual scaled gradient algorithm (PDSGA) with dynamic scaling matrices (DSC) for solving distributive NUM problems under time-varying fading channels. We shall also study a specific application example, namely the multi-commodity flow control and multi-carrier power allocation problem in multi-hop ad hoc networks. Our analysis shows that the PDSGA converges to a limit region rather than a single point under the finite state Markov chain (FSMC) fading channels. We also show that the order of growth of the tracking errors is given by O(T/N), where T and N are the update interval and the average sojourn time of the FSMC, respectively. Based on this analysis, we derive a low complexity distributive adaptation algorithm for determining the adaptive scaling matrices, which can be implemented distributively at each transmitter. The numerical results show the superior performance of the proposed dynamic scaling matrix algorithm over several baseline schemes, such as the regular primal-dual gradient algorithm

Comprehensive Security Framework for Global Threats Analysis

Cyber criminality activities are changing and becoming more and more professional. With the growth of financial flows through the Internet and the Information System (IS), new kinds of thread arise involving complex scenarios spread within multiple IS components. The IS information modeling and Behavioral Analysis are becoming new solutions to normalize the IS information and counter these new threads. This paper presents a framework which details the principal and necessary steps for monitoring an IS. We present the architecture of the framework, i.e. an ontology of activities carried out within an IS to model security information and User Behavioral analysis. The results of the performed experiments on real data show that the modeling is effective to reduce the amount of events by 91%. The User Behavioral Analysis on uniform modeled data is also effective, detecting more than 80% of legitimate actions of attack scenarios

Interprocedural Data Flow Analysis in Soot using Value Contexts

An interprocedural analysis is precise if it is flow sensitive and fully context-sensitive even in the presence of recursion. Many methods of interprocedural analysis sacrifice precision for scalability while some are precise but limited to only a certain class of problems. Soot currently supports interprocedural analysis of Java programs using graph reachability. However, this approach is restricted to IFDS/IDE problems, and is not suitable for general data flow frameworks such as heap reference analysis and points-to analysis which have non-distributive flow functions. We describe a general-purpose interprocedural analysis framework for Soot using data flow values for context-sensitivity. This framework is not restricted to problems with distributive flow functions, although the lattice must be finite. It combines the key ideas of the tabulation method of the functional approach and the technique of value-based termination of call string construction. The efficiency and precision of interprocedural analyses is heavily affected by the precision of the underlying call graph. This is especially important for object-oriented languages like Java where virtual method invocations cause an explosion of spurious call edges if the call graph is constructed naively. We have instantiated our framework with a flow and context-sensitive points-to analysis in Soot, which enables the construction of call graphs that are far more precise than those constructed by Soot's SPARK engine.Comment: SOAP 2013 Final Versio