Exponential Execution Time Research Articles

Resilient Team Formation with Stabilisability of Agent Networks for Task Allocation

Team formation (TF) faces the problem of defining teams of agents able to accomplish a set of tasks. Resilience on TF problems aims to provide robustness and adaptability to unforeseen events involving agent deletion. However, agents are unaware of the inherent social welfare in these teams. This article tackles the problem of how teams can minimise their effort in terms of organisation and communication considering these dynamics. Our main contribution is twofold: first, we introduce the Stabilisable Team Formation (STF) as a generalisation of current resilient TF model, where a team is stabilisable if it possesses and preserves its inter-agent organisation from a graph-based perspective. Second, our experiments show that stabilisability is able to reduce the exponential execution time in several units of magnitude with the most restrictive configurations, proving that communication effort in subsequent task allocation problems are relaxed compared with current resilient teams. To do so, we developed SBB-ST, a branch-and-bound algorithm based on Distributed Constrained Optimisation Problems (DCOP) to compute teams. Results evidence that STF improves their predecessors, extends the resilience to subsequent task allocation problems represented as DCOP, and evidence how Stabilisability contributes to resilient TF problems by anticipating decisions for saving resources and minimising the effort on team organisation in dynamic scenarios.

IoT networks 3D deployment using hybrid many-objective optimization algorithms

When resolving many-objective problems, multi-objective optimization algorithms encounter several difficulties degrading their performances. These difficulties may concern the exponential execution time, the effectiveness of the mutation and recombination operators or finding the tradeoff between diversity and convergence. In this paper, the issue of 3D redeploying in indoor the connected objects (or nodes) in the Internet of Things collection networks (formerly known as wireless sensor nodes) is investigated. The aim is to determine the ideal locations of the objects to be added to enhance an initial deployment while satisfying antagonist objectives and constraints. In this regard, a first proposed contribution aim to introduce an hybrid model that includes many-objective optimization algorithms relying on decomposition (MOEA/D, MOEA/DD) and reference points (Two_Arch2, NSGA-III) while using two strategies for introducing the preferences (PI-EMO-PC) and the dimensionality reduction (MVU-PCA). This hybridization aims to combine the algorithms advantages for resolving the many-objective issues. The second contribution concerns prototyping and deploying real connected objects which allows assessing the performance of the proposed hybrid scheme on a real world environment. The obtained experimental and numerical results show the efficiency of the suggested hybridization scheme against the original algorithms.

A partition-based optimization model and its performance benchmark for Generative Anatomy Modeling Language

BackgroundThis paper presents a novel iterative approach and rigorous accuracy testing for geometry modeling language - a Partition-based Optimization Model for Generative Anatomy Modeling Language (POM-GAML). POM-GAML is designed to model and create anatomical structures and their variations by satisfying any imposed geometric constraints using a non-linear optimization model. Model partitioning of POM-GAML creates smaller sub-problems of the original model to reduce the exponential execution time required to solve the constraints in linear time with a manageable error. MethodWe analyzed our model concerning the iterative approach and graph parameters for different constraint hierarchies. The iteration was used to reduce the error for partitions and solve smaller sub-problems generated by various clustering/community detection algorithms. We empirically tested our model with eleven graph parameters. Graphs for each parameter with increasing constraint sets were generated to evaluate the accuracy of our method. ResultsThe average decrease in normalized error with respect to the original problem using cluster/community detection algorithms for constraint sets was above 63.97%. The highest decrease in normalized error after five iterations for the constraint set of 3900 was 70.31%, while the lowest decrease for the constraint set of 3000 was with 63.97%. Pearson correlation analysis between graph parameters and normalized error was carried out. We identified that graph parameters such as diameter, average eccentricity, global efficiency, and average local efficiency showed strong correlations to the normalized error. ConclusionsWe observed that iteration monotonically decreases the error in all experiments. Our iteration results showed decreased normalized error using the partitioned constrained optimization by linear approximation to the non-linear optimization model.

Partition-based optimization model for generative anatomy modeling language (POM-GAML)

BackgroundThis paper presents a novel approach for Generative Anatomy Modeling Language (GAML). This approach automatically detects the geometric partitions in 3D anatomy that in turn speeds up integrated non-linear optimization model in GAML for 3D anatomy modeling with constraints (e.g. joints). This integrated non-linear optimization model requires the exponential execution time. However, our approach effectively computes the solution for non-linear optimization model and reduces computation time from exponential to linear time. This is achieved by grouping the 3D geometric constraints into communities.MethodsVarious community detection algorithms (k-means clustering, Clauset Newman Moore, and Density-Based Spatial Clustering of Applications with Noise) were used to find communities and partition the non-linear optimization problem into sub-problems. GAML was used to create a case study for 3D shoulder model to benchmark our approach with up to 5000 constraints.ResultsOur results show that the computation time was reduced from exponential time to linear time and the error rate between the partitioned and non-partitioned approach decreases with the increasing number of constraints. For the largest constraint set (5000 constraints), speed up was over 2689-fold whereas error was computed as low as 2.2%.ConclusionThis study presents a novel approach to group anatomical constraints in 3D human shoulder model using community detection algorithms. A case study for 3D modeling for shoulder models developed for arthroscopic rotator cuff simulation was presented. Our results significantly reduced the computation time in conjunction with a decrease in error using constrained optimization by linear approximation, non-linear optimization solver.

Efficient detection and validation of atomicity violations in concurrent programs

Atomicity violations are a major source of bugs in concurrent programs. Empirical studies have shown that the majority of atomicity violations are instances of the three-access pattern, where two accesses to a shared variable by a thread are interleaved by an access to the same variable by another thread. This article describes two advancements in atomicity violation detection. First, we describe a new technique that directs the execution of a dynamic analysis tool towards three-access pattern (TAP) instances. The directed search is based on constraint solving and concolic execution. We implemented this technique in a tool called AtomChase. Using 27 benchmarks comprising 5.4 million lines of Java, we compared AtomChase to five other tools. AtomChase found 20% more TAP instances than all five tools combined. Second, we show that not all TAP instances are atomicity violations and present a formally grounded approach to validating the non-atomicity of TAP instances. This approach, called HyperCV, prevents the inclusion of false positives in results presented to users. HyperCV uses a set of provably sufficient conditions for non-atomicity to efficiently validate TAP instances. Using the same benchmarks, HyperCV validated 79% of TAP instances in linear rather than exponential execution time.

Parallel discovery of network motifs

Many natural structures can be naturally represented by complex networks. Discovering network motifs, which are overrepresented patterns of inter-connections, is a computationally hard task related to graph isomorphism. Sequential methods are hindered by an exponential execution time growth when we increase the size of motifs and networks. In this article we study the opportunities for parallelism in existing methods and propose new parallel strategies that adapt and extend one of the most efficient serial methods known from the Fanmod tool. We propose both a master–worker strategy and one with distributed control, in which we employ a randomized receiver initiated methodology capable of providing dynamic load balancing during the whole computation process. Our strategies are capable of dealing both with exact and approximate network motif discovery. We implement and apply our algorithms to a set of representative networks and examine their scalability up to 128 processing cores. We obtain almost linear speedups, showcasing the efficiency of our proposed approach and are able to reach motif sizes that were not previously achievable using conventional serial algorithms.

Reliability analysis of N‐version programming with deadline mechanism

In this paper reliability models for fault tolerant N‐version programming and consensus recovery block (combination of N‐version programming and recovery block) with deadline mechanism are analysed. Explicit expressions for reliability of N‐version programming and consensus recovery block with exponential execution times are derived. The paper also presents optimisation models for real time N‐version programming. The objective of the optimisation problem is to maximise reliability of the software satisfying a budget constraint. The paper also includes efficient branch and bound procedure that can be used to solve the optimisation problem.

Transient solution of multiprocessor systems with state-dependent arrivals

In this paper, the transient solution is obtained for a multiprocessor system with multiple Poisson streams of task and exponential execution times. Each task requires exactly one processor for its execution and the scheduling policy is FCFS. The scheduler schedules a newly arriving task into any one of the idle processors, and the task is rejected if there is no idle processor. For this model, the exact time-dependent solution of system size probabilities at various streams, their means, variances and correlations are obtained using the properties of tridiagonal determinants.

Reliability Analysis of Fault Tolerant Recovery Blocks

Reliability models for fault tolerant recovery blocks with exponential execution time are analysed. Explicit expressions for the reliability of independent recovery block, with exponential execution time are derived. The paper presents conditions for the optimal arrangement of versions within a recovery block. The paper also presents two optimisation models for the independent recovery blocks with exponential execution time. The objective is to maximise the reliability of the fault tolerant software satisfying a budget constraint and a constraint on the mean execution time of the software. Simple branch and bound procedures are developed that can be used to solve the optimisation problem.