Efficient algorithms for dynamic bidirected Dyck-reachability

Dyck-reachability is a fundamental formulation for program analysis, which has been widely used to capture properly-matched-parenthesis program properties such as function calls/returns and field writes/reads. Bidirected Dyck-reachability is a relaxation of Dyck-reachability on bidirected graphs where each edge u → ( i v labeled by an open parenthesis “( i ” is accompanied with an inverse edge v → ) i u labeled by the corresponding close parenthesis “) i ”, and vice versa. In practice, many client analyses such as alias analysis adopt the bidirected Dyck-reachability formulation. Bidirected Dyck-reachability admits an optimal reachability algorithm. Specifically, given a graph with n nodes and m edges, the optimal bidirected Dyck-reachability algorithm computes all-pairs reachability information in O ( m ) time. This paper focuses on the dynamic version of bidirected Dyck-reachability. In particular, we consider the problem of maintaining all-pairs Dyck-reachability information in bidirected graphs under a sequence of edge insertions and deletions. Dynamic bidirected Dyck-reachability can formulate many program analysis problems in the presence of code changes. Unfortunately, solving dynamic graph reachability problems is challenging. For example, even for maintaining transitive closure, the fastest deterministic dynamic algorithm requires O ( n 2 ) update time to achieve O (1) query time. All-pairs Dyck-reachability is a generalization of transitive closure. Despite extensive research on incremental computation, there is no algorithmic development on dynamic graph algorithms for program analysis with worst-case guarantees. Our work fills the gap and proposes the first dynamic algorithm for Dyck reachability on bidirected graphs. Our dynamic algorithms can handle each graph update ( i.e. , edge insertion and deletion) in O ( n ·α( n )) time and support any all-pairs reachability query in O (1) time, where α( n ) is the inverse Ackermann function. We have implemented and evaluated our dynamic algorithm on an alias analysis and a context-sensitive data-dependence analysis for Java. We compare our dynamic algorithms against a straightforward approach based on the O ( m )-time optimal bidirected Dyck-reachability algorithm and a recent incremental Datalog solver. Experimental results show that our algorithm achieves orders of magnitude speedup over both approaches.

Proposal of a Dynamic Algorithm for the Maintenance and Vehicle Routing Problem with Time Windows

Context: In the context of business organizations, every process in which the product is immersed has a cost and time associated with it. The area of maintenance planning and scheduling is no exception; however, it is an aspect in which few companies specialize, tending to be outsourced. In this sense, the application of combinatorial models is a tool with a high potential to improve the overall performance of the organization through the understanding of the integral maintenance process. Method: A two-phase (maintenance and routing) dynamic algorithm is proposed which considers a set of clients distributed in a maintenance network (distance), where each of the technicians start from the same central node (depot), which, in turn, is the endpoint of each assigned route. The objective is to minimize the total cost associated with the development of preventive and corrective maintenance of all machines to be evaluated. With this purpose, the formulation of the mathematical problem for each of the phases and its interrelation method is proposed. Then, performance measures are expressed to evaluate the achieved objectives. Results: The results satisfy a consistent alternative for the resolution of problems of the NP-Hard type, which generates a high level of complexity to the model. That is, it proposes a tool for solving problems of these characteristics in low computational response times and with appealing results. Conclusions: The combined maintenance and routing model using a dynamic algorithm addresses the maintenance and routing problem satisfactorily. The model shows good results with respect to the comparison optimization model in percentage gaps of performance measures lower than 5%. As for the computational time required, a reduction of up to 98% was achieved, which makes it an ideal alternative for highly complex scenarios. Finally, achieving a higher level of characterization, employing multi-objective decision criteria and a greater number of constraints to the problem, is proposed in future research. Acknowledgements: To the High-Performance Computing Center (CECAD - Centro de computación de Alto Desempeño) of Universidad Distrital Francisco José de Caldas for their support, as well as for providing us with a virtual machine to run the proposed mathematical model, which was an essential element in the results obtained.

Exact Maximum Clique Algorithm for Different Graph Types Using Machine Learning

Finding a maximum clique is important in research areas such as computational chemistry, social network analysis, and bioinformatics. It is possible to compare the maximum clique size between protein graphs to determine their similarity and function. In this paper, improvements based on machine learning (ML) are added to a dynamic algorithm for finding the maximum clique in a protein graph, Maximum Clique Dynamic (MaxCliqueDyn; short: MCQD). This algorithm was published in 2007 and has been widely used in bioinformatics since then. It uses an empirically determined parameter, Tlimit, that determines the algorithm’s flow. We have extended the MCQD algorithm with an initial phase of a machine learning-based prediction of the Tlimit parameter that is best suited for each input graph. Such adaptability to graph types based on state-of-the-art machine learning is a novel approach that has not been used in most graph-theoretic algorithms. We show empirically that the resulting new algorithm MCQD-ML improves search speed on certain types of graphs, in particular molecular docking graphs used in drug design where they determine energetically favorable conformations of small molecules in a protein binding site. In such cases, the speed-up is twofold.

An MPA Design Approach to Benefit Fisheries: Maximising Larval Export and Minimising Redundancy

In the design of marine protected areas (MPAs), tailoring reserve placement to facilitate larval export beyond reserve boundaries may support fished populations and fisheries through recruitment subsidies. Intuitively, capturing such connectivity could be purely based on optimising larval dispersal metrics such as export strength. However, this can lead to inefficient or redundant larval connectivity, as the subset of sites with the best connectivity metrics might share many of the same connections, making them, collectively, poor MPA candidates to provide recruitment subsidies to unprotected sites. We propose a simple, dynamic algorithm for reserve placement optimisation designed to select MPAs sequentially, maximising larval export to the overall network, whilst accounting for redundancy in supply from multiple sources. When applied to four regions in the Caribbean, the algorithm consistently outperformed approaches that did not consider supply redundancy, leading to, on average, 20% greater fished biomass in a simulated model. Improvements were most apparent in dense, strongly connected systems such as the Bahamas. Here, MPA placement without redundancy considerations produced fishery benefits worse than random MPA design. Our findings highlight the importance of considering redundancy in MPA design, and offer a novel, simple approach to improving MPA design for achieving fishery objectives.

DACBench: A Benchmark Library for Dynamic Algorithm Configuration

Dynamic Algorithm Configuration (DAC) aims to dynamically control a target algorithm's hyperparameters in order to improve its performance. Several theoretical and empirical results have demonstrated the benefits of dynamically controlling hyperparameters in domains like evolutionary computation, AI Planning or deep learning. Replicating these results, as well as studying new methods for DAC, however, is difficult since existing benchmarks are often specialized and incompatible with the same interfaces. To facilitate benchmarking and thus research on DAC, we propose DACBench, a benchmark library that seeks to collect and standardize existing DAC benchmarks from different AI domains, as well as provide a template for new ones. For the design of DACBench, we focused on important desiderata, such as (i) flexibility, (ii) reproducibility, (iii) extensibility and (iv) automatic documentation and visualization. To show the potential, broad applicability and challenges of DAC, we explore how a set of six initial benchmarks compare in several dimensions of difficulty.