Hybrid Algorithms Based on Integer Programming for the Search of Prioritized Test Data in Software Product Lines

In Software Product Lines (SPLs) it is not possible, in general, to test all products of the family. The number of products denoted by a SPL is very high due to the combinatorial explosion of features. For this reason, some coverage criteria have been proposed which try to test at least all feature interactions without the necessity to test all products, e.g., all pairs of features (pairwise coverage). In addition, it is desirable to first test products composed by a set of priority features. This problem is known as the Prioritized Pairwise Test Data Generation Problem. In this work we propose two hybrid algorithms using Integer Programming (IP) to generate a prioritized test suite. The first one is based on an integer linear formulation and the second one is based on a integer quadratic (nonlinear) formulation. We compare these techniques with two state-of-the-art algorithms, the Parallel Prioritized Genetic Solver (PPGS) and a greedy algorithm called prioritized-ICPL. Our study reveals that our hybrid nonlinear approach is clearly the best in both, solution quality and computation time. Moreover, the nonlinear variant (the fastest one) is 27 and 42 times faster than PPGS in the two groups of instances analyzed in this work.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. Partially funded by the Spanish Ministry of Economy and Competitiveness and FEDER under contract TIN2014-57341-R, the University of Málaga, Andalucía Tech and the Spanish Network TIN2015-71841-REDT (SEBASENet)

QoS Constrained Optimal Sink and Relay Placement in Planned Wireless Sensor Networks

We are given a set of sensors at given locations, a set of potential locations for placing base stations (BSs, or sinks), and another set of potential locations for placing wireless relay nodes. There is a cost for placing a BS and a cost for placing a relay. The problem we consider is to select a set of BS locations, a set of relay locations, and an association of sensor nodes with the selected BS locations, so that number of hops in the path from each sensor to its BS is bounded by hmax, and among all such feasible networks, the cost of the selected network is the minimum. The hop count bound suffices to ensure a certain probability of the data being delivered to the BS within a given maximum delay under a light traffic model. We observe that the problem is NP-Hard, and is hard to even approximate within a constant factor. For this problem, we propose a polynomial time approximation algorithm (SmartSelect) based on a relay placement algorithm proposed in our earlier work, along with a modification of the greedy algorithm for weighted set cover. We have analyzed the worst case approximation guarantee for this algorithm. We have also proposed a polynomial time heuristic to improve upon the solution provided by SmartSelect. Our numerical results demonstrate that the algorithms provide good quality solutions using very little computation time in various randomly generated network scenarios

User-Base Station Association in HetSNets: Complexity and Efficient Algorithms

This work considers the problem of user association to small-cell base stations (SBSs) in a heterogeneous and small-cell network (HetSNet). Two optimization problems are investigated, which are maximizing the set of associated users to the SBSs (the unweighted problem) and maximizing the set of weighted associated users to the SBSs (the weighted problem), under signal-to-interference-plus-noise ratio (SINR) constraints. Both problems are formulated as linear integer programs. The weighted problem is known to be NP-hard and, in this paper, the unweighted problem is proved to be NP-hard as well. Therefore, this paper develops two heuristic polynomial-time algorithms to solve both problems. The computational complexity of the proposed algorithms is evaluated and is shown to be far more efficient than the complexity of the optimal brute-force (BF) algorithm. Moreover, the paper benchmarks the performance of the proposed algorithms against the BF algorithm, the branch-and-bound (B\&B) algorithm and standard algorithms, through numerical simulations. The results demonstrate the close-to-optimal performance of the proposed algorithms. They also show that the weighted problem can be solved to provide solutions that are fair between users or to balance the load among SBSs

JGraphT -- A Java library for graph data structures and algorithms

Mathematical software and graph-theoretical algorithmic packages to efficiently model, analyze and query graphs are crucial in an era where large-scale spatial, societal and economic network data are abundantly available. One such package is JGraphT, a programming library which contains very efficient and generic graph data-structures along with a large collection of state-of-the-art algorithms. The library is written in Java with stability, interoperability and performance in mind. A distinctive feature of this library is the ability to model vertices and edges as arbitrary objects, thereby permitting natural representations of many common networks including transportation, social and biological networks. Besides classic graph algorithms such as shortest-paths and spanning-tree algorithms, the library contains numerous advanced algorithms: graph and subgraph isomorphism; matching and flow problems; approximation algorithms for NP-hard problems such as independent set and TSP; and several more exotic algorithms such as Berge graph detection. Due to its versatility and generic design, JGraphT is currently used in large-scale commercial, non-commercial and academic research projects. In this work we describe in detail the design and underlying structure of the library, and discuss its most important features and algorithms. A computational study is conducted to evaluate the performance of JGraphT versus a number of similar libraries. Experiments on a large number of graphs over a variety of popular algorithms show that JGraphT is highly competitive with other established libraries such as NetworkX or the BGL.Comment: Major Revisio

How is a data-driven approach better than random choice in label space division for multi-label classification?

We propose using five data-driven community detection approaches from social networks to partition the label space for the task of multi-label classification as an alternative to random partitioning into equal subsets as performed by RAkELd: modularity-maximizing fastgreedy and leading eigenvector, infomap, walktrap and label propagation algorithms. We construct a label co-occurence graph (both weighted an unweighted versions) based on training data and perform community detection to partition the label set. We include Binary Relevance and Label Powerset classification methods for comparison. We use gini-index based Decision Trees as the base classifier. We compare educated approaches to label space divisions against random baselines on 12 benchmark data sets over five evaluation measures. We show that in almost all cases seven educated guess approaches are more likely to outperform RAkELd than otherwise in all measures, but Hamming Loss. We show that fastgreedy and walktrap community detection methods on weighted label co-occurence graphs are 85-92% more likely to yield better F1 scores than random partitioning. Infomap on the unweighted label co-occurence graphs is on average 90% of the times better than random paritioning in terms of Subset Accuracy and 89% when it comes to Jaccard similarity. Weighted fastgreedy is better on average than RAkELd when it comes to Hamming Loss

Analysis of Performance of Dynamic Multicast Routing Algorithms

In this paper, three new dynamic multicast routing algorithms based on the greedy tree technique are proposed; Source Optimised Tree, Topology Based Tree and Minimum Diameter Tree. A simulation analysis is presented showing various performance aspects of the algorithms, in which a comparison is made with the greedy and core based tree techniques. The effects of the tree source location on dynamic membership change are also examined. The simulations demonstrate that the Source Optimised Tree algorithm achieves a significant improvement in terms of delay and link usage when compared to the Core Based Tree, and greedy algorithm

Constructing lattice points for numerical integration by a reduced fast successive coordinate search algorithm

In this paper, we study an efficient algorithm for constructing node sets of high-quality quasi-Monte Carlo integration rules for weighted Korobov, Walsh, and Sobolev spaces. The algorithm presented is a reduced fast successive coordinate search (SCS) algorithm, which is adapted to situations where the weights in the function space show a sufficiently fast decay. The new SCS algorithm is designed to work for the construction of lattice points, and, in a modified version, for polynomial lattice points, and the corresponding integration rules can be used to treat functions in different kinds of function spaces. We show that the integration rules constructed by our algorithms satisfy error bounds of optimal convergence order. Furthermore, we give details on efficient implementation such that we obtain a considerable speed-up of previously known SCS algorithms. This improvement is illustrated by numerical results. The speed-up obtained by our results may be of particular interest in the context of QMC for PDEs with random coefficients, where both the dimension and the required numberof points are usually very large. Furthermore, our main theorems yield previously unknown generalizations of earlier results.Comment: 33 pages, 2 figure

Shortest Distances as Enumeration Problem

We investigate the single source shortest distance (SSSD) and all pairs shortest distance (APSD) problems as enumeration problems (on unweighted and integer weighted graphs), meaning that the elements $(u, v, d(u, v))$ -- where $u$ and $v$ are vertices with shortest distance $d(u, v)$ -- are produced and listed one by one without repetition. The performance is measured in the RAM model of computation with respect to preprocessing time and delay, i.e., the maximum time that elapses between two consecutive outputs. This point of view reveals that specific types of output (e.g., excluding the non-reachable pairs $(u, v, \infty)$, or excluding the self-distances $(u, u, 0)$) and the order of enumeration (e.g., sorted by distance, sorted row-wise with respect to the distance matrix) have a huge impact on the complexity of APSD while they appear to have no effect on SSSD. In particular, we show for APSD that enumeration without output restrictions is possible with delay in the order of the average degree. Excluding non-reachable pairs, or requesting the output to be sorted by distance, increases this delay to the order of the maximum degree. Further, for weighted graphs, a delay in the order of the average degree is also not possible without preprocessing or considering self-distances as output. In contrast, for SSSD we find that a delay in the order of the maximum degree without preprocessing is attainable and unavoidable for any of these requirements.Comment: Updated version adds the study of space complexit