Set Cover Algorithm Research Articles

Morphological Decomposition and Compression of Binary Images via a Minimum Set Cover Algorithm

In this paper, by a novel morphological decomposition method, we propose an efficient compression approach. Our presented decomposition arises from solving a minimum set cover problem (MSCP) obtained from the image skeleton data. We first use the skeleton pixels to create a collection of blocks which cover the foreground. The given blocks are both overlapped and too many. Hence, in order to find the minimum number of the blocks that cover the foreground, we form an MCSP. To solve this problem, we present a new algorithm of which accuracy is better than those of the known methods in the literatures. Also, its error analysis is studied to obtain an error bound. In the sequel, we present a fast algorithm which include an extra parameter by which the relation between the accuracy and CPU time can be controlled. Finally, several examples are given to confirm the efficiency of our approach.

SCAPE: Safe Charging With Adjustable Power

Wireless power transfer technology is considered as one of the promising solutions to address the energy limitation problems for end-devices, but its incurred potential risk of electromagnetic radiation (EMR) exposure is largely overlooked by most existing works. In this paper, we consider the Safe Charging with Adjustable PowEr (SCAPE) problem, namely, how to adjust the power of chargers to maximize the charging utility of devices, while assuring that EMR intensity at any location in the field does not exceed a given threshold $R_{t}$ . We present novel techniques to reformulate SCAPE into a traditional linear programming problem, and then remove its redundant constraints as much as possible to reduce computational effort. Next, we propose a series of distributed algorithms, including a fully distributed algorithm that provably achieves $(1-\epsilon)$ approximation ratio and requires only communications with neighbors within a constant distance for each charger. Through extensive simulation and testbed experiments, we demonstrate that our proposed algorithms can outperform the set-cover algorithm by up to 17.05%, and has an average performance gain of 41.1% over the existing algorithm in terms of the overall charging utility.

Localized algorithms for redundant readers elimination in RFID networks

ABSTRACTRedundant readers elimination is one of the fundamental optimization research problems in RFID networks. The problem is NP-hard and can be solved approximately using best known centralised set cover algorithms. However, either distributed or localised solutions for this problem are much more realistic and useful in practice. Different distributed and a few local algorithms are known in the literature. We propose a set of cellular automaton based algorithms for the redundant readers elimination optimization problem that are strictly local. We compare the performance of our algorithms in terms of eliminating redundant readers, tag read/write operation with other local algorithms and establish that our algorithms give much better results. We also compare our algorithms with the best known centralised approximation algorithms and find very competitive results even though our algorithms are localised.

Shortest Path Network Interdiction With Goal Threshold

Network defense and attack problems can be modeled as network interdictions. In this paper, we consider a new version of the network interdiction problem that optimizes the interdictor’s resource consumption while limiting network capacities (e.g., the shortest path) to a specified threshold. Interdictors would balance the interdiction performance and resource consumption when maximizing the performance costs too much. The most frequently-used technique is to relax the maximization restraint to certain specified threshold; however, the known algorithms provide little help in calculating the threshold restraint. We present a novel model named minimizing the interdiction resource with goal threshold based on the shortest path interdiction problem and propose two basic algorithms to solve it based on Benders decomposition and Lagrange duality, respectively. To consider the situation of complete interdiction and that of a large threshold, a corresponding set-covering algorithm and a Lagrange approximate algorithm are presented. Computational experiments show that decomposition-based algorithms generally perform better on small-world networks while duality-based algorithms perform better on regular grid networks. Analyses on network property sensitivity show that the decomposition-based algorithms are sensitive to the threshold value while the duality-based algorithms become weaker as the interdiction increment grows. Furthermore, we evaluate the performance of these two basic algorithms on a real-world Chicago transportation network. The result illustrates a significant advance; both algorithms can compute an optimal strategy for problems that scale up to real-world sizes.

A New Population of Galactic Bulge Planetary Nebulae

January 2016 – title page.%%%%The Academic Senate of Macquarie University granted this degree in 2015, but the date 2016 appears on the title page, the verso of the title page and the spine.%%%%%%%%%%%%1. Planetary nebulas - history and overview – 2. The planetary nebula luminosity function – 3. New bulge PNs – 4. Duplicate objects – 5. Other observations – 6. New bulge PNLF – 7. Results and discussion – A. Spectral features – B. Galactic bulge mosaic II survey fields – C. Galactic bulge PNs – D. Publications – References.%%%%A new population of Galactic bulge planetary nebulas is presented. Nebula candidates were discovered by systematically reviewing archival [OIII] on/off band survey imaging of the central -5⁰ ≤ l ≤ 5⁰, -5⁰ ≤ b ≤ 5⁰ region around the Galactic centre. An image segmentation and interleaving scheme was developed to facilitate this review. The resultant candidates (> 200) were then double checked against complementary archival Hα sky survey data to screen for obvious planetary nebula (PN) mimics or spurious image artefacts.%%%%Confirmatory spectroscopy of the PN candidates was pursued with thin slit, fibre multiobject and wide field spectrographs. Custom software was built to streamline interfacing with third-party spectroscopic management tools and a parallel greedy set cover algorithm implemented for efficient field selection in constrained multi-object observations.%%%%The combined imaging and spectroscopic evidence yielded true (4), probable (31) and possible (83) PNs toward the bulge. Secondary discoveries such as new PN mimics and late type stars were by-products of the confirmatory spectroscopy. Instances of literature PN duplication encountered during the investigation were noticed and documented.%%%%Spectral analysis of new PNs, including those obtained with a new optimised sky subtraction technique devised and demonstrated here, provided diagnostic data allowing radial velocity and Balmer decrement determination. Using a combined diameter and radial velocity criterion, bona fide bulge PNs were distinguished from new foreground PNs. Where Balmer decrements were available for new bulge PNs, differential aperture photometry was used to provide a modest data increment to Galactic bulge planetary nebula luminosity function (PNLF).%%%%The PNLF was revised with data from some new bulge PNs, but more significantly, by a series of corrections to the data derived from previously known bulge PNs (~225), such as improved filter transmission effects, statistically justified binning and application of a uniform bulge-relevant extinction law. The result was the most rigorous bulge PNLF to date. An improvement on the legacy PNLF, the revised PNLF exhibited a form inconsistent with typical extragalactic examples, an expected result of the unusual extinction correction method used to address bulge-specific observational limitations. Issues restricting the accuracy of the bulge PNLF were identified. Until those restrictions are ameliorated, the utility of the PNLF in aiding physical understanding…

Towards Information Diffusion in Mobile Social Networks

The emerging of mobile social networks opens opportunities for viral marketing. However, before fully utilizing mobile social networks as a platform for viral marketing, many challenges have to be addressed. In this paper, we address the problem of identifying a small number of individuals through whom the information can be diffused to the network as soon as possible, referred to as the diffusion minimization problem. Diffusion minimization under the probabilistic diffusion model can be formulated as an asymmetric $k$ -center problem which is NP-hard, and the best known approximation algorithm for the asymmetric $k$ -center problem has approximation ratio of $\log ^*n$ and time complexity $O(n^5)$ . Clearly, the performance and the time complexity of the approximation algorithm are not satisfiable in large-scale mobile social networks. To deal with this problem, we propose a community based algorithm and a distributed set-cover algorithm. The performance of the proposed algorithms is evaluated by extensive experiments on both synthetic networks and a real trace. The results show that the community based algorithm has the best performance in both synthetic networks and the real trace compared to existing algorithms, and the distributed set-cover algorithm outperforms the approximation algorithm in the real trace in terms of diffusion time.

Approximation Algorithms for Stochastic Submodular Set Cover with Applications to Boolean Function Evaluation and Min-Knapsack

We present a new approximation algorithm for the stochastic submodular set cover (SSSC) problem called adaptive dual greedy . We use this algorithm to obtain a 3-approximation algorithm solving the stochastic Boolean function evaluation (SBFE) problem for linear threshold formulas (LTFs). We also obtain a 3-approximation algorithm for the closely related stochastic min-knapsack problem and a 2-approximation for a variant of that problem. We prove a new approximation bound for a previous algorithm for the SSSC problem, the adaptive greedy algorithm of Golovin and Krause. We also consider an approach to approximating SBFE problems using the adaptive greedy algorithm, which we call the Q -value approach. This approach easily yields a new result for evaluation of CDNF (conjunctive / disjunctive normal form) formulas, and we apply variants of it to simultaneous evaluation problems and a ranking problem. However, we show that the Q -value approach provably cannot be used to obtain a sublinear approximation factor for the SBFE problem for LTFs or read-once disjunctive normal form formulas.

Decentralized RFID coverage algorithms using writeable tags

A Radio Frequency IDentification (RFID) reader network is as a collaboration of RFID readers that aim to cover (i.e., identify, monitor, and track) every RFID tag in a given area. The RFID coverage (RFC) problem is defined as follows. Given a reader network, assign to each tag t a specific reader v in its proximity such that v is responsible for covering t (called its owner), while minimizing the number of owner readers. The problem has applications in energy conservation and in eliminating readers and data redundancy from the reader networks. We introduce a number of decentralized algorithms for the RFID coverage problem: 1) algorithms RANDOM, RANDOM+, and MAX-MIN which are randomized algorithms that run in O(1) write/read rounds, 2) algorithm GDE which is an efficient decentralized implementation of the greedy set cover algorithm, and 3) an improvement of GDE which is called . Our algorithms assume that the RFID tags are writeable, where a writeable tag is a passive RFID tag with writeable memory. We show using simulation experiments that our algorithms outperform major RFID coverage algorithms in various scenarios with respect to a number of performance metrics.

Robust allocation of RF device capacity for distributed spectrum functions

Real-time awareness of radio spectrum use across frequency, geography and time is crucial to effective communications and information gathering in congested airway environments, yet acquiring this awareness presents a challenging sensing and data integration problem. A recent proposal has argued that real-time generation of spectrum usage maps might be possible through the use of existing radios in the area of interest, by exploiting their sensing capacity when they are not otherwise being used. In this paper, we assume this approach and consider the task allocation problem that it presents. We focus specifically on the development of a network-level middleware for task management, that assigns resources to prospective mapping applications based on a distributed model of device availability, and allows mapping applications (and other related RF applications) to specify what is required without worrying about how it will be accomplished. A distributed, auction-based framework is specified for task assignment and coordination, and instantiated with a family of minimum set cover algorithms for addressing "coverage" tasks. An experimental analysis is performed to investigate and quantify two types of performance benefits: (1) the basic advantage gained by exploiting knowledge of device availability, and (2) the additional advantage gained by adding redundancy in subregions where the probability of availability of assigned devices is low. To assess the effectiveness of our minimum set cover algorithms, we compute optimal solutions to a static version of the real-time coverage problem and compare performance of the algorithms to these upper bound solutions.

Active Base Station Set Optimization for Minimal Energy Consumption in Green Cellular Networks

To decrease potentially harmful effects to the environment and reduce costs of cellular network operators, the exploration of energy saving is significant. In this paper, we shed light on the following energy consumption minimization (ECM) problem: “how to select the smallest set of active base stations (BSs) that can preserve the quality of service (the minimum data rate) required by the users.” Since the ECM problem belongs to the field of integer programming and is NP-hard, we propose two low-complexity approximation algorithms that yield performance guarantees: the iterative minimal set cover algorithm and the iterative maximal coverage (IMC) algorithm. Moreover, by leveraging the submodularity theory, we establish the performance bound of the IMC algorithm. Finally, the computational complexity of our proposed algorithms is analyzed, and a simulation platform is developed to evaluate the number of active BSs of proposed approaches. The numerical results demonstrate that our proposed algorithms outperform the conventional counterpart.

Directed self-assembly cut mask assignment for unidirectional design

Recently, directed self-assembly (DSA) has emerged as a promising lithography solution for cut manufacturing. We perform a comprehensive study on the DSA aware mask optimization problem to provide a DSA friendly design on cut layers. We first formulate the problem as an integer linear programming (ILP) to assign cuts to different guiding templates, targeting both conflict minimization and line-end extension minimization. As ILP may not be scalable for very large size problems, we then propose two speed-up strategies. The first one is to decompose the initial problem into smaller ones and solve them separately, followed by solution merging without much loss of quality. The second one is using the set cover algorithm to decide the DSA guiding pattern assignment, and then legalize the template placement. Our approaches can be naturally extended to handle arbitrary DSA guiding template patterns with complicated shapes. Experimental results show that our methodologies can significantly improve the DSA friendly, i.e., both the unresolved pattern number and the line-end extensions can be reduced.

Constrained Multilinear Detection and Generalized Graph Motifs

We introduce a new algebraic sieving technique to detect constrained multilinear monomials in multivariate polynomial generating functions given by an evaluation oracle. The polynomials are assumed to have coefficients from a field of characteristic two. As applications of the technique, we show an $$O^*(2^k)$$O?(2k)-time polynomial space algorithm for the $$k$$k-sized Graph Motif problem. We also introduce a new optimization variant of the problem, called Closest Graph Motif and solve it within the same time bound. The Closest Graph Motif problem encompasses several previously studied optimization variants, like Maximum Graph Motif, Min-Substitute Graph Motif, and Min-Add Graph Motif. Finally, we provide a piece of evidence that our result might be essentially tight: the existence of an $$O^*((2-\epsilon )^k)$$O?((2-∈)k)-time algorithm for the Graph Motif problem implies an $$O((2-\epsilon ')^n)$$O((2-∈?)n)-time algorithm for Set Cover.

Greedy Algorithms for Target Coverage Lifetime Management Problem in Wireless Sensor Networks

When several low power sensors are randomly deployed in a field for monitoring targets located at fixed positions, managing the network lifetime is useful as long as replacing battery of dead sensors is not often feasible. The most commonly investigated mechanism for coverage preserving while maximizing the network lifetime is to design efficient sleep scheduling protocols, so that sensors can alternate their state between being active or not. Maximizing lifetime of a sensor network while satisfying a predefined coverage requirement is an optimization problem, which most of times cannot be optimally solved in polynomial time. In this paper, we address this problem by using set cover approach. We propose a greedy algorithm that distributes sensors among disjoints and non-disjoints set covers with the requirement that each set cover satisfies full targets coverage. The algorithm is an improvement of the classical greedy set cover algorithm, and its approximation ratio is verified to be not worse than ������ ⁡��). Simulation results show good performance over some other solutions found in the literature. We provide also a comparison of several greedy techniques found in the literature addressed in the context of different design choices linked to the target coverage problem.

SET COVER PROBLEM OF COVERAGE PLANNING IN LTE-ADVANCED RELAY NETWORKS

Various mobile devices are developing rapidly in contemporary society, such as smart phones and tablet PCs. Users are able to acquire different multimedia services through wireless communication anytime and anywhere. However, the increased demand also gives rise to a problem of insufficient bandwidth. Therefore, a fourth generation mobile telecommunications (4G) technology was proposed and widely investigated. One of the popular technologies is Long Term Evolution Advanced (LTE-Advanced), which was proposed by the Third Generation Project Partnership (3GPP). The Evolved Node B (eNB) and Relay Node (RN) are the major components in an LTE-Advanced network. How best to deploy these two components to extend network coverage and expand performance is a vital issue. In this paper, we utilize an integer linear programming model (ILP) to formulate the coverage problem, and refer to a well-known problem called the SetCover problem. Then we propose a heuristic algorithm named as the Set Covering algorithm to solve it. The ultimate object is achieving the highest network coverage and capacity with the least uncovered mobile user. In the simulation result, we use MATLAB to simulate a network deployment, and evaluate the planning results. According to the simulation results, we accomplished better network capacity and a higher number of covered users.

On the Set Cover Problem for Broadcasting in Wireless Ad Hoc Networks

The set cover problem has been extensively used in broadcast algorithms to model the process of selecting the nodes that should forward a message. Surprisingly, none of the research efforts focuses on solving the set cover problem. Instead, virtually every broadcast scheme uses the well known and generic purpose Greedy Set Cover (GSC) algorithm to tackle the problem. We focus on solving the set cover problem in the context of wireless ad hoc networks and show that providing an efficient solution has a significant performance impact on broadcast algorithms.

Exact algorithms and APX-hardness results for geometric packing and covering problems

We study several geometric set cover and set packing problems involving configurations of points and geometric objects in Euclidean space. We show that it is APX-hard to compute a minimum cover of a set of points in the plane by a family of axis-aligned fat rectangles, even when each rectangle is an ϵ-perturbed copy of a single unit square. We extend this result to several other classes of objects including almost-circular ellipses, axis-aligned slabs, downward shadows of line segments, downward shadows of graphs of cubic functions, fat semi-infinite wedges, 3-dimensional unit balls, and axis-aligned cubes, as well as some related hitting set problems. We also prove the APX-hardness of a related family of discrete set packing problems. Our hardness results are all proven by encoding a highly structured minimum vertex cover problem which we believe may be of independent interest.In contrast, we give a polynomial-time dynamic programming algorithm for geometric set cover where the objects are pseudodisks containing the origin or are downward shadows of pairwise 2-intersecting x-monotone curves. Our algorithm extends to the weighted case where a minimum-cost cover is required. We give similar algorithms for several related hitting set and discrete packing problems.

Analysis and visualisation of structure of smartphone application services using text mining and the set-covering algorithm: a case of App Store

This paper analyses and visualises the structure of smartphone application services to identify which smartphone application services are being developed and provided in detail. Using text information contained in web documents, the structure of smartphone application services is quantitatively and systematically analysed through two steps. First, representative services are identified and characterised to find distinctive features of current smartphone application services in the App Store by using text–mining and the set–covering algorithm. Second, based on representative services, three visual forms ? grid, tree, and network ? are illustrated to illuminate the structure of smartphone application services.

Data and task parallelism in ILP using MapReduce

Nearly two decades of research in the area of Inductive Logic Programming (ILP) have seen steady progress in clarifying its theoretical foundations and regular demonstrations of its applicability to complex problems in very diverse domains. These results are necessary, but not sufficient, for ILP to be adopted as a tool for data analysis in an era of very large machine-generated scientific and industrial datasets, accompanied by programs that provide ready access to complex relational information in machine-readable forms (ontologies, parsers, and so on). Besides the usual issues about the ease of use, ILP is now confronted with questions of implementation. We are concerned here with two of these, namely: can an ILP system construct models efficiently when (a) Dataset sizes are too large to fit in the memory of a single machine; and (b) Search space sizes becomes prohibitively large to explore using a single machine. In this paper, we examine the applicability to ILP of a popular distributed computing approach that provides a uniform way for performing data and task parallel computations in ILP. The MapReduce programming model allows, in principle, very large numbers of processors to be used without any special understanding of the underlying hardware or software involved. Specifically, we show how the MapReduce approach can be used to perform the coverage-test that is at the heart of many ILP systems, and to perform multiple searches required by a greedy set-covering algorithm used by some popular ILP systems. Our principal findings with synthetic and real-world datasets for both data and task parallelism are these: (a) Ignoring overheads, the time to perform the computations concurrently increases with the size of the dataset for data parallelism and with the size of the search space for task parallelism. For data parallelism this increase is roughly in proportion to increases in dataset size; (b) If a MapReduce implementation is used as part of an ILP system, then benefits for data parallelism can only be expected above some minimal dataset size, and for task parallelism can only be expected above some minimal search-space size; and (c) The MapReduce approach appears better suited to exploit data-parallelism in ILP.

Hierarchical Clustering of Shotgun Proteomics Data

A new result report for Mascot search results is described. A greedy set cover algorithm is used to create a minimal set of proteins, which is then grouped into families on the basis of shared peptide matches. Protein families with multiple members are represented by dendrograms, generated by hierarchical clustering using the score of the nonshared peptide matches as a distance metric. The peptide matches to the proteins in a family can be compared side by side to assess the experimental evidence for each protein. If the evidence for a particular family member is considered inadequate, the dendrogram can be cut to reduce the number of distinct family members.

Emergency Medical Service Location Problem

This paper suggests emergency medical service vehicle (ambulance) algorithm when the emergency patient occurs in order to be sufficient the maximum permission time T of arrival about all sectors in one city that is divided in the various areas. This problem cannot be solved in polynomial times. One can obtains the solution using the integer programming. In this paper we suggest vertex set (or dominating set) algorithm and easily decide the location of ambulances. The core of the algorithm decides the location of ambulance is to the maximum degree vertex among the neighborhood of minimum degree vertex. For the 33 sectors Ostin city in Texas, we apply minutes. The traditional set cover algorithm with integer programming cannot obtains the solution in several T in 18 cases. But, this algorithm obtains solution for all of the 18 cases.