Set Covering Research Articles

Mitigating false negatives in imbalanced datasets: An ensemble approach

Imbalanced datasets present a challenge in machine learning, especially in binary classification scenarios where one class significantly outweighs the other. This imbalance often leads to models favoring the majority class, resulting in inadequate predictions for the minority class, specifically in false negatives. In response to this issue, this work introduces the MinFNR ensemble algorithm, designed to minimize False Negative Rates (FNR) in imbalanced datasets. The new approach strategically combines data-level, algorithmic-level, and hybrid-level approaches to enhance overall predictive capabilities while minimizing computational resources using the Set Covering Problem (SCP) formulation. Through a comprehensive evaluation of diverse datasets, MinFNR consistently outperforms individual algorithms, showing its potential for applications where the cost of false negatives is substantial, such as fraud detection and medical diagnosis. This work also contributes to ongoing efforts to improve the reliability and effectiveness of machine learning algorithms in real imbalanced scenarios.

Set Covering Routing Problems: A review and classification scheme

Set Covering Routing Problems: A review and classification scheme

The Exact Subset MultiCover problem

In this paper, we study the Exact Subset MultiCover problem (or ESM), which can be seen as an extension of the well-known Set Cover problem. Let (U,f) be a multiset built from set U={e1,e2,…,em} and function f:U→N⁎. ESM is defined as follows: given (U,f) and a collection S={S1,S2,…,Sn} of n subsets of U, is it possible to find a multiset (S′,g) with S′={S1′,S2′,…,Sn′} and g:S′→N, such that (i) Si′⊆Si for every 1≤i≤n, and (ii) each element of U appears as many times in (U,f) as in (S′,g)? We study this problem under an algorithmic viewpoint and provide diverse complexity results such as polynomial cases, NP-hardness proofs and FPT algorithms. We also study two variants of ESM: (i) Exclusive Exact Subset MultiCover (EESM), which asks that each element of U appears in exactly one subset Si′ of S′; (ii) Maximum Exclusive Exact Subset MultiCover (Max-EESM), an optimization version of EESM, which asks that a maximum number of elements of U appear in exactly one subset Si′ of S′. For both variants, we provide several complexity results; in particular we present a 2-approximation algorithm for Max-EESM, that we prove to be tight. For these three problems, we also provide an Integer Linear Programming (ILP) formulation.

DETERMINING THE OPTIMAL TEMPORARY WASTE DISPOSAL SITES IN THE ALANG-ALANG LEBAR SUB-DISTRICT PALEMBANG USING THE P-CENTRE LOCATION PROBLEM AND P-MEDIAN PROBLEM MODELS

The rapid development of Palembang City comes with an increase in population and a proportionate increase in waste. Providing Temporary Waste Disposal Sites (TWDS) with ideal locations is one way to address the waste problem in Palembang City. The location of the existing TWDS could be more regular and optimal. The problem of determining the optimal TWDS location can be solved by optimization science, as classified in the Set Covering Problem (SCP) model. The SCP model is divided into the -Center Location Problem and -Median Problem models. This study aims to determine the optimal locations for TWDS in the Alang-Alang Lebar Sub-District, Palembang City, by comparing the results of the p-Center Location Problem and p-Median Problem models. Initially, the Alang-Alang Lebar Sub-District had 33 TWDS. After formulating the Set Covering Location Problem and Maximal Covering Location Problem models, we obtain the optimal solution, which we then solve using the -Center Location Problem and -Median Problem models. Based on the results and discussion, the optimal TWDS can meet the demand of each village in the Alang-Alang Lebar Sub-District. The -Center Location Problem and -Median Problem models produce the same optimal TWDS, namely TWDS Pramuka 2 Street and around, TWDS Colonel Sulaiman Amin Street, TWDS Talang Kelapa Ujung, and TWDS Beside Soekarno Hatta Street. This study recommends using both models to determine the optimal TWDS.

Using Online Algorithms to Solve NP-Hard Problems

This paper explores the application of online algorithms to tackle NP-hard problems, a class of computational challenges characterized by their intractability and wide-ranging real-world implications. Unlike traditional offline algorithms that have access to complete input data, online algorithms make decisions sequentially, often under constraints of incomplete information. We investigate various strategies, including greedy approaches, randomization, and competitive analysis, to assess their effectiveness in solving NP-hard problems such as the Traveling Salesman Problem, the Knapsack Problem, and the Set Cover Problem. Our analysis highlights the trade-offs between solution quality and computational efficiency, emphasizing the significance of the competitive ratio in evaluating algorithm performance. Additionally, we discuss the practical applications of online algorithms in dynamic environments, such as real-time systems and streaming data processing. Through a comprehensive review of existing literature and novel algorithmic designs, we aim to provide insights into the viability of online algorithms as a robust framework for addressing NP-hard problems in scenarios where immediate decision-making is crucial. The findings underscore the potential for future research to enhance these algorithms, making them increasingly applicable in complex, real-world contexts.

Competitive Data-Structure Dynamization

Data-structure dynamization is a general approach for making static data structures dynamic. It is used extensively in geometric settings and in the guise of so-called merge (or compaction) policies in big-data databases such as LevelDB and Google Bigtable. Previous theoretical work is based on worst-case analyses for uniform inputs—insertions of one item at a time and non-varying read rate. In practice, merge policies must not only handle batch insertions and varying read/write ratios, they can take advantage of such non-uniformity to reduce cost on a per-input basis. To model this, we initiate the study of data-structure dynamization through the lens of competitive analysis via two new online set-cover problems. For each, the input is a sequence of disjoint sets of weighted items. The sets are revealed one at a time. The algorithm must respond to each with a set cover that covers all items revealed so far. It obtains the cover incrementally from the previous cover by adding one or more sets and optionally removing existing sets. For each new set the algorithm incurs build cost equal to the weight of the items in the set. In the first problem the objective is to minimize total build cost plus total query cost , where the algorithm incurs a query cost at each time \(t\) equal to the current cover size. In the second problem, the objective is to minimize the build cost while keeping the query cost from exceeding \(k\) (a given parameter) at any time. We give deterministic online algorithms for both variants, with competitive ratios of \(\Theta(\log^{*}n)\) and \(k\) , respectively. The latter ratio is optimal for the second variant.

Efficient Algorithm for Generating Optimal Inequality Candidates for MILP Modeling of Boolean Functions

Mixed-Integer Linear Programming (MILP) modeling has become an important tool for both the analysis and the design of symmetric cryptographic primitives. The bit-wise modeling of their nonlinear components, especially the S-boxes, is of particular interest since it allows more informative analysis compared to word-oriented models focusing on counting active S-boxes. At the same time, the size of these models, especially in terms of the number of required inequalities, tends to significantly influence and ultimately limit the applicability of this method to real-world ciphers, especially for larger number of rounds. It is therefore of great cryptographic significance to study optimal linear inequality descriptions for Boolean functions. The pioneering works of Abdelkhalek et al. (FSE 2017), Boura and Coggia (FSE 2020) and Li and Sun (FSE 2023) provided various heuristic techniques for this computationally hard problem, decomposing it into two algorithmic steps, coined Problem 1 and Problem 2, with the latter being identical to the well-known NP-hard set cover problem, for which there are many heuristic and exact algorithms in the literature. In this paper, we introduce a novel and efficient branch-and-bound algorithm for generating all minimal, non-redundant candidate inequalities that satisfy a given Boolean function, therefore solving Problem 1 in an optimal manner without relying on heuristics. We furthermore prove that our algorithm correctly computes optimal solutions. Using a number of dedicated optimizations, it provides significantly improved runtimes compared to previous approaches and allows the optimal modeling of the difference distribution tables (DDT) and linear approximation tables (LAT) of many practically used S-boxes. The source code for our algorithm is publicly available as a tool for researchers and practitioners in symmetric cryptography.

Hybrid Naïve Bayes Gaussian mixture models and SAR polarimetry based automatic flooded vegetation studies using PALSAR-2 data

Flood mapping using Synthetic Aperture Radar (SAR) data impose limitations in fully distinguishing flood under vegetation due to false double bounce returns from inundated tree trunks along with seasonal heterogeneities devised from changing land cover settings. In addition, rapid mapping of flooded vegetation is challenging during near real time applications. In this paper a fully automatic novel supervised classification approach called polarimetric Naïve Bayes is proposed that combines polarimetric information with series of Gaussian mixture models in Naïve Bayes framework to detect various flooded vegetation classes. It also allows the user to choose class configuration and eliminates creation of Region of Interest (ROI) for supervised training. The proposed approach uses scattering information from pre monsoon PolSAR dataset in training step to create ROIs for buildings and other features. In the next step series of Gaussian Mixtures are used for density estimation for different features in Bayesian multiclass problem. The newly developed classifier applied on 2016 Assam flood event resulted in precise mapping of at least three different vegetation classes under flood such as submerged vegetation, wetlands and floating vegetation. Under optimal class configuration, the approach showed better performance compared to other supervised techniques applied on the same data set such as MLE, Mahalanobis, Minimum Euclidean distance, and SVM classifications in delineating flood, submerged vegetation, wetlands and floating vegetation with Producer’s Accuracy of 98.6%, 81.1%, 94% and 51.5% respectively and combined Overall accuracy of 95.5% for flooded vegetation class. This method also detected multiple vegetation classes with better accuracy compared to similar methods.

On approximating partial scenario set cover

The Partial Scenario Set Cover problem (PSSC) generalizes the Partial Set Cover problem, which is itself a generalization of the classical Set Cover problem. We are given a finite ground set Q, a collection S of subsets of Q to choose from, each of which is associated with a nonnegative cost, and a second collection U of subsets of Q of which a given number l must be covered. The task is to choose a minimum cost sub-collection from S that covers at least l sets from U. PSSC is motivated by an application for locating emergency doctors.We present two approximation approaches. The first one combines LP-based rounding with a greedy consideration of the scenarios. The other is a variant of the greedy set cover algorithm, and in each iteration tries to minimize the ratio of cost to number of newly covered scenarios. We show that this subproblem, which we call Dense Scenario Set Cover (DSSC), is itself as hard to approximate as Set Cover and NP-hard, even when there is only a single scenario and all sets contain at most three elements. Furthermore, we consider a special case of DSSC where the sets are pairwise disjoint and show that in this case DSSC can be solved in polynomial time. We also provide an approximation for the general case, which we use as a subroutine in the greedy algorithm to obtain an approximation for PSSC.

Combined Location Set Covering Model and Multi-Criteria Decision Analysis for Emergency Medical Service Assessment

Combined Location Set Covering Model and Multi-Criteria Decision Analysis for Emergency Medical Service Assessment

Quadratic p-Median Problem: A Bender’s Decomposition and a Meta-Heuristic Local-Based Approach

In this paper, the quadratic p-median optimization problem is discussed, where the goal is to connect users to a selected group of facilities (emergency services, telecommunications servers, healthcare facilities) at the lowest possible cost. The problem is aimed at minimizing the cost of connecting these selected facilities. The costs are symmetric, meaning connecting two different points is the same in both directions. This problem extends the traditional p-median problem, a combinatorial problem used in various fields like facility location, network design, transportation, supply chain networks, emergency services, healthcare, and education planning. Surprisingly, the quadratic version has not been thoroughly considered in the literature. The paper highlights the formulation of two mixed-integer quadratic programming models to find optimal solutions to this problem. One model is a classic formulation, and the other is based on set cover theory. Linear versions and Bender’s decomposition formulations for each model are also derived. A Bender’s decomposition is solved using an algorithm that adds constraints during each iteration to improve the solution. Lazy constraints in the Gurobi solver’s branch and cut algorithm are dynamically added whenever a mixed-integer programming solution is found. Additionally, an efficient local search meta-heuristic is proposed that usually finds optimal solutions for tested instances. Challenging instances with up to 60 facilities and 2000 users are successfully solved. Our results show that Bender’s models with lazy constraints are the most effective for Euclidean and random test cases, achieving optimal solutions in less CPU time. The meta-heuristic also finds near-optimal solutions rapidly for these cases.

CellCover Captures Neural Stem Cell Progression in Mammalian Neocortical Development.

Definition of cell classes across the tissues of living organisms is central in the analysis of growing atlases of single-cell RNA sequencing (scRNA-seq) data across biomedicine. Marker genes for cell classes are most often defined by differential expression (DE) methods that serially assess individual genes across landscapes of diverse cells. This serial approach has been extremely useful, but is limited because it ignores possible redundancy or complementarity across genes that can only be captured by analyzing multiple genes simultaneously. We aim to identify discriminating panels of genes. To efficiently explore the vast space of possible marker panels, leverage the large number of cells often sequenced, and overcome zero-inflation in scRNA-seq data, we propose viewing gene panel selection as a variation of the "minimal set-covering problem" in combinatorial optimization. We show that this new method, CellCover, captures cell-class-specific signals in the developing mouse neocortex that are distinct from those defined by DE methods. Transfer learning experiments across mouse, primate, and human data demonstrate that CellCover identifies markers of conserved cell classes in neurogenesis, as well as temporal progression in both progenitors and neurons. Exploring markers of human outer radial glia (oRG, or basal RG) across mammals, we show that transcriptomic elements of this key cell type in the expansion of the human cortex appeared in gliogenic precursors of the rodent before the full program emerged in the primate lineage. We have assembled the public datasets we use in this report at NeMO analytics where the expression of individual genes {NeMO Individual Genes} and marker gene panels can be freely explored {NeMO: Telley 3 Sets Covering Panels}, {NeMO: Telley 12 Sets Covering Panels}, and {NeMO: Sorted Brain Cell Covering Panels}. CellCover is available in {CellCover R} and {CellCover Python}.

Approximating power node-deletion problems

In the Power Vertex Cover(PVC) problem introduced in [1] as a generalization of the well-known Vertex Cover, we are allowed to specify costs for covering edges in a graph individually. Namely, two (nonnegative) weights, w(u,v) and w(v,u), are associated with each edge {u,v}∈E of an input graph G=(V,E), and to cover an edge {u,v}, it is required to assign “power” p∈R+V on vertices of G such that either p(u)≥w(u,v) or p(v)≥w(v,u). The objective is to minimize the total power assigned on V, ∑v∈Vp(v), while covering all the edges of G by p.The node-deletion problem for a graph property π is the problem of computing a minimum vertex subset C⊆V in a given graph G=(V,E), such that the graph satisfies π when all the vertices in C are removed from G. In this paper we consider node-deletion problems extended with the “covering-by-power” condition as in PVC, and present a unified approach for effectively approximating them. The node-deletion problems considered are Partial Vertex Cover (PartVC), Bounded Degree Deletion (BDD), and Feedback Vertex Set (FVS), each corresponding to graph properties π= “the graph has at most |E|−k edges”, π= “vertex degree of v is no larger than b(v)”, and π= “the graph is acyclic”, respectively. After reducing these problems to the Submodular Set Cover (SSC) problem, we conduct an extended analysis of the approximability of these problems in the new setting of power covering by applying some of the existing techniques for approximating SSC. It will be shown that 1) PPartVC can be approximated within a factor of 2, 2) PBDD for b∈Z+V within max⁡{2,1+bmax}, where bmax=maxv∈V⁡b(v), or within 2+log⁡bmax (for bmax≥1) by a combination of the greedy SSC algorithm and the local ratio method extended for power node-deletion problems, and 3) PFVS within 2, resulting in each of these bounds matching the best one known for the corresponding original problem.

Utilizing Heuristics and Metaheuristics for Solving the Set Covering Problem

A basic combinatorial optimization problem, the Set Covering Problem (SCP) finds extensive use in computer science, operations research, and logistics, among other domains. The SCP’s goal is to determine the smallest number of subsets, or sets, needed to cover every element precisely once given a finite set of items and a collection of subsets of these elements. Numerous practical uses for the SCP exist, such as crew scheduling, truck routing, and facility locating. This paper focuses on obtaining feasible solutions, applying to the obtained solutions constructive heuristics (CH), followed by a redundancy elimination procedure to remove unnecessary sets. To further optimize the quality of the solution, a local search method is also implemented based on the First and Best improvement algorithms. Additionally, the Greedy Randomized Adaptive Search Procedure (GRASP) and Variable Neighborhood Search (VNS) metaheuristics are designed and implemented. Each implemented heuristic underwent testing across 42 instances, with the average deviation from the optimal solution calculated for each instance. The GRASP heuristic demonstrated the most favorable performance, achieving a maximum deviation of 2.26% from the optimal solution, while the VNS approach yielded a maximum deviation of 11.46% from the optimal solution at its best.

Utilizing Heuristics and Metaheuristics for Solving the Set Covering Problem

A basic combinatorial optimization problem, the Set Covering Problem (SCP) finds extensive use in computer science, operations research, and logistics, among other domains. The SCP’s goal is to determine the smallest number of subsets, or sets, needed to cover every element precisely once given a finite set of items and a collection of subsets of these elements. Numerous practical uses for the SCP exist, such as crew scheduling, truck routing, and facility locating. This paper focuses on obtaining feasible solutions, applying to the obtained solutions constructive heuristics (CH), followed by a redundancy elimination procedure to remove unnecessary sets. To further optimize the quality of the solution, a local search method is also implemented based on the First and Best improvement algorithms. Additionally, the Greedy Randomized Adaptive Search Procedure (GRASP) and Variable Neighborhood Search (VNS) metaheuristics are designed and implemented. Each implemented heuristic underwent testing across 42 instances, with the average deviation from the optimal solution calculated for each instance. The GRASP heuristic demonstrated the most favorable performance, achieving a maximum deviation of 2.26% from the optimal solution, while the VNS approach yielded a maximum deviation of 11.46% from the optimal solution at its best.

A Branch-and-Cut-and-Price Algorithm for Cutting Stock and Related Problems

In this project, we introduce a branch-and-cut-and-price framework to solve the Cutting Stock Problems with strong relaxations using the Set Covering (Packing) Formulations, which are solved through column generation. We propose an extended Ryan-Foster branching scheme tailored to non-binary models, a pricing algorithm that produces convergence in a few iterations, and a variable selection technique based on branching history. These strategies are combined with subset-row cuts and custom primal heuristics to create a framework that overcomes the current state-of-the-art of Cutting Stock Problem, Skiving Stock Problem, and other related problems, being at least twice faster in the first problem and at least 60% faster in the second one.

A succinct and approximate greedy algorithm for the Minimum Set Cover Problem

The Minimum Set Cover Problem (MSCP) is a combinatorial optimization problem belonging to the NP-Hard class in computer science. For this reason, there is no algorithm that in the worst case ensures finding an optimal solution in polynomial-time. For a given universe X, the popular greedy heuristic, called Greedy-SetCover, is the main theoretical contribution to obtain an approximate solution for the MSCP in polynomial-time, offering an optimal approximate ratio of (ln|X|+1). In this article, we propose an approximate algorithm for MSCP within a succinct representation of the input dataset, whose empirical performance improves Greedy-SetCover both in quality and execution time, while offering the same optimal approximation ratio for the problem. Our experiments show that the proposed algorithm is magnitudes of times faster than the aforementioned greedy one, obtaining on average a cardinality much closer to the optimal solution. Furthermore, because we work on a succinct representation that allows us to compute operations between sets using bitwise operators, we can process much larger datasets than state-of-the-art solutions. As a result, our proposal is also a suitable alternative for processing large datasets as required by the current Big Data era.

An efficient approach for discovering Graph Entity Dependencies (GEDs)

Graph entity dependencies (GEDs) are novel graph constraints, unifying keys and functional dependencies, for property graphs. They have been found useful in many real-world data quality and data management tasks, including fact checking on social media networks and entity resolution. In this paper, we study the discovery problem of GEDs—finding a minimal cover of valid GEDs in a given graph data. We formalise the problem, and propose an effective and efficient approach to overcome major bottlenecks in GED discovery. In particular, we leverage existing graph partitioning algorithms to enable fast GED-scope discovery, and employ effective pruning strategies over the prohibitively large space of candidate dependencies. Furthermore, we define an interestingness measure for GEDs based on the minimum description length principle, to score and rank the mined cover set of GEDs. Finally, we demonstrate the scalability and effectiveness of our GED discovery approach through extensive experiments on real-world benchmark graph data sets; and present the usefulness of the discovered rules in different downstream data quality management applications.

PPB-MCTS: A novel distributed-memory parallel partial-backpropagation Monte Carlo tree search algorithm

Monte-Carlo Tree Search (MCTS) is an adaptive and heuristic tree-search algorithm designed to uncover sub-optimal actions at each decision-making point. This method progressively constructs a search tree by gathering samples throughout its execution. Predominantly applied within the realm of gaming, MCTS has exhibited exceptional achievements. Additionally, it has displayed promising outcomes when employed to solve NP-hard combinatorial optimization problems. MCTS has been adapted for distributed-memory parallel platforms. The primary challenges associated with distributed-memory parallel MCTS are the substantial communication overhead and the necessity to balance the computational load among various processes. In this work, we introduce a novel distributed-memory parallel MCTS algorithm with partial backpropagations, referred to as Parallel Partial-Backpropagation MCTS (PPB-MCTS). Our design approach aims to significantly reduce the communication overhead while maintaining, or even slightly improving, the performance in the context of combinatorial optimization problems. To address the communication overhead challenge, we propose a strategy involving transmitting an additional backpropagation message. This strategy avoids attaching an information table to the communication messages exchanged by the processes, thus reducing the communication overhead. Furthermore, this approach contributes to enhancing the decision-making accuracy during the selection phase. The load balancing issue is also effectively addressed by implementing a shared transposition table among the parallel processes. Furthermore, we introduce two primary methods for managing duplicate states within distributed-memory parallel MCTS, drawing upon techniques utilized in addressing duplicate states within sequential MCTS. Duplicate states can transform the conventional search tree into a Directed Acyclic Graph (DAG). To evaluate the performance of our proposed parallel algorithm, we conduct an extensive series of experiments on solving instances of the Job-Shop Scheduling Problem (JSSP) and the Weighted Set-Cover Problem (WSCP). These problems are recognized for their complexity and classified as NP-hard combinatorial optimization problems with considerable relevance within industrial applications. The experiments are performed on a cluster of computers with many cores. The empirical results highlight the enhanced scalability of our algorithm compared to that of the existing distributed-memory parallel MCTS algorithms. As the number of processes increases, our algorithm demonstrates increased rollout efficiency while maintaining an improved load balance across processes.

Trajectory tracking attack for vehicular ad‐hoc networks

AbstractMaintaining user privacy and security is a critical concern in vehicular ad hoc networks (VANETs). However, prior research has neglected the study of matrix recovery attack methods in VANETs and the challenge of reducing the number of roadside units (RSUs). In this article, we formulate a path recovery strategy using matrix recovery techniques from an adversarial view. Subsequently, the challenge of minimizing RSUs while monitoring all user vehicles in a region is converted into a set cover problem. We introduce a heuristic algorithm that utilizes clustering to address this issue. To minimize matrix recovery errors, a Kalman filter based method is integrated to enhance the performance. This paper also presents an initial deployment of path recovery attacks, maintaining effectiveness even with certain defense mechanisms in place. Furthermore, we conduct simulation experiments to evaluate the effectiveness of the proposed attack strategy. The simulation results demonstrate the performance across various dimensions. Finally, the results show that the success rate of our proposed counter‐defense strategy in overcoming user defenses surpasses 50%.