Journal of Combinatorial Optimization最新文献

In the Vertex Triangle 2-Club problem, we are given an undirected graph G and aim to find a maximum-vertex subgraph of G that has diameter at most 2 and in which every vertex is contained in at least (ell ) triangles in the subgraph. So far, the only algorithm for solving Vertex Triangle 2-Club relies on an ILP formulation (Almeida and Brás in Comput Oper Res 111:258–270, 2019). In this work, we develop a combinatorial branch-and-bound algorithm that, coupled with a set of data reduction rules, outperforms the existing implementation and is able to find optimal solutions on sparse real-world graphs with more than 100,000 vertices in a few minutes. We also extend our algorithm to the Edge Triangle 2-Club problem where the triangle constraint is imposed on all edges of the subgraph.

This paper addresses the minmax regret 1-sink location problem on a dynamic flow path network with parametric weights. A dynamic flow path network consists of an undirected path with positive edge lengths, positive edge capacities, and nonnegative vertex weights. A path can be considered as a road, an edge length as the distance along the road, and a vertex weight as the number of people at the site. An edge capacity limits the number of people that can enter the edge per unit time. We consider the problem of locating a sink where all the people evacuate quickly. In our model, each weight is represented by a linear function of a common parameter t, and the decision maker who determines the sink location does not know the value of t. We formulate the problem under such uncertainty as the minmax regret problem. Given t and sink location x, the cost is the sum of arrival times at x for all the people determined by t. The regret for x under t is the gap between this cost and the optimal cost under t. The problem is to find the sink location minimizing the maximum regret over all t. For the problem, we propose an (O(n^4 2^{alpha (n)} alpha (n)^2 log n)) time algorithm, where n is the number of vertices in the network and (alpha (cdot )) is the inverse Ackermann function. Also, for the special case in which every edge has the same capacity, we show that the complexity can be reduced to (O(n^3 2^{alpha (n)} alpha (n) log n)).

Gromov–Hausdorff distances measure shape difference between the objects representable as compact metric spaces, e.g. point clouds, manifolds, or graphs. Computing any Gromov–Hausdorff distance is equivalent to solving an NP-hard optimization problem, deeming the notion impractical for applications. In this paper we propose a polynomial algorithm for estimating the so-called modified Gromov–Hausdorff (mGH) distance, a relaxation of the standard Gromov–Hausdorff (GH) distance with similar topological properties. We implement the algorithm for the case of compact metric spaces induced by unweighted graphs as part of Python library scikit-tda, and demonstrate its performance on real-world and synthetic networks. The algorithm finds the mGH distances exactly on most graphs with the scale-free property. We use the computed mGH distances to successfully detect outliers in real-world social and computer networks.

Software vulnerabilities are flaws that may be exploited to cause loss or harm. Various automated machine-learning techniques have been developed in preceding studies to detect software vulnerabilities. This work tries to develop a technique for securing the software on the basis of their vulnerabilities that are already known, by developing a hybrid deep learning model to detect those vulnerabilities. Moreover, certain countermeasures are suggested based on the types of vulnerability to prevent the attack further. For different software projects taken as the dataset, feature fusion is done by utilizing canonical correlation analysis together with Deep Residual Network (DRN). A hybrid deep learning technique trained using AdamW-Rat Swarm Optimizer (AdamW-RSO) is designed to detect software vulnerability. Hybrid deep learning makes use of the Deep Belief Network (DBN) and Generative Adversarial Network (GAN). For every vulnerability, its location of occurrence within the software development procedures and techniques of alleviation via implementation level or design level activities are described. Thus, it helps in understanding the appearance of vulnerabilities, suggesting the use of various countermeasures during the initial phases of software design, and therefore, assures software security. Evaluating the performance of vulnerability detection by the proposed technique regarding recall, precision, and f-measure, it is found to be more effective than the existing methods.

This study investigates the prize-collecting single machine scheduling with bounds and penalties (PC-SMS-BP). In this problem, a set of n jobs and a single machine are considered, where each job (J_j) has a processing time (p_{j}), a profit (pi _{j}) and a rejection penalty (w_{j}). The upper bound on the processing number is U. The objective of this study is to find a feasible schedule that minimizes the makespan of the accepted jobs and the total rejection penalty of the rejected jobs under the condition that the number of the accepted jobs does not exceed a given threshold U while the total profit of the accepted jobs does not fall below a specified profit bound (varPi ). We first demonstrate that this problem is NP-hard. Then, a pseudo-polynomial time dynamic programming algorithm and a fully polynomial time approximation scheme (FPTAS) are proposed. Finally, numerical experiments are conducted to compare the effectiveness of the two proposed algorithms.

Low-Acy-Matching asks to find a maximal matching M in a given graph G of minimum cardinality such that the set of M-saturated vertices induces an acyclic subgraph in G. The decision version of Low-Acy-Matching is known to be ({textsf{NP}})-complete. In this paper, we strengthen this result by proving that the decision version of Low-Acy-Matching remains ({textsf{NP}})-complete for bipartite graphs with maximum degree 6 and planar perfect elimination bipartite graphs. We also show the hardness difference between Low-Acy-Matching and Max-Acy-Matching. Furthermore, we prove that, even for bipartite graphs, Low-Acy-Matching cannot be approximated within a ratio of (n^{1-epsilon }) for any (epsilon >0) unless ({textsf{P}}={textsf{NP}}). Finally, we establish that Low-Acy-Matching exhibits (textsf{APX})-hardness when restricted to 4-regular graphs.

Let G be a connected graph and (t ge 1) a (rational) constant. A t-spanner of G is a spanning subgraph of G in which the distance between any pair of vertices is at most t times its distance in G. We address two problems on spanners. The first one, known as the minimum t-spanner problem (MinS (_t)), seeks in a connected graph a t-spanner with the smallest possible number of edges. In the second one, called minimum cost tree t-spanner problem (MCTS (_t)), the input graph has costs assigned to its edges and seeks a t-spanner that is a tree with minimum cost. It is an optimization version of the tree t-spanner problem (TreeS (_t)), a decision problem concerning the existence of a t-spanner that is a tree. MinS (_t) is known to be ({textsc {NP}})-hard for every (t ge 2). On the other hand, TreeS (_t) admits a polynomial-time algorithm for (t le 2) and is ({textsc {NP}})-complete for (t ge 4); but its complexity for (t=3) remains open. We focus on the class of subcubic graphs. First, we show that for such graphs MinS (_3) can be solved in polynomial time. These results yield a practical polynomial algorithm for TreeS (_3) that is of a combinatorial nature. We also show that MCTS (_2) can be solved in polynomial time. To obtain this last result, we prove a complete linear characterization of the polytope defined by the incidence vectors of the tree 2-spanners of a subcubic graph. A recent result showing that MinS (_3) on graphs with maximum degree at most 5 is NP-hard, together with the current result on subcubic graphs, leaves open only the complexity of MinS (_3) on graphs with maximum degree 4.

The Probabilistic p-Center problem under Pressure (Min P p CP) is a variant of the usual Min p-Center problem we recently introduced in the context of wildfire management. The problem is to locate p shelters minimizing the maximum distance people will have to cover in case of fire in order to reach the closest accessible shelter. The landscape is divided into zones and is modeled as an edge-weighted graph with vertices corresponding to zones and edges corresponding to direct connections between two adjacent zones. The risk associated with fire outbreaks is modeled using a finite set of fire scenarios. Each scenario corresponds to a fire outbreak on a single zone (i.e., on a vertex) with the main consequence of modifying evacuation paths in two ways. First, an evacuation path cannot pass through the vertex on fire. Second, the fact that someone close to the fire may not take rational decisions when selecting a direction to escape is modeled using new kinds of evacuation paths. In this paper, we characterize the set of feasible solutions of Min P p CP-instance. Then, we propose some approximation results for Min P p CP. These results require approximation results for two variants of the (deterministic) Min p-Center problem called Min MAC p-Center and Min Partial p-Center.

In this paper, we address an extension of the classical two-dimensional bin packing (2BPP) that considers the spread of customer orders (2BPP-OS). The 2BPP-OS addresses a set of rectangular items, required from different customer orders, to be cut from a set of rectangular bins. All the items of a customer order are dispatched together to the next stage of production or distribution after its completion. The objective is to minimize the number of bins used and the spread of customer orders over the cutting process. The 2BPP-OS gains relevance in manufacturing environments that seek minimum waste solutions with satisfactory levels of customer service. We propose integer linear programming (ILP) models for variants of the 2BPP-OS that consider non-guillotine, 2-stage, restricted 3-stage, and unrestricted 3-stage patterns. We are not aware of integrated approaches for the 2BPP-OS in the literature despite its relevance in practical settings. Using a general-purpose ILP solver, the results show that the 2BPP-OS takes more computational effort to solve than the 2BPP, as it has to consider several symmetries that are often disregarded by the traditional 2BPP approaches. The solutions obtained by the proposed approaches have similar bin usage and significantly better metrics of customer satisfaction concerning the approaches that neglect the customer order spread.

With the advancement of electronic service platforms, customers exhibit various purchasing behaviors. Given the extensive array of options and minimal exit barriers, customer migration from one digital service to another has become a common challenge for businesses. Customer churn prediction (CCP) emerges as a crucial marketing strategy aimed at estimating the likelihood of customer abandonment. In this paper, we aim to predict customer churn intentions using a novel robust meta-classifier. We utilized three distinct datasets: transaction, telecommunication, and customer churn datasets. Employing Decision Tree, Random Forest, XGBoost, AdaBoost, and Extra Trees as the five base supervised classifiers on these three datasets, we conducted cross-validation and evaluation setups separately. Additionally, we employed permutation and SelectKBest feature selection to rank the most practical features for achieving the highest accuracy. Furthermore, we utilized BayesSearchCV and GridSearchCV to discover, optimize, and tune the hyperparameters. Subsequently, we applied the refined classifiers in a funnel of a new meta-classifier for each dataset individually. The experimental results indicate that our proposed meta-classifier demonstrates superior accuracy compared to conventional classifiers and even stacking ensemble methods. The predictive outcomes serve as a valuable tool for businesses in identifying potential churners and taking proactive measures to retain customers, thereby enhancing customer retention rates and ensuring business sustainability.