Journal of Combinatorial Optimization最新文献

Motivated by the result of balanced connected graph edge partition problem for trees, we investigate the 2-balanced connected graph vertex k-partition problem. This paper leverages the charity vertex method and proposes several algorithms for 2-balanced vertex-connected partitioning. Furthermore, we prove that these algorithms are polynomial-time solvable on degree-bounded graphs, thereby refining and extending the results of Caragiannis et al.

We study the robust maximum flow problem and the robust maximum flow over time problem where a given number of arcs (Gamma ) may fail or may be delayed. Two prominent models have been introduced for these problems: either one assigns flow to arcs fulfilling weak flow conservation in any scenario, or one assigns flow to paths where an arc failure or delay affects a whole path. We provide a unifying framework by presenting novel general models, in which we assign flow to subpaths. These models contain the known models as special cases and unify their advantages in order to obtain less conservative robust solutions.

We give a thorough analysis with respect to complexity of the general models. In particular, we show that the general models are essentially NP-hard, whereas, e.g., in the static case with (Gamma =1) an optimal solution can be computed in polynomial time. Further, we answer the open question about the complexity of the dynamic path model for (Gamma =1). We also compare the solution quality of the different models. In detail, we show that the general models have better robust optimal values than the known models and we prove bounds on these gaps.

In this paper, we investigate the maximum weight k-cycle (k-path) partition problem (MaxWkCP/MaxWkPP for short). The input consists of an undirected complete graph (G=(V,E)) with (|V|=kn), where k, n are positive integers, and a non-negative weight function on E, the objective is to determine n vertex disjoint k-cycles (k-paths), which are cycles (paths) containing exactly k vertices, covering all the vertices such that the total edge weight of these cycles (paths) is as large as possible. We propose improved approximation algorithms for the MaxWkCP/MaxWkPP in graphs with weights one and two. For the MaxWkCP in graphs with weights one and two, we obtain an approximation algorithm having an approximation ratio of (frac{37}{48}) for (k=6), which improves upon the best available (frac{91}{120})-approximation algorithm by Zhao and Xiao 2024a. When (k=4), we show that the same algorithm is a (frac{7}{8})-approximation algorithm and give a tight example. This ratio ties with the state-of-the-art result, also given by Zhao and Xiao 2024a. However, we demonstrate that our algorithm can be applied to the minimization variant of MaxWkCP in graphs with weights one and two and achieve a tight approximation ratio of (frac{5}{4}). For the MaxW5PP in graphs with weights one and two, we devise a novel (frac{19}{24})-approximation algorithm by combining two separate algorithms, each of which handles one of the two complementary scenarios of the optimal solution well. This ratio is better than the previous best ratio of (frac{3}{4}) due to Li and Yu 2023.

For graphs G and H, the Ramsey number R(G, H) is the smallest r such that any red-blue edge coloring of (K_r) contains a red G or a blue H. The path-critical Ramsey number (R_{pi }(G,H)) is the largest n such that any red-blue edge coloring of (K_r setminus P_{n}) contains a red G or a blue H, where (r=R(G,H)) and (P_{n}) is a path of order n. In this note, we show a general upper bound for (R_{pi }(G,H)), and determine the exact values for some cases of (R_{pi }(G,H)).

The Internet of Things (IoT) application is an application and service that incorporates both the physical and information world. Similarly, it is difficult for existing health systems to provide privacy-aware aggregate authentication and fine-grained access control. To bridge the concern, a smart health system (SHS) with Deep Kronecker Network_key generation (DKN_keyGen) for privacy-aware aggregate authentication and access control in IoT is implemented. Here, entities employed for this model such as data owner (DO), registration center (RC), data user (DU) and cloud service provider (CSP). The method follows four steps, such as system initialization, user registration, Health data outsourcing and Health data access. Initially, the RC needs to initialize the security parameters, random parameters and public keys. After that, DO and DU must be registered in RC. Moreover, the smart health care data of DO generates the secret parameter and also obtains the secret parameter from the RC. The cloud storage stores and manages health care data in the health data outsourcing step. Finally, for health data access, the user gives appropriate parameters and access to the data which is implemented in the data access phase. The model is established considering different security functionalities including Encryption, ECC, XoR and hashing function. Here, the key is generated using DKN. The proposed model obtained a minimum computation time of 6.857 s, memory usage of 30 MB, and communication cost of 20.

Coflow scheduling is a challenging optimization problem that underlies many data transmission and parallel computing applications. In this paper, we study the indivisible coflow scheduling problem on parallel identical machines with the objective to minimize the makespan, i.e., the completion time of the last flow. In our problem setting, the number of the input/output ports in each machine is a fixed constant, each port has a unit capacity, and all the flows inside a coflow should be scheduled on the same machine. We present a ((2 + epsilon ))-approximation algorithm for the problem, for any (epsilon > 0), in which the number of machines can be either a fixed constant or part of the input.

In this ever-evolving world of threats, e-mail security is becoming one of the biggest concerns because attackers are constantly searching for new techniques to bypass the existing security measures. Emails containing phishing, malware and other security threats have become far more common place, which is why there is a need to implement new and more efficient adaptive threat detection frameworks. Typically, email security products are outdated within these emerging threats hence the need to evolve into something more effective and smarter in the detection systems. In this regard, Zero Short learning based Artificial Intelligence (ZeSAI)-model is proposed as a new approach to improve threat identification in the context of email security. Initially, to ensure generalization and robust performance, the model uses three broad sets of input data: augmented data based on Context-Preserving Synthetic Email Generation (CPSEG) method and adversarial data, both generated from six datasets and Threat Intelligence feeds offering real-time updates. The proposed ZeSAI model enhances email threat detection through a structured workflow: eXtreme Language Network (XLNet) first generates bidirectional contextual embeddings from email content, capturing nuanced semantic relationships. The Recurrent GRU Network (RGN) then analyses temporal patterns in the email data, identifying complex relationships and variations over time. These RGN-extracted features are integrated with XLNet-generated semantic embeddings in the Cross-Modal Fusion Layer. Finally, Zero-Shot Learning (ZSL) utilizes these combined semantic descriptions and contextual insights to identify new threats based on their similarities to known threats, enabling robust and adaptive threat detection. The proposed approach yields good accuracy and other performance measures; precision, recall, and F1-score; under fivefold and tenfold cross-validation. An ablation study is also carried out to pinpoint the contribution of each module. Specifically, ZeSAI has accuracy of 98.51% in Business Email Compromise (BEC) threat detection, 96.8% in spam detection, 99.18% in phishing detection, 97.2% in malware attachment detection and 98.58% in detecting insider threats.

As global climate change intensifies, the agricultural sector, responsible for over 30% of global greenhouse gas emissions, faces an urgent imperative to mitigate emissions and align with international climate commitments. Carbon sink trading, a market-based mechanism that incentivizes emission reductions through sequestration credits, has emerged as an important tool for accelerating carbon peaking and neutrality goals. This study investigates the influence of carbon sink trading on the strategic interactions between farmers and retailers in agricultural supply chains. Employing differential game theory, we construct three cooperative models: decentralized, Stackelberg leader-follower, and centralized, and derive equilibrium strategies for each using the Hamilton-Jacobi-Bellman framework. Through numerical simulations, we evaluate the influence of carbon sink trading on the emission reduction efforts of farmers and retailers, the extent of emission reductions in the supply chain, and the overall profits. Comparative analysis against baseline scenarios without carbon trading reveals that the integration of carbon sink markets enhances profit margins across all models and improves the level of emission reduction in the agricultural supply chain. In addition, our results show that the centralized model outperforms other configurations, followed by the Stackelberg model, with the decentralized model exhibiting the least effectiveness. These findings provide actionable insights for policymakers and supply chain managers to design carbon trading frameworks that harmonize economic incentives with ecological sustainability.

We study a class of binary fractional programs commonly encountered in important application domains such as assortment optimization and facility location. These problems are known to be NP-hard to approximate within any constant factor, and existing solution approaches typically rely on mixed-integer linear programming or second-order cone programming reformulations. These methods often utilize linearization techniques (e.g., big-M or McCormick inequalities), which can result in weak continuous relaxations. In this work, we propose a novel approach based on an exponential cone reformulation combined with piecewise linear approximation. This allows the problem to be solved efficiently using standard cutting-plane or branch-and-cut procedures. We further provide a theoretical analysis of the approximation quality yielded by our reformulation and discuss strategies for optimizing the problem size of the exponential cone formulation. Experiments on instances of various sizes demonstrate that our approach delivers competitive performance on small and medium instances while offering superior performance on large instances compared to state-of-the-art baselines.

In this paper, we consider the partition set cover problem with penalties. In this problem, we have a universe U, a partition (mathscr {P}={P_{1},ldots ,P_{r}}) of U, and a collection (mathscr {S}={S_{1},ldots ,S_{m}}) of nonempty subsets of U satisfying (bigcup _{S_iin mathscr {S}} S_i=U). In addition, each (P_t) ((tin [r])) is associated with a covering requirement (k_t) as well as a penalty (pi _t), and each (S_i) ((iin [m])) is associated with a cost. A class (P_t) attains its covering requirement by a subcollection (mathscr {A}) of (mathscr {S}) if at least (k_t) elements in (P_t) are contained in (bigcup _{S_iin mathscr {A}} S_i). Each (P_t) is either attaining its covering requirement or paid with its penalty. The objective is to find a subcollection (mathscr {A}) of (mathscr {S}) such that the sum of the cost of (mathscr {A}) and the penalties of classes not attaining covering requirements by (mathscr {A}) is minimized. We present two approximation algorithms for this problem. The first is based on the LP-rounding technique with approximation ratio (K+O(beta +ln r)), where (K=max _{tin [r]}k_t), and (beta ) denotes the approximation guarantee for a related set cover instance obtained by rounding the standard LP. The second is based on the primal-dual method with approximation ratio lf, where (f=max _{ein U}|{S_iin mathscr {S}mid ein S_i}|) and (l=max _{tin [r]}|P_t|).