Journal of Combinatorial Optimization最新文献

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 Typically, email security products are outdated within these emerging threats hence the need to evolve into something more effective and smarter in the detection systems.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|).

We explore the problem of combinatorial contract design, a subject introduced and studied by Dütting et al. (2023). Previous research has focused on the challenge of selecting an unconstrained subset of agents, particularly when the principal’s utility function exhibits XOS or submodular characteristics related to the subset of agents that exert effort. Our study extends this existing line of research by examining scenarios in which the principal aims to select a subset of agents with a specific k-cardinality constraint. In these scenarios, the actions that each agent can take are binary values: effort or no effort. We focus on linear contracts, where the expected reward function is XOS or submodular. Our contribution is an approximation of 0.0197 for the problem of designing multi-agent hidden-action principal-agent contracts with the k-cardinality constraint. This result stands in contrast to the unconstrained setting, where Dütting et al. (2023) achieved an approximation of nearly 0.0039.

In this paper, we consider the W-prize-collecting scheduling problem on a single machine with submodular rejection penalties. In this problem, we are given one machine, n jobs and a value W. Every job has a processing time and a profit. Each job is either accepted and processed on the machine, or rejected and a rejection penalty is paid. The objective is to minimize the sum of the makespan of the accepted jobs and the rejection penalties of the rejected jobs which is determined by a submodular function, provided that the total profit of the accepted jobs is at least W. Under the assumption that the submodular penalty function is polymatriod, we design a 2-approximation algorithm based on the primal-dual framework.

We study mechanism design with predictions in the single (obnoxious) facility location games with candidate locations on the real line, which complements the existing literature on mechanism design with predictions. We first consider the single facility location games with candidate locations, where each agent prefers the facility (e.g., a school) to be located as close to her as possible. We study two social objectives: minimizing the maximum cost and the social cost, and provide deterministic, anonymous, and group strategy-proof mechanisms with predictions that achieve the best possible trade-offs between consistency and robustness, respectively. Additionally, we represent the approximation ratio as a function of the prediction error, indicating that mechanisms can achieve better performance even when predictions are not fully accurate. We also consider the single obnoxious facility location games with candidate locations, where each agent prefers the facility (e.g., a garbage transfer station) to be located as far away from her as possible. For the objective of maximizing the minimum utility, we prove that any strategy-proof mechanism with predictions is unbounded robust. For the objective of maximizing the social utility, we provide a deterministic, anonymous, and group strategy-proof mechanism with prediction that achieves the best possible trade-off between consistency and robustness.

Currently, many countries are on the process of reforming their health care payment systems from post-payment to pre-payment. To explore the impact of pre-payment schemes on health system performance we investigate the two payment schemes, bundled payment (BP) and total prepayment (TP), on performance in a medical cost-sharing system. Under the BP scheme, the government compensates hospitals with a lump sum for the entire course of each patient’s care. Under the TP scheme, the government provides the total amount of integrated compensation within a period. A three Stackelberg game with an embedded queueing model is used to explore the interactions among participants: government, hospital, and patients. The government determines the compensation received by hospitals and the copayment paid by patients to maximize social welfare. Next, the hospital determines its service rate for each medical episode to maximize profit. Last, patients make decisions on whether to appeal to the hospital for medical services. We derive the optimal strategy for the participants under the BP and TP schemes, and compare the system performance through numerical analysis. Results show that BP is better than TP in reducing patient expected waiting time, while it outperforms TP in terms of system accessibility and service quality. Our study is the first to consider the total prepayment scheme in the healthcare system decision analysis and the findings offer important insights for policymakers regarding implementing medical insurance reform in practice.

For a real number (omega ), a weak game of threats (N, v) consists of a set N of n players and a function (v:2^Nrightarrow mathbb {R}) such that (omega v(emptyset )+(1-omega )v(N)=0), where (v(emptyset )ne 0) possibly. It is shown that there exists a unique value with respect to (omega ) for weak games of threats that satisfies efficiency, linearity, symmetry and the null player property.