Journal of Combinatorial Optimization最新文献

We present improvements to famous algorithms for community detection, namely Newman’s spectral method algorithm and the Louvain algorithm. The Newman algorithm begins by treating the original graph as a single cluster, then repeats the process to split each cluster into two, based on the signs of the eigenvector corresponding to the second-largest eigenvalue. Our improvement involves replacing the time-consuming computation of eigenvalues with a random walk during the splitting process. The Louvain algorithm iteratively performs the following steps until no increase in modularity can be achieved anymore: each step consists of two phases–phase 1 for partitioning the graph into clusters, and phase 2 for constructing a new graph where each vertex represents one cluster obtained from phase 1. We propose an improvement to this algorithm by adding our random walk algorithm as an additional phase for refining clusters obtained from phase 1. It maintains a complexity comparable to the Louvain algorithm while exhibiting superior efficiency. To validate the robustness and effectiveness of our proposed algorithms, we conducted experiments using randomly generated graphs and real-world data.

The proliferation of Internet of Things (IoT) devices has intensified the need for intelligent, adaptive, and energy-efficient resource management across mobile edge–fog–cloud infrastructures. Conventional optimization approaches often fail to manage the dynamic interplay among fluctuating workloads, energy constraints, and real-time scheduling. To address this, a Hybrid Quantum-Enhanced Reinforcement Learning (HQERL) framework is introduced, unifying quantum-inspired heuristics, swarm intelligence, and reinforcement learning into a co-adaptive sched uling system. HQERL employs a feedback-driven architecture to synchronize exploration, optimization, and policy refinement for enhanced task scheduling and resource control. The Maximum Likelihood Swarm Whale Optimization (MLSWO) module encodes dynamic task and system states using swarm intelligence guided by statistical likelihood, generating information-rich inputs for the learning controller. To prevent premature convergence and expand the scheduling search space, the Quantum Brainstorm Optimization (QBO) component incorporates probabilistic memory and collective learning to diversify scheduling solutions. These enhanced representations and exploratory strategies feed into the Proximal Policy Optimization (PPO) controller, which dynamically adapts resource allocation policies in real time based on system feedback, ensuring resilience to workload shifts. Furthermore, Dynamic Voltage Scaling (DVS) is integrated to improve energy efficiency by adjusting processor voltages and frequencies according to workload demands. This seamless coordination enables HQERL to balance task latency, resource use, and power consumption. Evaluation on the LSApp dataset reveals HQERL yields a 15% energy efficiency gain, 12% makespan reduction, and a 23.3% boost in peak system utility, validating its effectiveness for sustainable IoT resource management.

The Priority value (Béal et al. in Int J Game Theory 51:431–450, 2022) is an allocation rule for TU-games with a priority structure, which distributes the Harsanyi dividend of each coalition among the set of its priority players. In this paper we propose two variants of the differential marginality of mutually dependent players axiom for TU-games with a priority structure, and extend the classical axiom of balanced contributions to TU-games with a priority structure. We provide several new characterizations of the Priority value which invoke these modified axioms and the standard axioms: efficiency, the null player property, the priority player out and the null player out.

This paper addresses an integrated operating room (OR) and physician scheduling problem driven by the real-world needs in the surgical department. The OR scheduling problem involves determining the number of ORs to be opened each day, the operation date of each surgery, and the schedule of surgeries in each OR. The physician scheduling problem considers two primary work for physicians: surgery service and consultation service, aiming to assign physicians to shifts and determine their responsibilities for either performing surgeries or providing consultation services in the outpatient department. The integration of these two scheduling problems improves coordination between OR availability and physician schedules, which can directly reduce operational costs and enhance resource utilization in the surgical department. The objective of the integrated problem is to minimize the total costs of the hospital and the patients, including the total waiting cost of patients, the total working cost of physicians, the total opening cost of ORs, and the total overtime cost of ORs. To solve the problem, a hybrid approach DP-H-VNS is proposed, which incorporates dynamic programming (DP), heuristics, and a variable neighborhood search (VNS) algorithm. The DP algorithm is used to assign surgeries to specific ORs, while the proposed heuristic rules are presented to determine the number of ORs to open each day and the scheduling of physicians. The presented VNS algorithm can search for high-quality solutions for the proposed problem and serves as a framework to integrate the DP, heuristics, local search, and shaking procedures. Experimental results demonstrate that the proposed DP-H-VNS is superior to the other compared algorithms on the quality of the found solutions and the performance. These results confirm the effectiveness of the proposed approach in optimizing the resource allocation in the surgical department and improving patient care.

In this paper, we propose a Branch–Reduction–Bound (BRB) algorithm to solve fractional multiplicative product programming problems, with the aim of finding globally optimal solutions. The method introduces two innovative linear transformation techniques that simplify the solution process by converting the original problem into two equivalent linear relaxation problems. Building on this, a novel branch-and-delete rule is developed to efficiently manage sub-problem selection using a dynamic priority queue approach, and the computational process is further optimized through a region deletion rule. The synergy of these techniques significantly accelerates the algorithm's convergence rate, providing an efficient global optimization strategy. We compare the BRB algorithm with four other algorithms through numerical experiments, and the results confirm its feasibility, effectiveness, and superior computational efficiency, highlighting its advantages in solving complex optimization problems.

The topology-aware Massively Parallel Computation (MPC) model is proposed and studied recently, which enhances the classical MPC model by the awareness of network topology. The work of Hu et. al. on topology-aware MPC model considers only the tree topology. In this paper a more general case is considered, where the underlying network is a weighted complete graph. We then call this model as Weighted Massively Parallel Computation (WMPC) model, and study the problem of minimizing communication cost under it. Three communication cost minimization problems are defined based on different patterns of communication, which are the Data Redistribution Problem, Data Allocation Problem on Continuous data, and Data Allocation Problem on Categorized data. We also define four kinds of objective functions for communication cost, which consider the total cost, bottleneck cost, maximum of send and receive cost, and summation of send and receive cost, respectively. Combining the three problems in different communication patterns with the four kinds of objective cost functions, 12 problems are obtained. The hardness results and algorithms of the 12 problems make up the content of this paper. With rigorous proof, we prove that some of the 12 problems are in P, some FPT, some NP-complete, and some W[1]-complete. Approximate algorithms are proposed for several selected problems.