Journal of Combinatorial Optimization最新文献

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.

There are numerous combinatorial algorithms for classical min-cost flow problems and their simpler variants like max flow or shortest path problems. It is well-known that many of these algorithms are related to the Simplex method and the more general circuit augmentation schemes: prime examples are the network Simplex method, a refinement of the primal Simplex method, and min-mean cycle canceling, which corresponds to a steepest-descent circuit augmentation scheme. We are interested in a deeper understanding of the relationship between circuit augmentation and combinatorial network flows algorithms. To this end, we generalize from primal flows to so-called pseudoflows, which adhere to arc capacities but allow for a violation of flow balance. We introduce ‘pseudoflow polyhedra,’ wherein slack variables are used to quantify this violation, and characterize their circuits. This enables the study of combinatorial network flows algorithms in view of the walks they trace in these polyhedra, and the pivot rules for the steps. In doing so, we provide an ‘umbrella,’ a general framework, that captures several algorithms. We show that the Successive Shortest Path Algorithm for min-cost flow problems, the Shortest Augmenting Path Algorithm for max flow problems, and the Preflow-Push algorithm for max flow problems lead to (non-edge) circuit walks in these polyhedra. The former two are replicated by circuit augmentation schemes for simple pivot rules. Further, we show that the Hungarian Method leads to an edge walk and is replicated, equivalently, as a circuit augmentation scheme or a primal Simplex run for a simple pivot rule.

In this paper, we study the independent quadratic assignment problem which is a variation of the well-known Koopmans–Beckman quadratic assignment problem. The problem is strongly NP-hard and is also hard to approximate. Some polynomially solvable special cases are identified along with a complete characterization of linearizable instances of the problem, the validity of which is shown to be verifiable in linear time. This improves the existing quadratic bound for this problem. Additional complexity results are also presented.

Substar reliability defined as the probability that a fault-free substar of a certain scale is still available in the star network (S_n) when the occurrence of faults. The substar reliability is one of the most practical reliability measures because a user in the current star multiprocessors is given a certain substar for the execution of his/her program. Wu and Latifi(Inf. Sci. 178 (2008)) derived upper-bound on the substar reliability of (S_n) by analysing the intersection of no more than three substars. Later, Li et al.(IEEE. Trans. Rel. 65 (2016)) derived lower-bound on the substar reliability of (S_n) by considering the intersection of no more than four substars. In the paper, we further derive the upper- and lower bounds on the substar reliability of (S_n) by taking into account the intersection of no more than five or four substars, respectively. At a result, we obtain more accurate value of the upper-bound on substar reliability of (S_n). The experimental study indicates that both the upper- and lower bounds are very close to approximate results especially for the low value of the node reliability.

We study the SONET edge partition problem that models telecommunication network design to partition the edge set of a given graph into several edge-disjoint subgraphs, such that each subgraph has size no greater than a given capacity k and the sum of the orders of these subgraphs is minimized. The problem is NP-hard when (k ge 3) and admits an (O(log k))-approximation algorithm. For small capacity (k = 3, 4, 5), by observing that some subgraph structures are more favorable than the others, we propose modifications to existing algorithms and design novel amortization schemes to prove their improved performance. Our algorithmic results include a (frac{4}{3})-approximation for (k = 3), improving the previous best (frac{13}{9})-approximation, a (frac{4}{3})-approximation for (k = 4), improving the previous best ((frac{4}{3} + epsilon ))-approximation, and a (frac{3}{2})-approximation for (k = 5), improving the previous best (frac{5}{3})-approximation. Besides these improved algorithms, our main contribution is the amortization scheme design, which can be helpful for similar algorithms and problems.

L-shaped floorplans are defined by rectangular modules enclosed within a rectilinear outer boundary, forming an L-shape that can not be altered through simple extension or contraction of a boundary wall. The boundary of such floorplans comprises five convex corners and one concave corner. The concave corner on the boundary of the plan can not be converted into a convex corner without altering the horizontal and vertical adjacency among the modules. This paper introduces a linear-time algorithm based on canonical ordering to generate L-shaped floorplans from properly triangulated plane graphs (PTPGs). Here, modules in the floorplan correspond to the nodes of the given graph, while edges in the graph represent wall adjacency between modules. The proposed algorithm assigns a unique labeling to the given graph, ensuring the presence of a concave corner on the resulting floorplan’s boundary. Simple boundary wall extensions or contractions cannot eliminate this concave corner. It also produces multiple L-shaped floorplans corresponding to the given PTPG, with variations mainly on their concave corners, highlighting the unique configurations possible within the same boundary constraints. Our algorithm offers simplicity over existing methods and is easy to implement. Additionally, we have implemented the algorithm in Python, enabling easy integration for generating L-shaped floorplans in various architectural and VLSI circuit design applications.