A survey of approximability and inapproximability results for social welfare optimization in multiagent resource allocation

Multiagent resource allocation provides mechanisms to allocate bundles of resources to agents, where resources are assumed to be indivisible and nonshareable. A central goal is to maximize social welfare of such allocations, which can be measured in terms of the sum of utilities realized by the agents (utilitarian social welfare), in terms of their minimum (egalitarian social welfare), and in terms of their product (Nash product social welfare). Unfortunately, social welfare optimization is a computationally intractable task in many settings. We survey recent approximability and inapproximability results on social welfare optimization in multiagent resource allocation, focusing on the two most central representation forms for utility functions of agents, the bundle form and the k-additive form. In addition, we provide some new (in)approximability results on maximizing egalitarian social welfare and social welfare with respect to the Nash product when restricted to certain special cases.     

Minimising inequality in multiagent resource allocation

Annals of Mathematics and Artificial Intelligence - We analyse the problem of finding an allocation of resources in a multiagent system that is as fair as possible in terms of minimising inequality...     

Distributed optimal resource allocation of second‐order multiagent systems

In this paper, the resource allocation problems of multiagent systems are investigated. Different from the well‐studied resource allocation problems, the dynamics of agents are taken into account in our problem, which results that the problem could not be solved by most of existing resource allocation algorithms. Here, the agents are in the form of second‐order dynamics, which causes the difficulties in designing and analyzing distributed resource allocation algorithms. Based on gradient descent and state feedback, two distributed resource allocation algorithms are proposed to achieve the optimal allocation, and their convergence are analyzed by constructing suitable Lyapunov functions. One of the two algorithms can ensure that the decisions of all agents asymptotically converge to the exact optimal solution, and the other algorithm achieves the exponential convergence. Finally, numerical examples about the economic dispatch problems of power grids are given to verify the effectiveness of the obtained results.     

网络功能虚拟化资源配置及优化研究综述

网络功能虚拟化(network functions virtualization,NFV)利用虚拟化技术将网络功能从专用硬件中分离形成虚拟网络功能,然后把虚拟网络功能映射到通用服务器、交换机或者存储器中,能有效地降低网络投资成本和运营成本,并提高网络服务部署的灵活性。网络功能虚拟化资源配置是实施NFV需要解决的一个关键问题。为深入剖析网络功能虚拟化资源配置,介绍了NFV的体系结构,重点阐述了资源配置的三个阶段及资源配置的优化,最后对高效资源配置面临的挑战和有价值的研究方向进行了思考,为NFV的研究提供参考。     

Computational complexity of determining resource loops inre-entrant flow lines

This paper presents a comparison study of the computational complexity of the general job shop protocol and the more structured flow line protocol in a flexible manufacturing system. It is shown that the representative problem of finding resource invariants is NP-complete in the case of the job shop, while in the flow line case it admits a closed form solution. The importance of correctly selecting part flow and job routing protocols in flexible manufacturing systems to reduce complexity is thereby conclusively demonstrated     

Distributed resource allocation of second‐order multiagent systems with exogenous disturbances

In this paper, we study the resource allocation problem of second‐order multiagent systems with exogenous disturbances, and the communication networks are weight‐balanced digraphs. Different from the well‐studied resource allocation problems, our problem involves the disturbed second‐order dynamics of agents. In order to achieve the optimal allocation, we propose a distributed algorithm based on gradient descent and internal model approach. Furthermore, we analyze the convergence of the algorithm by constructing a suitable Lyapunov function. Moreover, we prove that the agents in the network can achieve the exact optimal allocation even in the presence of external disturbances. Finally, we provide two examples to illustrate our result.     

Weighted Coloring: further complexity and approximability results

Given a vertex-weighted graph G=(V,E;w), w(v)?0 for any v∈V, we consider a weighted version of the coloring problem which consists in finding a partition S=(S₁,…,Sk) of the vertex set of G into stable sets and minimizing where the weight of S is defined as . In this paper, we continue the investigation of the complexity and the approximability of this problem by answering some of the questions raised by Guan and Zhu [D.J. Guan, X. Zhu, A coloring problem for weighted graphs, Inform. Process. Lett. 61 (2) (1997) 77-81].     

移动音频带宽扩展算法计算复杂度优化

移动通信设备由于计算资源有限,对计算复杂度较为敏感。我国自主研发提出的移动音频编解码算法标准AVS P10中的带宽扩展算法有利于提高移动音频编解码质量,但其计算复杂度较高,不利于该编解码算法在移动环境中应用。通过分析该带宽扩展算法的流程,发现其计算复杂度较高的主要原因是时频变换次数过多,为此从算法和代码两个方面对该算法进行优化:算法方面通过减少快速傅里叶变换(FFT)次数来降低算法计算复杂度;而代码方面则通过空间换时间等方法来减少算法消耗时间。测试结果表明,在不降低整体音频编解码主观质量的情况下,带宽扩展模块在编码端和解码端运行时间比例分别降低了4.5和14.3个百分点,算法计算复杂度显著降低,这有利于进一步在移动音频领域推广应用该编解码算法。     

On the complexity of market equilibria with maximum social welfare

We consider the computational complexity of the market equilibrium problem by exploring the structural properties of the Leontief exchange economy. We prove that, for economies guaranteed to have a market equilibrium, finding one with maximum social welfare or maximum individual welfare is NP-hard. In addition, we prove that counting the number of equilibrium prices is #P-hard.     

基于广义资源日历约束的项目资源调配优化问题

资源受限项目调度问题(RCPSP)是最具代表性的项目调度问题之一,针对实际情况中考虑资源投入的必要性,建立一种以资源投入为变量的基于广义资源日历约束的项目调度优化模型.首先,引入组合优先关系的概念对广义资源日历的概念和具体内容进行整合和完善,为了避免传统网络图在表示组合优先关系时出现的网络循环等弊端,使用节点表示活动开始和结束的瞬时状态改进节点网络图;其次,考虑活动优先关系、活动持续时间、不可更新资源总量和资源日历约束,以项目工期最短和项目成本最小为优化目标,运用CP优化器求解所建立的多目标优化模型;最后,通过设计仿真算例并进行数值实验验证模型的准确性和高效性.