Approximation and complexity of the optimization and existence problems for maximin share,proportional share,and minimax share allocation of indivisible goods

This paper is concerned with various types of allocation problems in fair division of indivisible goods, aiming at maximin share, proportional share, and minimax share allocations. However, such allocations do not always exist, not even in very simple settings with two or three agents. A natural question is to ask, given a problem instance, what is the largest value c for which there is an allocation such that every agent has utility of at least c times her fair share. We first prove that the decision problem of checking if there exists a minimax share allocation for a given problem instance is \(\mathrm {NP}\)-hard when the agents’ utility functions are additive. We then show that, for each of the three fairness notions, one can approximate c by a polynomial-time approximation scheme, assuming that the number of agents is fixed. Next, we investigate the restricted cases when utility functions have values in \(\{0,1\}\) only or are defined based on scoring vectors (Borda and lexicographic vectors), and we obtain several tractability results for these cases. Interestingly, we show that maximin share allocations can always be found efficiently with Borda utilities, which cannot be guaranteed for general additive utilities. In the nonadditive setting, we show that there exists a problem instance for which there is no c-maximin share allocation, for any constant c. We explore a class of symmetric submodular utilities for which there exists a tight \(\frac{1}{2}\)-maximin share allocation, and show how it can be approximated to within a factor of \(\nicefrac {1}{4}\).     

Characterizing conflicts in fair division of indivisible goods using a scale of criteria

We investigate five different fairness criteria in a simple model of fair resource allocation of indivisible goods based on additive preferences. We show how these criteria are connected to each other, forming an ordered scale that can be used to characterize how conflicting the agents’ preferences are: for a given instance of a resource allocation problem, the less conflicting the agents’ preferences are, the more demanding criterion this instance is able to satisfy, and the more satisfactory the allocation can be. We analyze the computational properties of the five criteria, give some experimental results about them, and further investigate a slightly richer model with \(k\)-additive preferences.     

基于马尔可夫决策的应急物资动态分配模型

研究供需不平衡环境下的应急物资动态分配问题.考虑到台风灾害演变导致应急物资需求不断增长与应急物资供应相对紧缺之间的矛盾,将需求的演变设计成一个马尔可夫决策过程,建立基于马尔可夫决策的应急物资动态分配模型.通过二进制粒子群优化算法求解,最后将所提出模型应用于某台风发生时的救灾实例.实例分析表明,马尔可夫决策方法可以动态地做出合适的需求扑灭策略,使得整体的需求演变趋势保持平稳,整体的需求水平降到最低.     

Positional group pursuit

A general scheme is proposed deriving different types of sufficient conditions for a group pursuit starting from given initial positions to terminate in a finite time. The results are applied to some examples of group pursuit.Translated from Kibernetika, No. 1, pp. 55–62, January–February, 1989.     

A note on a single-machine lot scheduling problem with indivisible orders

In this paper, a lot scheduling problem on a single machine with indivisible orders is studied. The objective is to minimize the total completion time of all orders. We show that the problem is NP-hard in the strong sense. Then, a binary integer programming approach and four simple heuristics are proposed to solve the problem. The binary integer programming approach with running time limit is considered as one heuristic method. As compared to a lower bound, the average performances of the heuristic method are really good and better than those of the four simple heuristics.     

基于位置语言模型的中文信息检索系统的研究

在大多数现有的检索模型中常常忽略了如下事实:一个文档中匹配到的查询词项的近邻性和打分时所基于的段落检索也可以被用来促进文档的打分。受此启发,提出了基于位置语言模型的中文信息检索系统,首先通过定义位置传播数的概念,为每个位置单独地建立语言模型;然后通过引入KL-divergence检索模型,并结合位置语言模型给每个位置单独打分;最后由多参数打分策略得到文档的最终得分。实验中还重点比较了基于词表和基于二元两种中文索引方法在位置语言模型中的检索效果。在标准NTCIR5、NTCIR6测试集上的实验结果表明,该检索方法在两种索引方式上都显著改善了中文检索系统的性能,并且优于向量空间模型、BM25概率模型、统计语言模型。     

Positional Strategy of Forming the Investment Portfolio

The problem of optimal control of a multiplicative system modeling capital investments in securities of two kinds was considered. The stock market paradox was discussed. The logarithmic and quantile strategies belonging to the class of program strategies and aimed at overcoming this paradox were compared. A distinction of the logarithmic strategy was analyzed. A new positional strategy based on the confidence method was proposed.     

Negotiating for goods and services

Can a negotiation protocol be both fair and “envy-free” when more than two agents are involved? The authors consider how envy-free apportioning is more difficult than fair apportioning, but both can help to manage critical resources. They discuss an envy-free protocol and agent-based Web auctions