Fair draws for group rounds in sport tournaments

We propose two draw systems for the group round of sport tournaments where there are some geographical and/or seeding restrictions. One of the systems, related to the equal-sum partition problem, is "perfect, " since it yields perfectly balanced groups. The other system, which uses the classical scheme of extracting teams from pots, is heuristic and gives results where the groups have very similar scores. We apply our results to Federation Internationale de Football Association (FIFA) Soccer World Cups and show that our proposals are much better than the FIFA system and also outperform other recently developed systems

Performance ratios for the differencing method applied to the balanced number partitioning problem

We consider the problem of partitioning a set of n numbers into m subsets of cardinality k = ¿n/m¿ or ¿n/m¿, such that the maximum subset sum is minimal. We prove that the performance ratios of the Differencing Method of Karmarkar and Karp for k = 3,4,5, and 6 are precisely 4/3, 19/12, 103/60, and 643/360, respectively, by means of a novel approach in which the ratios are explicitly calculated using mixed integer linear programming. Moreover, we show that for k = 7 the performance ratio lies between 2/3 - 2/k and 2/3 - 1/(k/3 - 1). For the case that m is given instead of k, we prove a performance ratio of precisely 2 - 1/m. The results settle the problem of determining theworst-case performance of the Differencing Method

Performance ratios for the differencing method applied to the balanced number partitioning problem

We consider the problem of partitioning a set of n numbers into m subsets of cardinality k = ¿n/m¿ or ¿n/m¿, such that the maximum subset sum is minimal. We prove that the performance ratios of the Differencing Method of Karmarkar and Karp for k = 3,4,5, and 6 are precisely 4/3, 19/12, 103/60, and 643/360, respectively, by means of a novel approach in which the ratios are explicitly calculated using mixed integer linear programming. Moreover, we show that for k = 7 the performance ratio lies between 2/3 - 2/k and 2/3 - 1/(k/3 - 1). For the case that m is given instead of k, we prove a performance ratio of precisely 2 - 1/m. The results settle the problem of determining theworst-case performance of the Differencing Method

Performance ratios for the differencing method applied to the balanced number partitioning problem

Abstract. We consider the problem of partitioning a set of n numbers into m subsets of cardinality k ¡ ¢ n £ m ¤ or ¥ n £ m ¦ , such that the maximum subset sum is minimal. We prove that the performance ratios of the Differencing Method of Karmarkar and Karp for k ¡ 3 § 4 § 5 § and 6 are precisely 4/3, 19/12, 103/60, and 643/360, respectively, by means of a novel approach in which the ratios are explicitly calculated using mixed integer linear programming. Moreover, we show that for k ¨ 7 the performance ratio lies between 2 © 2 £ k and 2 © 1£� � k © 1 �. For the case that m is given instead of k, we prove a performance ratio of precisely 2 © 1 £ m. The results settle the problem of determining the worst-case performance of the Differencing Method.

Enhancing Access Privacy of Range Retrievals over B+Trees

National Research Foundation (NRF) Singapore under International Research Centre @ Singapore Funding Initiativ

Changing the focus: worker-centric optimization in human-in-the-loop computations

A myriad of emerging applications from simple to complex ones involve human cognizance in the computation loop. Using the wisdom of human workers, researchers have solved a variety of problems, termed as “micro-tasks” such as, captcha recognition, sentiment analysis, image categorization, query processing, as well as “complex tasks” that are often collaborative, such as, classifying craters on planetary surfaces, discovering new galaxies (Galaxyzoo), performing text translation. The current view of “humans-in-the-loop” tends to see humans as machines, robots, or low-level agents used or exploited in the service of broader computation goals. This dissertation is developed to shift the focus back to humans, and study different data analytics problems, by recognizing characteristics of the human workers, and how to incorporate those in a principled fashion inside the computation loop. The first contribution of this dissertation is to propose an optimization framework and a real world system to personalize worker’s behavior by developing a worker model and using that to better understand and estimate task completion time. The framework judiciously frames questions and solicits worker feedback on those to update the worker model. Next, improving workers skills through peer interaction during collaborative task completion is studied. A suite of optimization problems are identified in that context considering collaborativeness between the members as it plays a major role in peer learning. Finally, “diversified” sequence of work sessions for human workers is designed to improve worker satisfaction and engagement while completing tasks