Approximate Pareto Set for Fair and Efficient Allocation: Few Agent Types or Few Resource Types

In fair division of indivisible goods, finding an allocation that satisfies fairness and efficiency simultaneously is highly desired but computationally hard. We solve this problem approximately in polynomial time by modeling it as a bi-criteria optimization problem that can be solved efficiently by determining an approximate Pareto set of bounded size. We focus on two criteria: max-min fairness and utilitarian efficiency, and study this problem for the setting when there are only a few item types or a few agent types. We show in both cases that one can construct an approximate Pareto set in time polynomial in the input size, either by designing a dynamic programming scheme, or a linear-programming algorithm. Our techniques strengthen known methods and can be potentially applied to other notions of fairness and efficiency as well.

Modified method of dynamic programming for optimization of hydraulic modes of distribution heating networks

Предложена оригинальная модификация метода динамического программирования, предназначенная для оптимизации гидравлических режимов распределительных тепловых сетей, опирающаяся на специальные свойства задачи. Продемонстрировано, что предложенная модификация метода динамического программирования обладает высокой вычислительной эффективностью по сравнению с возможными альтернативными методами дискретно-непрерывной оптимизации и гарантирует получение оптимального решения задачи. The paper discusses the problem of optimizing the hydraulic modes of the distribution of heat networks (RTS), which arises at the stage of preparing heating systems for the next heating season. The urgency of this task is due to the significant reserves of energy saving, improving the reliability and quality of heat supply to consumers, which can be realized through the optimal organization of RTS operation modes. Currently, there are no formally rigorous and simultaneously computationally efficient methods for solving this problem. A new effective method for optimizing RTS modes is presented, based on a dynamic programming scheme, which takes into account the specifics of the problem (specified flow distribution) and RTS topology (a tree in a single-line representation, multicontourness in a two-line representation, symmetry of supply and return pipelines). The proposed solution overcomes the main problem of applying the traditional dynamic programming scheme when optimizing multi-loop pipe networks associated with the need to comply with the second Kirchhoff law on contours when building conditionally optimal trajectories. The basic idea is to reduce the contours of the design scheme to parallel connections of branches (on the direct course of the algorithm) with simultaneous cutting of both non-optimal and inadmissible fragments of trajectories. And the latter here are easily cut off both in terms of the membership of the phase variables of the admissible region and in satisfying Kirchhoff’s second law. The reverse move is reduced to a simple procedure of unfolding the design scheme in the reverse sequence of reduction, in order to restore the optimal values of phase variables on it. Numerical examples illustrate the effectiveness of the proposed method, its suitability for solving problems with discrete and continuous optimality criteria, multi-criteria optimization, the possibility of solving several optimization problems simultaneously.

Optimal Sequential Grouping for Robust Video Scene Detection Using Multiple Modalities

Video scene detection is the task of dividing a video into semantic sections. To perform this fundamental task, we propose a novel and effective method for temporal grouping of scenes using an arbitrary set of features computed from the video. We formulate the task of video scene detection as a generic optimization problem to optimally group shots into scenes, and propose an efficient procedure for solving the optimization problem based on a novel dynamic programming scheme. This unique formulation directly results in a temporally consistent segmentation, and has the advantage of being parameter-free, making it applicable across various domains. We provide detailed experimental results, showing that our algorithm outperforms current state-of-the-art methods. To assess the comprehensiveness of this method even further, we present experimental results testing different types of modalities and their applicability in this formulation.

A Grouping Cache Based Joins Query Algorithm in MANET

Aiming at the problem of joins query in MANET, we proposed a grouping cache mechanism, which builds grouping cache considering the features of data. The proposed mechanism can implement the cooperating cache between groups and update cache information dynamically, which leads to the improvement of query hit ratio and decrease of response time. Based on the grouping cache, a novel joins query algorithm is presented. The algorithm optimizes the query plan using dynamic programming scheme. Then it constructs an optimal execution plan for each sub join query with available cache data taken into account. Simulation results indicated that the group-based cache mechanism can improve the hit ratio, reduce query response time and conserve energy of the network efficiently.

Simultaneous Optimization of Final Pit and Production Schedule in Open-Pit Coal Mines

A dynamic sequencing method has been developed that can simultaneously optimize the final pit and the production schedule of an open-pit coal mine. The method first establishes a geological seam model of a bedded coal deposit which estimates the relevant attributes of coal seams at the center of each block on the X-Y plane. Based on the seam model, a sequence of “geologically optimum final pits” is generated and, in each of these pits, a sequence of “geologically optimum push-backs” is generated. The geologically optimum push-backs are then put into a dynamic programming scheme and the best production schedule which has the highest NPV is obtained for each final pit. After the best production schedules for all the final pits are obtained, the one with the highest overall NPV is the optimum final pit and its associated best schedule is the overall best production schedule.

PACKING SHELVES WITH ITEMS THAT DIVIDE THE SHELVES' LENGTH: A CASE OF A UNIVERSAL NUMBER PARTITION PROBLEM

This note examines the likelihood of packing two identical one dimensional shelves of integer length L by items whose individual lengths are divisors of L, given that their combined length sums-up to 2L. We compute the number of packing failures and packing successes for integer shelve lengths L, 1 ≤ L ≤ 1000, by implementing a dynamic programming scheme using a problem specific "boundedness property". The computational results indicate that the likelihood of a packing failure is very rare. We observe that the existence of packing failures is tied to the number of divisors of L and prove that the number of divisors has to be at least 8 for a packing failure to exist.