A Constant Factor Approximation Algorithm for Unsplittable Flow on Paths

In the unsplittable flow problem on a path, we are given a capacitated path $P$ and $n$ tasks, each task having a demand, a profit, and start and end vertices. The goal is to compute a maximum profit set of tasks, such that for each edge $e$ of $P$, the total demand of selected tasks that use $e$ does not exceed the capacity of $e$. This is a well-studied problem that has been studied under alternative names, such as resource allocation, bandwidth allocation, resource constrained scheduling, temporal knapsack and interval packing. We present a polynomial time constant-factor approximation algorithm for this problem. This improves on the previous best known approximation ratio of $O(\log n)$. The approximation ratio of our algorithm is $7+\epsilon$ for any $\epsilon>0$. We introduce several novel algorithmic techniques, which might be of independent interest: a framework which reduces the problem to instances with a bounded range of capacities, and a new geometrically inspired dynamic program which solves a special case of the maximum weight independent set of rectangles problem to optimality. In the setting of resource augmentation, wherein the capacities can be slightly violated, we give a $(2+\epsilon)$-approximation algorithm. In addition, we show that the problem is strongly NP-hard even if all edge capacities are equal and all demands are either~1,~2, or~3.Comment: 37 pages, 5 figures Version 2 contains the same results as version 1, but the presentation has been greatly revised and improved. References have been adde

Improved Online Algorithms for Knapsack and GAP in the Random Order Model

The knapsack problem is one of the classical problems in combinatorial optimization: Given a set of items, each specified by its size and profit, the goal is to find a maximum profit packing into a knapsack of bounded capacity. In the online setting, items are revealed one by one and the decision, if the current item is packed or discarded forever, must be done immediately and irrevocably upon arrival. We study the online variant in the random order model where the input sequence is a uniform random permutation of the item set. We develop a randomized (1/6.65)-competitive algorithm for this problem, outperforming the current best algorithm of competitive ratio 1/8.06 [Kesselheim et al. SIAM J. Comp. 47(5)]. Our algorithm is based on two new insights: We introduce a novel algorithmic approach that employs two given algorithms, optimized for restricted item classes, sequentially on the input sequence. In addition, we study and exploit the relationship of the knapsack problem to the 2-secretary problem. The generalized assignment problem (GAP) includes, besides the knapsack problem, several important problems related to scheduling and matching. We show that in the same online setting, applying the proposed sequential approach yields a (1/6.99)-competitive randomized algorithm for GAP. Again, our proposed algorithm outperforms the current best result of competitive ratio 1/8.06 [Kesselheim et al. SIAM J. Comp. 47(5)]

Learning process: Multi-Agent Tutoring System

A multi-agent architecture has been developed for tutorial assignation scheduling. It has two main types of agents: the students and the teachers. These two are coordinated by an algorithm which assigns the classes in order of arrival. The architecture will provide the necessary tools to the students, so they get the maximum profit from the tutorials. Students and Lecturers can coordinate their tutorial meeting in an efficient way with the help of the multi-agent system

Decentralized Greedy-Based Algorithm for Smart Energy Management in Plug-in Electric Vehicle Energy Distribution Systems

Variations in electricity tariffs arising due to stochastic demand loads on the power grids have stimulated research in finding optimal charging/discharging scheduling solutions for electric vehicles (EVs). Most of the current EV scheduling solutions are either centralized, which suffer from low reliability and high complexity, while existing decentralized solutions do not facilitate the efficient scheduling of on-move EVs in large-scale networks considering a smart energy distribution system. Motivated by smart cities applications, we consider in this paper the optimal scheduling of EVs in a geographically large-scale smart energy distribution system where EVs have the flexibility of charging/discharging at spatially-deployed smart charging stations (CSs) operated by individual aggregators. In such a scenario, we define the social welfare maximization problem as the total profit of both supply and demand sides in the form of a mixed integer non-linear programming (MINLP) model. Due to the intractability, we then propose an online decentralized algorithm with low complexity which utilizes effective heuristics to forward each EV to the most profitable CS in a smart manner. Results of simulations on the IEEE 37 bus distribution network verify that the proposed algorithm improves the social welfare by about 30% on average with respect to an alternative scheduling strategy under the equal participation of EVs in charging and discharging operations. Considering the best-case performance where only EV profit maximization is concerned, our solution also achieves upto 20% improvement in flatting the final electricity load. Furthermore, the results reveal the existence of an optimal number of CSs and an optimal vehicle-to-grid penetration threshold for which the overall profit can be maximized. Our findings serve as guidelines for V2G system designers in smart city scenarios to plan a cost-effective strategy for large-scale EVs distributed energy management