Periodic Reporting for period 4 - APEG (Algorithmic Performance Guarantees: Foundations and Applications)
Período documentado: 2021-04-01 hasta 2021-09-30
Optimization problems are ubiquitous in computer science and, as such, omnipresent in modern society. However, a major part of these problems cannot be solved to optimality. Consequently, algorithms that achieve provably good performance guarantees are of immense importance. The goal of this project is to significantly advance the state of the art on algorithmic performance guarantees, breaking new grounds in the areas of online algorithms, approximations algorithms and algorithmic game theory. The project develops new algorithmic techniques. These novel approaches are applied to solve fundamental algorithmic problems. Specifically, the project attacks long-standing open problems and explores new algorithmic settings arising in modern applications. The research agenda encompasses a wide spectrum of classical and urgent topics including (a) resource allocation in computer systems, (b) data structuring, (c) graph problems, with relations to Internet advertising, (d) complex networks and (e) massively parallel systems. The contributions advance modern algorithmics, with a focus on problems of high theoretical or practical relevance.
In the project we have investigated a broad spectrum of fundamental optimization problems. We examined classical scheduling problems, such as makespan minimization, as well as basic packing problems, such as knapsack and bin packing. We have also considered essential selection problems, including the secretary problem. Additionally, our research has addressed central resource management and data structuring problems. For each of these settings, we have developed new and significantly improved performance guarantees. In some cases, we were able to provide the first progress after 25 years. Our results rely on new algorithms, input models and analysis techniques. In the area of graphs algorithms, we have explored fundamental online matching and graph coloring problems. We have studied the value of randomizing and settled the performance of the most popular and widely used strategies. In the project we have also investigated various problems in the area of energy-efficient algorithms. In particular, we have conducted the first comprehensive algorithmic study of energy conservation in data centers. Finally, our project work has addressed time-inconsistent planning, a modern problem at the interface of computer science and behavioral economics. We have settled the computational complexity and approximability of basic problems. Moreover, we have introduced novel performance measures and related their expressiveness.
Many of our contributions bring algorithms research closer to practice. Specifically, we have developed results and techniques in the modern research direction entitled “Beyond Worst-Case Analysis”. For resource management and data structuring problems, we have defined and examined new input models in which, for the first time, theoretically proven and experimentally observed algorithmic performance guarantees match. Additionally, we have studied the popular random-order model, for a number of fundamental optimization problems. For some settings, we have presented the first performance guarantees that beat those in the standard adversarial setting. Furthermore, our research had defined fundamental optimization problems in energy conservation so that they are amenable to algorithmic investigations. Specifically, we have developed tight analyses for data centers with heterogeneous architectures. At the interface of computer science and behavioral economics, our work on time-inconsistent planning has introduced an array of new concepts towards a computational understanding of present-biased behavior. In summary, several of our conference publications have been invited to journal special issues, containing the best articles of the respective venues. One paper received a best paper award.