Final Report Summary - EUSACOU (European South American network on Combinatorial Optimization under Uncertainty) The purpose of this program is to stimulate research cooperation between Europe and South America in the field of uncertainty in combinatorial optimization. Combinatorial optimization is a lively field in mathematics and computer science. It aims at finding a best solution among a finite or countably infinite number of solutions. In standard optimization techniques, we assume that all the relevant data to the problem are completely known. However, this assumption is not always realistic. In many scenarios, we need to optimize when the data is not fully available and decisions with wide-ranging implications have to be made in the face of incomplete data. In this project, we study methods for dealing with uncertainty in combinatorial optimization. We will study three different models for uncertainty. The first one is online optimization in which decisions have to be made without any knowledge of future information to be released. A second model is stochastic optimization in which the uncertainty is modeled by the assumption that part of the data is given only by probability distributions. The third model for uncertainty is by an algorithmic game theory approach. Here it is assume that the solution is obtained by the interaction of a multitude of autonomous agents, each of which is holding private information. Therefore, there is no centralized control that has access to all relevant input data and that is able to enforce the computed solution as the final outcome. The objectives of this international research staff exchange program are: (i) Intensify the joint research in optimization under uncertainty among researchers in Europe and South America, (ii) Training of junior researchers, (iii) Disseminate and transfer knowledge obtained during the program among academics in South America and the European Research Area.In WP2, we worked on scheduling problems. During and after the visit of Marban (UM) to UChile, a new model for scheduling in the dark was developed. This work resulted in a chapter in the PhD thesis of Marban. Furthermore, during the secondments of Vredeveld (UM) to UChile, Rivera Letelier (UChile) to UM and Olver (VU) to UChile, we considered the quality of solutions when the to be scheduled jobs can be seen as selfish agents. Split scheduling problems were considered during and after the secondment of Verdugo (UChile) to VU. This work resulted in two presentations at MAPSP 2013, a paper that has been accepted in Journal of Scheduling and another paper that has been submitted to Operations Research Letters. During the secondment of Van der Zwaan (UM) to UChile, the knapsack cover problem was investigated. In WP3, the Stougie (VUA), Marchetti-Spaccamela (UOR) and Feuerstein (UBA) started during the secondments of the first two to UBA their work on a family of optimization problems arising in social networks. Furthermore, Stougie (VU) and Marchetti-Spaccamela (UOR) visited UChile where they worked with the team of UChile on strong LP formulations. This resulted in a paper presented at IPCO 2014 and an extended version of this paper has been submitted to Mathematical Programming B. These researchers also investigated some stochastic scheduling problem that was started 7 years ago by Stougie in collaboration with Megow (TU Berlin) and resulted in a paper presented at MAPSP 2013.Furthermore in WP 3, Feuerstein (UBA) visited VU as well as UOR. He worked with the team of VU and Marchetti-Spaccamela (UOR) on an apriori scheduling problem, where they considered the makespan objective. Some first results were obtained during this visit and subsequentresults were obtained in collaboration with other researchers. The results were presented in a paper and a presentation at the 20th COCOON.Verdugo (UChile) visited UOR in 2014. Together with the team of UOR, he worked on group scheduling problems. Some first results have been obtained, but further research is necessary to present the results in a paper.Finally, in WP3, Gabriel Tolosa (UBA) visited UOR. With the team of UOR, he worked on search engine caching. The results of this visit were presented in a paper which will be presented at the 21st SPIRE.In WP4, during and after the stay of Rodrigues (UFRGS) at VUA, research was done on the traffic assignment problem. They studied the inefficiency of Nash equilibria under random permutations, introducing the concept of smoothed price of anarchy and obtained several results. Furthermore, during and after the secondment of Schäfer (VUA) and Anagnostopolous (UOR) to UFRGS continued research on the smoothed price of anarchy by applying it to other type of combinatorial optimization problems.Buriol (UFRGS) visited UOR in 2013. She worked together with the team of UOR on an extension of previous work on developing graph data stream algorithms. As a result, they wrote a paper that was submitted to Transactions on Knowledge Discovery in Data. Schäfer and Rahn (VU) visited UChile in 2014. Together with the team of UChile, they worked on upper and lower bounds for the price of anarchy in some scheduling games. Moreover, they studied the existence of subgame perfect Nash equilibria in Hotelling games and they did research on coordination games on graphs. Verschae (UChile) visited VU as well as UM. He worked together with the team of UM on some stochastic scheduling policies and with the team of the VU he worked on scheduling with buffers. They considered several LP relaxations and approximation algorithms as well as hardness proofs. De Keijzer (UOR) visited UChile. Together with Correa (UChile) he worked on existence and computation of equilibria in two player "cops-and-robbers"-games on undirected graphs, computation of an optimal strategy in a specific type of shortest-path game, and on inefficiency of subgame perfect equilibria in symmetric linear congestion games. The latter resulted in a working paper. To finish this paper a second visit of De Keijzer is planned for the end of 2014.Finally, in WP5, we organized a closing workshop in which several of these above mentioned results were presented.The EUSACOU project brings together scientists from different traditions on both sides of the Atlantic. The value added consists in the combination of researchers from different schools of thoughts and academic traditions, working on joint research. The exchanges with the purpose of undertaking joint research and participating in common activities have led to significant results, due to the cross-fertilization taking place between different research traditions. By paying particular attention to both formal and informal cooperation, EUSACOU will provide new insights and contribute to the conceptualization of combinatorial optimization in general and, more specifically, combinatorial optimization under uncertainty. This project has led to lasting research cooperations across the Atlantic, which is shown among others by planned research visits of Vera (UChile) to VU, Vredeveld (UM) and De Keijzer (UOR) to UChile and of Schäfer (VU) to UFRGS. Moreover, there are several joint research projects involving several of the European partners, showing that the collaboration among the European partners is also lasting.