Magnus Roos

A survey of approximability and inapproximability results for social welfare optimization in multiagent resource allocation

Multiagent resource allocation provides mechanisms to allocate bundles of resources to agents, where resources are assumed to be indivisible and nonshareable. A central goal is to maximize social welfare of such allocations, which can be measured in terms of the sum of utilities realized by the agents (utilitarian social welfare), in terms of their minimum (egalitarian social welfare), and in terms of their product (Nash product social welfare). Unfortunately, social welfare optimization is a computationally intractable task in many settings. We survey recent approximability and inapproximability results on social welfare optimization in multiagent resource allocation, focusing on the two most central representation forms for utility functions of agents, the bundle form and the k-additive form. In addition, we provide some new (in)approximability results on maximizing egalitarian social welfare and social welfare with respect to the Nash product when restricted to certain special cases.

On the time synchronization of distributed log files in networks with local broadcast media

Real-world experiments in computer networks typically result in a set of log files, one for each system involved in the experiment. Each log file contains event timestamps based on the local clock of the respective system. These clocks are not perfectly accurate, and deviate from each other. For a thorough analysis, however, a common time basis is necessary. In this paper, we tackle the fundamental problem of creating such a common time base for experiments in networks with local broadcast media, where transmissions can be received by more than one node. We show how clock deviations and event times can be estimated with very high accuracy, without introducing any additional traffic in the network. The proposed method is applied after the experiment is completed, using just the set of local log files as its input. It leads to a large linear program with a very specific structure. We exploit the structure to solve the synchronization problem quickly and efficiently, and present an implementation of a specialized solver. Furthermore, we give analytical and numerical evaluation results and present real-world experiments, all underlining the performance and accuracy of the method.

Binary linear programming solutions and non-approximability for control problems in voting systems

In this paper we consider constructive control by adding and deleting candidates in Copeland and Llull voting systems from a theoretical and an experimental point of view. We show how to characterize the optimization versions of these four control problems as special digraph problems and binary linear programming formulations of linear size. Our digraph characterizations allow us to prove the hardness of approximations with absolute performance guarantee for optimal constructive control by deleting candidates in Copeland and by adding candidates in Llull voting schemes and the nonexistence of efficient approximation schemes for optimal constructive control by adding and deleting candidates in Copeland and Llull voting schemes. Our experimental study of running times using LP solvers shows that for a lot of practical instances even the hard control problems can be solved very efficiently.