Utilitarian resource assignment

This paper studies a resource allocation problem introduced by Koutsoupias and Papadimitriou. The scenario is modelled as a multiple-player game in which each player selects one of a finite number of known resources. The cost to the player is the total weight of all players who choose that resource, multiplied by the ``delay'' of that resource. Recent papers have studied the Nash equilibria and social optima of this game in terms of the $L_\infty$ cost metric, in which the social cost is taken to be the maximum cost to any player. We study the $L_1$ variant of this game, in which the social cost is taken to be the sum of the costs to the individual players, rather than the maximum of these costs. We give bounds on the size of the coordination ratio, which is the ratio between the social cost incurred by selfish behavior and the optimal social cost; we also study the algorithmic problem of finding optimal (lowest-cost) assignments and Nash Equilibria. Additionally, we obtain bounds on the ratio between alternative Nash equilibria for some special cases of the problem.Comment: 19 page

PAC Classification based on PAC Estimates of Label Class Distributions

A standard approach in pattern classification is to estimate the distributions of the label classes, and then to apply the Bayes classifier to the estimates of the distributions in order to classify unlabeled examples. As one might expect, the better our estimates of the label class distributions, the better the resulting classifier will be. In this paper we make this observation precise by identifying risk bounds of a classifier in terms of the quality of the estimates of the label class distributions. We show how PAC learnability relates to estimates of the distributions that have a PAC guarantee on their $L_1$ distance from the true distribution, and we bound the increase in negative log likelihood risk in terms of PAC bounds on the KL-divergence. We give an inefficient but general-purpose smoothing method for converting an estimated distribution that is good under the $L_1$ metric into a distribution that is good under the KL-divergence.Comment: 14 page

Preference Elicitation in Matching Markets Via Interviews: A Study of Offline Benchmarks

In this paper we study two-sided matching markets in which the participants do not fully know their preferences and need to go through some costly deliberation process in order to learn their preferences. We assume that such deliberations are carried out via interviews, thus the problem is to find a good strategy for interviews to be carried out in order to minimize their use, whilst leading to a stable matching. One way to evaluate the performance of an interview strategy is to compare it against a nave ïalgorithm that conducts all interviews. We argue however that a more meaningful comparison would be against an optimal offline algorithm that has access to agents' preference orderings under complete information. We show that, unless P=NP, no offline algorithm can compute the optimal interview strategy in polynomial time. If we are additionally aiming for a particular stable matching, we provide restricted settings under which efficient optimal offline algorithms exist

Preference Elicitation in Matching Markets Via Interviews: A Study of Offline Benchmarks

The stable marriage problem and its extensions have been extensively studied, with much of the work in the literature assuming that agents fully know their own preferences over alternatives. This assumption however is not always practical (especially in large markets) and agents usually need to go through some costly deliberation process in order to learn their preferences. In this paper we assume that such deliberations are carried out via interviews, where an interview involves a man and a woman, each of whom learns information about the other as a consequence. If everybody interviews everyone else, then clearly agents can fully learn their preferences. But interviews are costly, and we may wish to minimize their use. It is often the case, especially in practical settings, that due to correlation between agents’ preferences, it is unnecessary for all potential interviews to be carried out in order to obtain a stable matching. Thus the problem is to find a good strategy for interviews to be carried out in order to minimize their use, whilst leading to a stable matching. One way to evaluate the performance of an interview strategy is to compare it against a na¨ıve algorithm that conducts all interviews. We argue however that a more meaningful comparison would be against an optimal offline algorithm that has access to agents’ preference orderings under complete information. We show that, unless P=NP, no offline algorithm can compute the optimal interview strategy in polynomial time. If we are additionally aiming for a particular stable matching (perhaps one with certain desirable properties), we provide restricted settings under which efficient optimal offline algorithms exist

Problems in merging Earth sensing satellite data sets

Satellite remote sensing systems provide a tremendous source of data flow to the Earth science community. These systems provide scientists with data of types and on a scale previously unattainable. Looking forward to the capabilities of Space Station and the Earth Observing System (EOS), the full realization of the potential of satellite remote sensing will be handicapped by inadequate information systems. There is a growing emphasis in Earth science research to ask questions which are multidisciplinary in nature and global in scale. Many of these research projects emphasize the interactions of the land surface, the atmosphere, and the oceans through various physical mechanisms. Conducting this research requires large and complex data sets and teams of multidisciplinary scientists, often working at remote locations. A review of the problems of merging these large volumes of data into spatially referenced and manageable data sets is presented