Shortest Unique Substring Query Revisited

We revisit the problem of finding shortest unique substring (SUS) proposed recently by [6]. We propose an optimal $O(n)$ time and space algorithm that can find an SUS for every location of a string of size $n$. Our algorithm significantly improves the $O(n^2)$ time complexity needed by [6]. We also support finding all the SUSes covering every location, whereas the solution in [6] can find only one SUS for every location. Further, our solution is simpler and easier to implement and can also be more space efficient in practice, since we only use the inverse suffix array and longest common prefix array of the string, while the algorithm in [6] uses the suffix tree of the string and other auxiliary data structures. Our theoretical results are validated by an empirical study that shows our algorithm is much faster and more space-saving than the one in [6]

Mechanisms with costly knowledge

Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2016.Cataloged from PDF version of thesis.Includes bibliographical references (pages 18-21).We propose investigating the design and analysis of game theoretic mechanisms when the players have very unstructured initial knowledge about themselves, but can refine their own knowledge at a cost. We consider several set-theoretic models of "costly knowledge". Specifically, we consider auctions of a single good in which a player i's only knowledge about his own valuation, [theta]i, is that it lies in a given interval [a, b]. However, the player can pay a cost, depending on a and b (in several ways), and learn a possibly arbitrary but shorter (in several metrics) sub-interval, which is guaranteed to contain [theta]i. In light of the set-theoretic uncertainty they face, it is natural for the players to act so as to minimize their regret. As a first step, we analyze the performance of the second-price mechanism in regret-minimizing strategies, and show that, in all our models, it always returns an outcome of very high social welfare.by Atalay M. Ileri.S.M