National Research University – Higher School of Economics

About: National Research University – Higher School of Economics is a education organization based out in Moscow, Russia. It is known for research contribution in the topics: Population & Computer science. The organization has 12873 authors who have published 23376 publications receiving 256396 citations.

Wavelet trees meet suffix trees

Abstract: We present an improved wavelet tree construction algorithm and discuss its applications to a number of rank/select problems for integer keys and strings.Given a string of length n over an alphabet of size σ ≤ n, our method builds the wavelet tree in O(n log σ / [EQUATION]log n) time, improving upon the state-of-the-art algorithm by a factor of [EQUATION]log n. As a consequence, given an array of n integers we can construct in O(n[EQUATION]log n) time a data structure consisting of O(n) machine words and capable of answering rank/select queries for the subranges of the array in O(log n/ log log n) time. This is a log log n-factor improvement in query time compared to Chan and Patrascu (SODA 2010) and a [EQUATION]log n-factor improvement in construction time compared to Brodal et al. (Theor. Comput. Sci. 2011).Next, we switch to stringological context and propose a novel notion of wavelet suffix trees. For a string w of length n, this data structure occupies O(n) words, takes O(n[EQUATION]log n) time to construct, and simultaneously captures the combinatorial structure of substrings of w while enabling efficient top-down traversal and binary search. In particular, with a wavelet suffix tree we are able to answer in O(log|x|) time the following two natural analogues of rank/select queries for suffixes of substrings:1) For substrings x and y of w (given by their endpoints) count the number of suffixes of x that are lexicographically smaller than y;2) For a substring x of w (given by its endpoints) and an integer k, find the k-th lexicographically smallest suffix of x.We further show that wavelet suffix trees allow to compute a run-length-encoded Burrows-Wheeler transform of a substring x of w (again, given by its endpoints) in O(s log |x|) time, where s denotes the length of the resulting run-length encoding. This answers a question by Cormode and Muthukrishnan (SODA 2005), who considered an analogous problem for Lempel-Ziv compression.All our algorithms, except for the construction of wavelet suffix trees, which additionally requires O(n) time in expectation, are deterministic and operate in the word RAM model.

Winning by Losing: Incentive Incompatibility in Multiple Qualifiers

Abstract: In sport tournaments, the rules are presumably structured in a way that any team cannot be better off (e.g., to advance to the next round of competition) by losing instead of winning a game. However, the organizers may overlook a drawback in the competition rules which allows for the possibility of perverse incentives. The existing national rules of awarding places for the UEFA Champions League and the UEFA Europa League, which are based on the results of the national championship, a round-robin tournament, and the national cup, a knock-out tournament, might produce a situation where a team will be strictly better off by losing a game. Competition rules of the European qualification tournament to the World Cup 2014 and qualification tournament to Euro 2016 suffer from the same problem. We consider arbitrary qualification systems (r, k) consisting of r round-robin and k knock-out tournaments, k,r ≥ 0, k r ≥ 1, and show that incentive incompatibility arises in two cases: (i) if r ≥ 2 or (ii) if r = 1, k ≥ 1 and the allocation of vacant slots, which appear when the intersection of a pair of sets of winners in all tournaments is non-empty, favors knock-out tournaments.