A New Ranking Algorithm for A Round-Robin Tournament

The problem of ranking players in a round- robin tournament, in which outcome of any match is a win or a loss, is to rank players according to their performances in the tournament. In this paper, we have improved previously developed MST (Majority Spanning Tree) algorithm for solving this problem, where the number of violations has been chosen as the criterion of optimality. We have compared the performance of our algorithm with the MST algorithm and GIK algorithm

Maxing, Ranking and Preference Learning

PAC maximum selection (maxing) and ranking of $n$ elements via randompairwise comparisons have diverse applications and have been studiedunder many models and assumptions. We consider $(\epsilon,\delta)$-PACmaxing and ranking using pairwise comparisons for \nobreak{general}probabilistic models. We present a comprehensive understanding ofthree important problems in PAC preference learning: maxing, ranking,and estimating \emph{all} pairwise preference probabilities, in theadaptive setting.{\bf SST + STI:} We consider $(\epsilon,\delta)$-PAC maximum-selectionand ranking using pairwise comparisons for \nobreak{general}probabilistic models whose comparison probabilities satisfy\emph{strong stochastic transitivity (SST)} and \emph{stochastic triangle inequality (STI)}. Modifying the popular knockouttournament, we propose a simple maximum-selection algorithm that uses$\mathcal{O}\left(\frac{n}{\epsilon^2} \log\frac1{\delta}\right)$ comparisons, optimal up to a constantfactor. We then derive a general framework that uses noisy binarysearch to speed up many ranking algorithms, and combine it with mergesort to obtain a ranking algorithm that uses \mathcal{O}\left(\fracn{\epsilon^2}\log n(\log \log n)^3\right) comparisons for$\delta=\frac1n$, optimal up to a $(\log \log n)^3$ factor.{\bf SST +/- STI and Borda:} With just one simple natural assumption:\emph{strong stochastic transitivity (SST)}, we show that maxing canbe performed with linearly many comparisons yet ranking requiresquadratically many. With no assumptions at all, we show that for theBorda-score metric, maximum selection can be performed with linearlymany comparisons and ranking can be performed with \cO(n\log n)comparisons.{\bf General Transitive Models} With just \emph{Weak Stochastic Transitivity (WST)}, we show that maxing requires $\Omega(n^2)$comparisons and with slightly more restrictive \emph{Medium Stochastic Transitivity (MST)}, we present a linear complexity maxingalgorithm. With \emph{Strong Stochastic Transitivity (SST)} and\emph{Stochastic Triangle Inequality (STI)}, we derive a rankingalgorithm with optimal $\mathcal{O}(n\log n)$ complexity and anoptimal algorithm that estimates all pairwise preferenceprobabilities.{\bf Sequential and Competitive} We extend the well-known\emph{secretary problem} to a probabilistic setting, and apply theintuition gained to derive the first query-optimal sequentialalgorithm for probabilistic-maxing. Furthermore, departing fromprevious assumptions, the algorithm and performance guarantees applyeven for infinitely many items, hence in particular do not requirea-priori knowledge of the number of items. The algorithm has linearcomplexity, and is optimal also in the streaming setting and for bothtraditional- and dueling-bandits. In a non-streaming setting, amodification of the algorithm is \emph{competitive} in that itrequires essentially the lowest number of queries not just in theworst case, but for every underlying distribution

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum

\u3ci\u3eA Pictorial History of Bryant University: 1989-2018 An Era of Transformation\u3c/i\u3e

https://digitalcommons.bryant.edu/bryantuniversity1989-2018/1000/thumbnail.jp

University of San Diego News Print Media Coverage 2009.02

Printed clippings housed in folders with a table of contents arranged by topic.https://digital.sandiego.edu/print-media/1073/thumbnail.jp

A Polyhedral Study of Mixed 0-1 Set

We consider a variant of the well-known single node fixed charge network flow set with constant capacities. This set arises from the relaxation of more general mixed integer sets such as lot-sizing problems with multiple suppliers. We provide a complete polyhedral characterization of the convex hull of the given set

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum

LIPIcs, Volume 244, ESA 2022, Complete Volume

LIPIcs, Volume 244, ESA 2022, Complete Volum