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On the Minimum Violations Ranking of a Tournament

Management Science, 1986
This paper examines the problem of rank ordering a set of players or objects on the basis of a set of pairwise comparisons arising from a tournament. The criterion for deriving this ranking is to have as few cases as possible where player i is ranked above j while i was actually defeated by j in the tournament.
Iqbal Ali, Wade D. Cook, Moshe Kress
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On Minimum Edge Ranking Spanning Trees

Journal of Algorithms, 1999
Summary: We introduce the problem of computing a Minimum Edge Ranking Spanning Tree (MERST); i.e., find a spanning tree of a given graph \(G\) whose edge ranking is minimum. Although the minimum edge ranking of a given tree can be computed in polynomial time, we show that problem MERST is NP-hard.
Kazuhisa Makino   +2 more
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Minimum Rank Error Language Modeling

IEEE Transactions on Audio, Speech, and Language Processing, 2009
Statistical language modeling has been successfully developed for speech recognition and information retrieval. The minimum classification error (MCE) training was undertaken to enhance speech recognition performance by minimizing the word error rate.
Jen-Tzung Chien, Meng-Sung Wu
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Statistical Inference of Minimum Rank Factor Analysis

Psychometrika, 2002
For any given number of factors, Minimum Rank Factor Analysis yields optimal communalities for an observed covariance matrix in the sense that the unexplained common variance with that number of factors is minimized, subject to the constraint that both the diagonal matrix of unique variances and the observed covariance matrix minus that diagonal matrix
Shapiro, A, Ten Berge, JMF
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Processing Ranked Queries with the Minimum Space

2006
Practical applications often need to rank multi-variate records by assigning various priorities to different attributes. Consider a relation that stores students' grades on two courses: database and algorithm. Student performance is evaluated by an “overall score” calculated as w1 · gdb + w2 · galg, where w1, w2 are two input “weights”, and gdb (galg ...
Yufei Tao 0001, Marios Hadjieleftheriou
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On the minimum rank of distance matrices

Mathematical Inequalities & Applications
Summary: Let \(X= \{x_1,\dots,x_n\}\) be afinite set endowed with a metric \(d\). The matrix \(A=(d(x_i,x_j))_{n \times n}\) is called a distance matrix. In this paper we discuss about the minimum rank that can be achieved by an \(n \times n\) distance matrix and prove that the rank of every \(5 \times 5\) and \(6 \times 6\) distance matrix is not less
Gachkooban, Zahra, Alizadeh, Rahim
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The Minimum Acceptable Violation Ranking of Alternatives from Voters’ Ordinal Rankings

2015
Motived by applications of ordinal ranking and adjustment consensus in group decision making, we study the problem of aggregating all voters' ordinal ranking on a set of alternatives into an adjusted "consensus" ranking. In this problem, every voter ranks a set of alternatives respectively, and we know the adjustment acceptability.
Kelin Luo, Yinfeng Xu
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Matroids and the Minimum Rank Problem for Matrix Patterns

The American Mathematical Monthly, 2020
Suppose the only thing we know about a matrix is which of its entries are zero. What can we say about its rank? We develop a framework for applying matroid theory to this question.
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Minimum rank of graphs

The minimum rank over a field F of a graph G is the smallest possible rank among all symmetric matrices over F whose ( i , j )th entry ( i ≠ j ) is nonzero whenever ij is an edge in G and is zero otherwise, where zero is the additive identity of F. A universally optimal matrix for a graph G is an integer symmetric matrix A such that every off-diagonal ...
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Minimum rank completions

Linear and Multilinear Algebra, 1991
Charles R. Johnson, Glen T. Whitney
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