Related papers: SONIK: Efficient In-situ All Item Rank Generation …
We show how to construct a dynamic ordered dictionary, supporting insert/delete/rank/select on a set of $n$ elements from a universe of size $U$, that achieves the optimal amortized expected time complexity of $O(1 + \log n / \log \log U)$,…
Condorcet domains are fundamental objects in the theory of majority voting; they are sets of linear orders with the property that if every voter picks a linear order from this set, assuming that the number of voters is odd, and alternatives…
The process of rank aggregation is intimately intertwined with the structure of skew-symmetric matrices. We apply recent advances in the theory and algorithms of matrix completion to skew-symmetric matrices. This combination of ideas…
We present a physically-inspired model and an efficient algorithm to infer hierarchical rankings of nodes in directed networks. It assigns real-valued ranks to nodes rather than simply ordinal ranks, and it formalizes the assumption that…
An efficient, accurate and reliable approximation of a matrix by one of lower rank is a fundamental task in numerical linear algebra and signal processing applications. In this paper, we introduce a new matrix decomposition approach termed…
Standard sequential generation methods assume a pre-specified generation order, such as text generation methods which generate words from left to right. In this work, we propose a framework for training models of text generation that…
In this paper we give a fast algorithm to generate all partitions of a positive integer $n$. Integer partitions may be encoded as either ascending or descending compositions for the purposes of systematic generation. It is known that the…
In this report, we summarize the set partition enumeration problems and thoroughly explain the algorithms used to solve them. These algorithms iterate through the partitions in lexicographic order and are easy to understand and implement in…
We present algorithms for generating alternative solutions for explicit acyclic AND/OR structures in non-decreasing order of cost. The proposed algorithms use a best first search technique and report the solutions using an implicit…
Generating irreducible site-occupancy configurations by taking advantage of crystal symmetry is a ubiquitous method for accelerating of disordered structure prediction, which plays an important role in condensed matter physics and material…
Ranking is at the core of Information Retrieval. Classic ranking optimization studies often treat ranking as a sorting problem with the assumption that the best performance of ranking would be achieved if we rank items according to their…
Smart Sort algorithm is a "smart" fusion of heap construction procedures (of Heap sort algorithm) into the conventional "Partition" function (of Quick sort algorithm) resulting in a robust version of Quick sort algorithm. We have also…
A randomized algorithm for computing a compressed representation of a given rank-structured matrix $A \in \mathbb{R}^{N\times N}$ is presented. The algorithm interacts with $A$ only through its action on vectors. Specifically, it draws two…
When factorizing binary matrices, we often have to make a choice between using expensive combinatorial methods that retain the discrete nature of the data and using continuous methods that can be more efficient but destroy the discrete…
Recht, Fazel, and Parrilo provided an analogy between rank minimization and $\ell_0$-norm minimization. Subject to the rank-restricted isometry property, nuclear norm minimization is a guaranteed algorithm for rank minimization. The…
Sorting an array is a fundamental routine in machine learning, one that is used to compute rank-based statistics, cumulative distribution functions (CDFs), quantiles, or to select closest neighbors and labels. The sorting function is…
There are several ideas being used today for Web information retrieval, and specifically in Web search engines. The PageRank algorithm is one of those that introduce a content-neutral ranking function over Web pages. This ranking is applied…
A "partial ordering" is a way to heuristically order a set of examples (partial orderings are a set where, for certain pairs of elements, one precedes the other). While these orderings may only be approximate, they can be useful for guiding…
Algorithms to generate various combinatorial structures find tremendous importance in computer science. In this paper, we begin by reviewing an algorithm proposed by Rohl that generates all unique permutations of a list of elements which…
In-place associative integer sorting technique was developed, improved and specialized for distinct integers. The technique is suitable for integer sorting. Hence, given a list S of n integers S[0...n-1], the technique sorts the integers in…