Related papers: Fast Differentiable Sorting and Ranking
Permutation patterns and pattern avoidance have been intensively studied in combinatorics and computer science, going back at least to the seminal work of Knuth on stack-sorting (1968). Perhaps the most natural algorithmic question in this…
This article introduces a new optimization method to improve mergesort's runtime complexity, when sorting sequences that have equal keys to $O(n log_2 k)$, where $k$ is the number of distinct keys in the sequence. When $k$ is constant, it…
For most algorithms dealing with sets of points in the plane, the only relevant information carried by the input is the combinatorial configuration of the points: the orientation of each triple of points in the set (clockwise,…
A key challenge with machine learning approaches for ranking is the gap between the performance metrics of interest and the surrogate loss functions that can be optimized with gradient-based methods. This gap arises because ranking metrics…
We present quantum algorithms to efficiently perform discriminant analysis for dimensionality reduction and classification over an exponentially large input data set. Compared with the best-known classical algorithms, the quantum algorithms…
Permutation patterns and pattern avoidance have been intensively studied in combinatorics and computer science, going back at least to the seminal work of Knuth on stack-sorting (1968). Perhaps the most natural algorithmic question in this…
Leader election is, together with consensus, one of the most central problems in distributed computing. This paper presents a distributed algorithm, called \STT, for electing deterministically a leader in an arbitrary network, assuming…
Machine learning pipelines often rely on optimization procedures to make discrete decisions (e.g., sorting, picking closest neighbors, or shortest paths). Although these discrete decisions are easily computed, they break the…
Given a signed permutation on $n$ elements, we need to sort it with the fewest reversals. This is a fundamental algorithmic problem motivated by applications in comparative genomics, as it allows to accurately model rearrangements in small…
In the online sorting problem, a sequence of $n$ numbers in $[0, 1]$ (including $\{0,1\}$) have to be inserted in an array of size $m \ge n$ so as to minimize the sum of absolute differences between pairs of numbers occupying consecutive…
Together with a characteristic function, idempotent permutations uniquely determine idempotent maps, as well as their linearly ordered arrangement simultaneously. Furthermore, in-place linear time transformations are possible between them.…
Sorting algorithms are fundamental to computer science, and their correctness criteria are well understood as rearranging elements of a list according to a specified total order on the underlying set of elements. As mathematical functions,…
A dynamic dictionary is a data structure that maintains sets of cardinality at most $n$ from a given universe and supports insertions, deletions, and membership queries. A filter approximates membership queries with a one-sided error that…
While modern general-purpose computing systems have ample amounts of memory, it is still the case that embedded computer systems, such as in a refrigerator, are memory limited; hence, such embedded systems motivate the need for strictly…
Rank and select queries on bitmaps are essential building bricks of many compressed data structures, including text indexes, membership and range supporting spatial data structures, compressed graphs, and more. Theoretically considered yet…
We present a novel technique for constructing differentiable order-type operations, including soft ranking, soft top-k selection, and soft permutations. Our approach leverages an efficient closed-form formula for the inverse of the function…
We consider the problem of computing the rank of an m x n matrix A over a field. We present a randomized algorithm to find a set of r = rank(A) linearly independent columns in \~O(|A| + r^\omega) field operations, where |A| denotes the…
The energy efficiency of analog forms of computing makes it one of the most promising candidates to deploy resource-hungry machine learning tasks on resource-constrained system such as mobile or embedded devices. However, it is well known…
Much of the copious literature on the subject of sorting has concentrated on minimizing the number of comparisons and/or exchanges/copies. However, a more appropriate yardstick for the performance of sorting algorithms is based on the total…
Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…