Related papers: Fast Enumeration of Combinatorial Objects
We propose RoBiRank, a ranking algorithm that is motivated by observing a close connection between evaluation metrics for learning to rank and loss functions for robust classification. The algorithm shows a very competitive performance on…
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 consider the problem of sorting $n$ items, given the outcomes of $m$ pre-existing comparisons. We present a simple and natural deterministic algorithm that runs in $O(m + \log T)$ time and does $O(\log T)$ comparisons, where $T$ is the…
Ranked enumeration is a query-answering paradigm where the query answers are returned incrementally in order of importance (instead of returning all answers at once). Importance is defined by a ranking function that can be specific to the…
We consider the embedding problem in coding theory: given an independence (a code-related property) and an independent language $L$, find a maximal independent language containing $L$. We consider the case where the code-related property is…
We consider the range mode problem where given a sequence and a query range in it, we want to find items with maximum frequency in the range. We give time- and space- efficient algorithms for this problem. Our algorithms are efficient for…
Many problems in information theory can be reduced to optimizations over matrices, where the rank of the matrices is constrained. We establish a link between rank-constrained optimization and the theory of quantum entanglement. More…
Object ranking or "learning to rank" is an important problem in the realm of preference learning. On the basis of training data in the form of a set of rankings of objects represented as feature vectors, the goal is to learn a ranking…
The rankability of data is a recently proposed problem that considers the ability of a dataset, represented as a graph, to produce a meaningful ranking of the items it contains. To study this concept, a number of rankability measures have…
Combinatorial optimization can be described as the problem of finding a feasible subset that maximizes a objective function. The paper discusses combinatorial optimization problems, where for each dimension the set of feasible subsets is…
In this work, we introduce a framework to study the effect of random operations on the combinatorial list-decodability of a code. The operations we consider correspond to row and column operations on the matrix obtained from the code by…
Many latent (factorized) models have been proposed for recommendation tasks like collaborative filtering and for ranking tasks like document or image retrieval and annotation. Common to all those methods is that during inference the items…
Assortment optimization refers to the problem of designing a slate of products to offer potential customers, such as stocking the shelves in a convenience store. The price of each product is fixed in advance, and a probabilistic choice…
Sparse coding, which represents a data point as a sparse reconstruction code with regard to a dictionary, has been a popular data representation method. Meanwhile, in database retrieval problems, learning the ranking scores from data points…
Motivated by a historical combinatorial problem that resembles the well-known Josephus problem, we investigate circular partition algorithms and formulate problems in deterministic finite automata with practical algorithms. The historical…
Ranking bit patterns -- finding the index of a given pattern in an ordered sequence -- is a major bottleneck scaling up numerical quantum many-body calculations, as fermionic and hard-core bosonic states translate naturally to bit patterns.…
The avalanche quantity of the information developed by mankind has led to concept of automation of knowledge extraction - Data Mining ([1]). This direction is connected with a wide spectrum of problems - from recognition of the fuzzy set to…
Prolog's ability to return multiple answers on backtracking provides an elegant mechanism to derive reversible encodings of combinatorial objects as Natural Numbers i.e. {\em ranking} and {\em unranking} functions. Starting from a…
In the combinatorial recommender systems, multiple items are fed to the user at one time in the result page, where the correlations among the items have impact on the user behavior. In this work, we model the combinatorial recommendation as…
The problem of frequent pattern mining has been studied quite extensively for various types of data, including sets, sequences, and graphs. Somewhat surprisingly, another important type of data, namely rank data, has received very little…