Related papers: Benchmarking of algorithms for set partitions
This article describes a geometric partitioning software that can be used for quick computation of data partitions on many-core HPC machines. It is most suited for dynamic applications with load distributions that vary with time.…
Ranking is one of the most fundamental problems in machine learning with applications in many branches of computer science such as: information retrieval systems, recommendation systems, machine translation and computational biology.…
We describe a seriation algorithm for ranking a set of items given pairwise comparisons between these items. Intuitively, the algorithm assigns similar rankings to items that compare similarly with all others. It does so by constructing a…
Benchmark data sets are a cornerstone of machine learning development and applications, ensuring new methods are robust, reliable and competitive. The relative rarity of benchmark sets in computational science, due to the uniqueness of the…
This paper is about how to partition decision variables while decomposing a large-scale optimization problem for the best performance of distributed solution methods. Solving a large-scale optimization problem sequen- tially can be…
A common way of doing algorithm selection is to train a machine learning model and predict the best algorithm from a portfolio to solve a particular problem. While this method has been highly successful, choosing only a single algorithm has…
The aim of this paper is to derive explicit formulas for two distinct values. The first is the total number of symmetric peaks in a set partition of $[n]$ with exactly $k$ blocks, and the second one is the total number of non-symmetric…
This paper develops new combinatorial approaches to analyze and compute special set partitions, called complementary set partitions, which are fundamental in the study of generalized cumulants. Moving away from traditional graph-based and…
Set partitioning is a key component of many algorithms in machine learning, signal processing, and communications. In general, the problem of finding a partition that minimizes a given impurity (loss function) is NP-hard. As such, there…
We study the problem of learning to partition users into groups, where one must learn the compatibilities between the users to achieve optimal groupings. We define four natural objectives that optimize for average and worst case…
We consider the {\em vector partition problem}, where $n$ agents, each with a $d$-dimensional attribute vector, are to be partitioned into $p$ parts so as to minimize cost which is a given function on the sums of attribute vectors in each…
We introduce a framework for benchmarking optimizers according to multiple criteria over various test functions. Based on a recently introduced union-free generic depth function for partial orders/rankings, it fully exploits the ordinal…
We tackle the problem of partitioning players into groups of fixed size, such as allocating eligible students to shared dormitory rooms. Each student submits preferences over the other individual students. We study several settings, which…
Consider the set $\{1,2,\ldots,3n\}$. We are interested in the number of partitions of this set into subsets of three elements each, where the sum of two of them equals the third. We give some criteria such a partition has to fulfill, which…
Number partitioning is one of the classical NP-hard problems of combinatorial optimization. It has applications in areas like public key encryption and task scheduling. The random version of number partitioning has an "easy-hard" phase…
Computing high-quality graph partitions is a challenging problem with numerous applications. In this paper, we present a novel meta-heuristic for the balanced graph partitioning problem. Our approach is based on integer linear programs that…
Benchmarks are a useful tool for empirical performance comparisons. However, one of the main shortcomings of existing benchmarks is that it remains largely unclear how they relate to real-world problems. What does an algorithm's performance…
Clustering is an unsupervised technique of Data Mining. It means grouping similar objects together and separating the dissimilar ones. Each object in the data set is assigned a class label in the clustering process using a distance measure.…
We prove a lemma that is useful to get upper bounds for the number of partitions without a given subsum. From this we can deduce an improved upper bound for the number of sets represented by the (unrestricted or into unequal parts)…
We study the enumeration of set partitions, according to their length, number of parts, cyclic type, and genus. We introduce genus-dependent Bell, Stirling numbers, and Fa\`a di Bruno coefficients. Besides attempting to summarize what is…