Related papers: Subset-lex: did we miss an order?
Order-preserving pattern matching was introduced recently but it has already attracted much attention. Given a reference sequence and a pattern, we want to locate all substrings of the reference sequence whose elements have the same…
As a kind of basic machine learning method, clustering algorithms group data points into different categories based on their similarity or distribution. We present a clustering algorithm by finding hyper-planes to distinguish the data…
The "Subset Sum problem" is a very well-known NP-complete problem. In this work, a top-k variation of the "Subset Sum problem" is considered. This problem has wide application in recommendation systems, where instead of k best objects the k…
A significant effort has been made to train neural networks that replicate algorithmic reasoning, but they often fail to learn the abstract concepts underlying these algorithms. This is evidenced by their inability to generalize to data…
Total degree reverse lexicographic order is currently generally regarded as most often fastest for computing Groebner bases. This article describes an alternate less mysterious algorithm for computing this order using exponent subtotals and…
We investigate coresets - succinct, small summaries of large data sets - so that solutions found on the summary are provably competitive with solution found on the full data set. We provide an overview over the state-of-the-art in coreset…
Training semantic segmentation models on multiple datasets has sparked a lot of recent interest in the computer vision community. This interest has been motivated by expensive annotations and a desire to achieve proficiency across multiple…
We give new algorithms for generating all n-tuples over an alphabet of m letters, changing only one letter at a time (Gray codes). These algorithms are based on the connection with variations of the Towers of Hanoi game. Our algorithms are…
A relational dataset is often analyzed by optimally assigning a label to each element through clustering or ordering. While similar characterizations of a dataset would be achieved by both clustering and ordering methods, the former has…
This application-oriented study concerns computational musicology, which makes use of grammar systems. We define multi-generative rule-synchronized scattered-context grammar systems (without erasing rules) and demonstrates how to…
We present a construction of subspace codes along with an efficient algorithm for list decoding from both insertions and deletions, handling an information-theoretically maximum fraction of these with polynomially small rate. Our…
Sorting, a classical combinatorial process, forms the bedrock of numerous algorithms with varied applications. A related problem involves efficiently finding the corresponding ranks of all the elements - catering to rank queries, data…
Simplicial partitions are a fundamental structure in computational geometry, as they form the basis of optimal data structures for range searching and several related problems. Current algorithms are built on very specific spatial…
Subset selection in multiple linear regression aims to choose a subset of candidate explanatory variables that tradeoff fitting error (explanatory power) and model complexity (number of variables selected). We build mathematical programming…
This paper presents an approach to parsing humans when there is significant occlusion. We model humans using a graphical model which has a tree structure building on recent work [32, 6] and exploit the connectivity prior that, even in…
A new algorithm, termed subspace evolution and transfer (SET), is proposed for solving the consistent matrix completion problem. In this setting, one is given a subset of the entries of a low-rank matrix, and asked to find one low-rank…
A boolean term order is a total order on subsets of [n]={1,...,n} such that \emptyset < alpha for all nonempty alpha contained in [n], and alpha < beta implies alpha \cup gamma < beta \cup gamma for all gamma which do not intersect alpha or…
Subgraph matching is a fundamental problem in various fields that use graph structured data. Subgraph matching algorithms enumerate all isomorphic embeddings of a query graph q in a data graph G. An important branch of matching algorithms…
Elegant and general algorithms for handling upwards-closed and downwards-closed subsets of WQOs can be developed using the filter-based and ideal-based representation for these sets. These algorithms can be built in a generic or…
We encode arrays as functions which, in turn, are encoded as sets of ordered pairs. The set cardinality of each of these functions coincides with the length of the array it is representing. Then we define a fragment of set theory that is…