Related papers: Nested Recursions, Simultaneous Parameters and Tre…
While most methods for solving mixed-integer optimization problems compute a single optimal solution, a diverse set of near-optimal solutions can often lead to improved outcomes. We present a new method for finding a set of diverse…
Decision trees and their ensembles are popular in machine learning as easy-to-understand models. Several techniques have been proposed in the literature for learning tree-based classifiers, with different techniques working well for data…
Random Indexing (RI) K-tree is the combination of two algorithms for clustering. Many large scale problems exist in document clustering. RI K-tree scales well with large inputs due to its low complexity. It also exhibits features that are…
A relaxed $k$-ary tree is an ordered directed acyclic graph with a unique source and sink in which every node has out-degree $k$. These objects arise in the compression of trees in which some repeated subtrees are factored and repeated…
This paper presents a new kind of self-balancing ternary search trie that uses a randomized balancing strategy adapted from Aragon and Seidel's randomized binary search trees ("treaps"). After any sequence of insertions and deletions of…
Recent studies have shown that Dense Retrieval (DR) techniques can significantly improve the performance of first-stage retrieval in IR systems. Despite its empirical effectiveness, the application of DR is still limited. In contrast to…
The tree inclusion problem is, given two node-labeled trees $P$ and $T$ (the ``pattern tree'' and the ``target tree''), to locate every minimal subtree in $T$ (if any) that can be obtained by applying a sequence of node insertion operations…
Each natural number can be associated with some tree graph. Namely, a natural number $n$ can be factorized as $$ n = p_1^{\alpha_1}\ldots p_k^{\alpha_k},$$ where $p_i$ are distinct prime numbers. Since $\alpha_i$ are naturals, they can be…
Graphs are extremely versatile and ubiquitous mathematical structures with potential to model a wide range of domains. For this reason, graph problems have been of interest since the early days of computer science. Some of these problems…
We exploit a bijection between plane recursive trees and Stirling permutations; this yields the equivalence of some results previously proven separately by different methods for the two types of objects as well as some new results. We also…
Analysis of sample survey data often requires adjustments to account for missing data in the outcome variables of principal interest. Standard adjustment methods based on item imputation or on propensity weighting factors rely heavily on…
Sparse residual tree (SRT) is an adaptive exploration method for multivariate scattered data approximation. It leads to sparse and stable approximations in areas where the data is sufficient or redundant, and points out the possible local…
Recurrent neural networks (RNNs) process input text sequentially and model the conditional transition between word tokens. In contrast, the advantages of recursive networks include that they explicitly model the compositionality and the…
We give two new expressions of subresultants, nested subresultant and reduced nested subresultant, for the recursive polynomial remainder sequence (PRS) which has been introduced by the author. The reduced nested subresultant reduces the…
Natural language semantics can be modeled using the phrase-structured model, which can be represented using a tree-type architecture. As a result, recent advances in natural language processing have been made utilising recursive neural…
We define a new family of generalized Stirling permutations that can be interpreted in terms of ordered trees and forests. We prove that the number of generalized Stirling permutations with a fixed number of ascents is given by a natural…
Generalized linear and additive models are very efficient regression tools but the selection of relevant terms becomes difficult if higher order interactions are needed. In contrast, tree-based methods also known as recursive partitioning…
A determined algorithm is presented for solving the rSUM problem for any natural r with a sub-quadratic assessment of time complexity in some cases. In terms of an amount of memory used the obtained algorithm is the nlog^3(n) order. The…
In this paper we firstly review how to \textit{explicitly} solve a system of $3$ \textit{first-order linear recursions }and outline the main properties of these solutions. Next, via a change of variables, we identify a class of systems of…
The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical…