Related papers: What Does Dynamic Optimality Mean in External Memo…
In a variety of applications, we need to keep track of the development of a data set over time. For maintaining and querying this multi version data I/O-efficiently, external memory data structures are required. In this paper, we present a…
We present an optimal partially-persistent external-memory search tree with amortized I/O bounds matching those achieved by the non-persistent $B^{\varepsilon}$-tree by Brodal and Fagerberg [SODA 2003]. In a partially-persistent data…
Tree-based data structures are ubiquitous across applications. Therefore, a multitude of different tree implementations exist. However, while these implementations are diverse, they share a tree structure as the underlying data structure.…
Decision tree learning is a widely used approach in machine learning, favoured in applications that require concise and interpretable models. Heuristic methods are traditionally used to quickly produce models with reasonably high accuracy.…
The $B^{\epsilon}$-tree [Brodal and Fagerberg 2003] is a simple I/O-efficient external-memory-model data structure that supports updates orders of magnitude faster than B-tree with a query performance comparable to the B-tree: for any…
Consider laying out a fixed-topology tree of N nodes into external memory with block size B so as to minimize the worst-case number of block memory transfers required to traverse a path from the root to a node of depth D. We prove that the…
Computing an optimal classification tree that provably maximizes training performance within a given size limit, is NP-hard, and in practice, most state-of-the-art methods do not scale beyond computing optimal trees of depth three.…
Dynamic regression trees are an attractive option for automatic regression and classification with complicated response surfaces in on-line application settings. We create a sequential tree model whose state changes in time with the…
We study the dynamic optimality conjecture, which predicts that splay trees are a form of universally efficient binary search tree, for any access sequence. We reduce this claim to a regular access bound, which seems plausible and might be…
An external memory data structure is presented for maintaining a dynamic set of $N$ two-dimensional points under the insertion and deletion of points, and supporting 3-sided range reporting queries and top-$k$ queries, where top-$k$ queries…
In this paper we describe a fully-dynamic data structure for the planar point location problem in the external memory model. Our data structure supports queries in $O(\log_B n(\log\log_B n)^3))$ I/Os and updates in $O(\log_B n(\log\log_B…
In this paper, a new and novel data structure is proposed to dynamically insert and delete segments. Unlike the standard segment trees[3], the proposed data structure permits insertion of a segment with interval range beyond the interval…
We present an axiomatic framework for analyzing the algorithmic properties of decision trees. This framework supports the classification of decision tree problems through structural and ancestral constraints within a rigorous mathematical…
In recent years, significant progress has been made on algorithms for learning optimal decision trees, primarily in the context of binary features. Extending these methods to continuous features remains substantially more challenging due to…
We give the first data structure for the problem of maintaining a dynamic set of n elements drawn from a partially ordered universe described by a tree. We define the Line-Leaf Tree, a linear-sized data structure that supports the…
This thesis presents a number of results related to path traversal in trees and graphs. In particular, we focus on data structures which allow such traversals to be performed efficiently in the external memory setting. In addition, for…
We study sequential search without priors. Our interest lies in decision rules that are close to being optimal under each prior and after each history. We call these rules dynamically robust. The search literature employs optimal rules…
We revisit self-adjusting external memory tree data structures, which combine the optimal (and practical) worst-case I/O performances of B-trees, while adapting to the online distribution of queries. Our approach is analogous to undergoing…
Uniquely represented data structures represent each logical state with a unique storage state. We study the problem of maintaining a dynamic set of $n$ keys from a totally ordered universe in this context. We introduce a two-layer data…
Survival analysis studies and predicts the time of death, or other singular unrepeated events, based on historical data, while the true time of death for some instances is unknown. Survival trees enable the discovery of complex nonlinear…