Related papers: Dynamic Trees with Almost-Optimal Access Cost
Decision trees are among the most popular machine learning models and are used routinely in applications ranging from revenue management and medicine to bioinformatics. In this paper, we consider the problem of learning optimal binary…
Autoregressive language models demonstrate excellent performance in various scenarios. However, the inference efficiency is limited by its one-step-one-word generation mode, which has become a pressing problem recently as the models become…
Assuming Zipf's Law to be accurate, we show that existing techniques for partially optimizing binary trees produce results that are approximately 10% worse than true optimal. We present a new approximate optimization technique that runs in…
A new method for constructing minimum-redundancy binary prefix codes is described. Our method does not explicitly build a Huffman tree; instead it uses a property of optimal prefix codes to compute the codeword lengths corresponding to the…
The edit distance between two rooted ordered trees with $n$ nodes labeled from an alphabet~$\Sigma$ is the minimum cost of transforming one tree into the other by a sequence of elementary operations consisting of deleting and relabeling…
Let $n$ denote the number of elements currently in a data structure. An in-place heap is stored in the first $n$ locations of an array, uses $O(1)$ extra space, and supports the operations: minimum, insert, and extract-min. We introduce an…
Min-Cut queries are fundamental: Preprocess an undirected edge-weighted graph, to quickly report a minimum-weight cut that separates a query pair of nodes $s,t$. The best data structure known for this problem simply builds a cut-equivalent…
Frequent tree mining asks us to enumerate tree patterns that occur frequently in a database of rooted trees. This problem is motivated by tree-structured data in bioinformatics, such as glycans and pseudoknot-free RNA secondary structures.…
In 1971, Knuth gave an $O(n^2)$-time algorithm for the classic problem of finding an optimal binary search tree. Knuth's algorithm works only for search trees based on 3-way comparisons, while most modern computers support only 2-way…
We introduce top trees as a design of a new simpler interface for data structures maintaining information in a fully-dynamic forest. We demonstrate how easy and versatile they are to use on a host of different applications. For example, we…
We consider the minimum spanning tree problem with predictions, using the weight-arrival model, i.e., the graph is given, together with predictions for the weights of all edges. Then the actual weights arrive one at a time and an…
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…
Temporal graphs represent interactions between entities over time. Deciding whether entities can reach each other through temporal paths is useful for various applications such as in communication networks and epidemiology. Previous works…
The Minimum Quartet Tree Cost problem is to construct an optimal weight tree from the $3{n \choose 4}$ weighted quartet topologies on $n$ objects, where optimality means that the summed weight of the embedded quartet topologies is optimal…
Interpretability is crucial for doctors, hospitals, pharmaceutical companies and biotechnology corporations to analyze and make decisions for high stakes problems that involve human health. Tree-based methods have been widely adopted for…
We consider the problems of computing maximal palindromes and distinct palindromes in a trie. A trie is a natural generalization of a string, which can be seen as a single-path tree. There is a linear-time offline algorithm to compute…
Decision Tree (DT) Learning is a fundamental problem in Interpretable Machine Learning, yet it poses a formidable optimisation challenge. Practical algorithms have recently emerged, primarily leveraging Dynamic Programming and Branch &…
Searching in P2P networks is fundamental to all overlay networks. P2P networks based on Distributed Hash Tables (DHT) are optimized for single key lookups, whereas unstructured networks offer more complex queries at the cost of increased…
Random forests and, more generally, (decision\nobreakdash-)tree ensembles are widely used methods for classification and regression. Recent algorithmic advances allow to compute decision trees that are optimal for various measures such as…
We address the problem of building and maintaining distributed spanning trees in highly dynamic networks, in which topological events can occur at any time and any rate, and no stable periods can be assumed. In these harsh environments, we…