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Trees can accelerate queries that search or aggregate values over large collections. They achieve this by storing metadata that enables quick pruning (or inclusion) of subtrees when predicates on that metadata can prove that none (or all)…
This article compares the performance of the AVL tree to the performance of the bottom-up, top-down, and left-leaning red-black trees. The bottom-up red-black tree is faster than the AVL tree for insertion and deletion of randomly ordered…
Previous work on Dynamic Complexity has established that there exist dynamic constant-time parallel algorithms for regular tree languages and context-free languages under label or symbol changes. However, these algorithms were not developed…
Short spanning trees subject to additional constraints are important building blocks in various approximation algorithms. Especially in the context of the Traveling Salesman Problem (TSP), new techniques for finding spanning trees with…
Replicated tree data structures are extensively used in collaborative applications and distributed file systems, where clients often perform move operations. Local move operations at different replicas may be safe. However, remote move…
Test-time compute scaling has emerged as a new axis along which to improve model accuracy, where additional computation is used at inference time to allow the model to think longer for more challenging problems. One promising approach for…
Behavior Trees (BTs) are becoming a popular tool to model the behaviors of autonomous agents in the computer game and the robotics industry. One of the key advantages of BTs lies in their composability, where complex behaviors can be built…
We present a study of several generic tree search techniques applied to the Sequential Ordering Problem. This study enables us to propose a simple and competitive tree search algorithm. It consists of an iterative Beam Search algorithm that…
The emerging class of instance-optimized systems has shown potential to achieve high performance by specializing to a specific data and query workloads. Particularly, Machine Learning (ML) techniques have been applied successfully to build…
Let $T$ be a binary search tree. We prove two results about the behavior of the Splay algorithm (Sleator and Tarjan 1985). Our first result is that inserting keys into an empty binary search tree via splaying in the order of either $T$'s…
Concurrency has been a subject of study for more than 50 years. Still, many developers struggle to adapt their sequential code to be accessed concurrently. This need has pushed for generic solutions and specific concurrent data structures.…
We give a general framework for inference in spanning tree models. We propose unified algorithms for the important cases of first-order expectations and second-order expectations in edge-factored, non-projective spanning-tree models. Our…
This paper describes a new and purely functional implementation technique of binary heaps. A binary heap is a tree-based data structure that implements priority queue operations (insert, remove, minimum/maximum) and guarantees at worst…
There has been a significant amount of work in the literature proposing semantic relaxation of concurrent data structures for improving scalability and performance. By relaxing the semantics of a data structure, a bigger design space, that…
Due to the coarse granularity of data accesses and the heavy use of latches, indices in the B-tree family are not efficient for in-memory databases, especially in the context of today's multi-core architecture. In this paper, we present PI,…
While modern biotechnologies allow synthesizing new proteins and function measurements at scale, efficiently exploring a protein sequence space and engineering it remains a daunting task due to the vast sequence space of any given protein.…
Many data are naturally modeled by an unobserved hierarchical structure. In this paper we propose a flexible nonparametric prior over unknown data hierarchies. The approach uses nested stick-breaking processes to allow for trees of…
Supervised machine learning often requires large training sets to train accurate models, yet obtaining large amounts of labeled data is not always feasible. Hence, it becomes crucial to explore active learning methods for reducing the size…
Red-black (RB) trees are one of the most efficient variants of balanced binary search trees. However, they have always been blamed for being too complicated, hard to explain, and not suitable for pedagogical purposes. In the pioneering work…
Indexes are critical for efficient data retrieval and updates in modern databases. Recent advances in machine learning have led to the development of learned indexes, which model the cumulative distribution function of data to predict…