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Ordered set (and map) is one of the most used data type. In addition to standard set operations, like insert, delete and contains, it can provide set-set operations such as union, intersection, and difference. Each of these set-set…
A sorted set (or map) is one of the most used data types in computer science. In addition to standard set operations, like Insert, Remove, and Contains, it can provide set-set operations such as Union,Intersection, and Difference. Each of…
Dynamic tree data structures maintain a forest while supporting insertion and deletion of edges and a broad set of queries in $O(\log n)$ time per operation. Such data structures are at the core of many modern algorithms. Recent work has…
The dynamic trees problem is to maintain a forest undergoing edge insertions and deletions while supporting queries for information such as connectivity. There are many existing data structures for this problem, but few of them are capable…
Dynamic trees are a well-studied and fundamental building block of dynamic graph algorithms dating back to the seminal work of Sleator and Tarjan [STOC'81, (1981), pp. 114-122]. The problem is to maintain a tree subject to online edge…
The dynamic trees problem is to maintain a forest subject to edge insertions and deletions while facilitating queries such as connectivity, path weights, and subtree weights. Dynamic trees are a fundamental building block of a large number…
$k$d-trees are widely used in parallel databases to support efficient neighborhood/similarity queries. Supporting parallel updates to $k$d-trees is therefore an important operation. In this paper, we present BDL-tree, a parallel,…
Balanced search trees are widely used in computer science to efficiently maintain dynamic ordered data. To support efficient set operations (e.g., union, intersection, difference) using trees, the join-based framework is widely studied.…
Algorithms for dynamically maintaining minimum spanning trees (MSTs) have received much attention in both the parallel and sequential settings. While previous work has given optimal algorithms for dense graphs, all existing parallel…
The $k$d-tree is one of the most widely used data structures to manage multi-dimensional data. Due to the ever-growing data volume, it is imperative to consider parallelism in $k$d-trees. However, we observed challenges in existing parallel…
This paper investigates the execution of tree-shaped task graphs using multiple processors. Each edge of such a tree represents some large data. A task can only be executed if all input and output data fit into memory, and a data can only…
Design of an efficient thread-safe concurrent data structure is a balancing act between its implementation complexity and performance. Lock-based concurrent data structures, which are relatively easy to derive from their sequential…
Minimum Spanning Tree (MST) is an important graph algorithm that has wide ranging applications in the areas of computer networks, VLSI routing, wireless communications among others. Today virtually every computer is built out of multi-core…
Tree of Thoughts (ToT) enhances Large Language Model (LLM) reasoning by structuring problem-solving as a spanning tree. However, recent methods focus on search accuracy while overlooking computational efficiency. The challenges of…
In concurrent data structures, the efficiency of set operations can vary significantly depending on the workload characteristics. Numerous concurrent set implementations are optimized and fine-tuned to excel in scenarios characterized by…
N-body algorithms for long-range unscreened interactions like gravity belong to a class of highly irregular problems whose optimal solution is a challenging task for present-day massively parallel computers. In this paper we describe a…
Data processing systems offer an ever increasing degree of parallelism on the levels of cores, CPUs, and processing nodes. Query optimization must exploit high degrees of parallelism in order not to gradually become the bottleneck of query…
In this paper we develop optimal algorithms in the binary-forking model for a variety of fundamental problems, including sorting, semisorting, list ranking, tree contraction, range minima, and ordered set union, intersection and difference.…
Deep research agents, which synthesize information across diverse sources, are significantly constrained by the sequential nature of reasoning. This bottleneck results in high latency, poor runtime adaptability, and inefficient resource…
Tree-structured multi-task architectures have been employed to jointly tackle multiple vision tasks in the context of multi-task learning (MTL). The major challenge is to determine where to branch out for each task given a backbone model to…