Related papers: Worst-Case Optimal Tree Layout in External Memory
Recent advancements in large language models have significantly improved their context windows, yet challenges in effective long-term memory management remain. We introduce MemTree, an algorithm that leverages a dynamic, tree-structured…
When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in…
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.…
We consider the parameterized version of the maximum internal spanning tree problem, which, given an $n$-vertex graph and a parameter $k$, asks for a spanning tree with at least $k$ internal vertices. Fomin et al. [J. Comput. System Sci.,…
A maximal repetition, or run, in a string, is a maximal periodic substring whose smallest period is at most half the length of the substring. In this paper, we consider runs that correspond to a path on a trie, or in other words, on a…
B-slack trees, a subclass of B-trees that have substantially better worst-case space complexity, are introduced. They store $n$ keys in height $O(\log_b n)$, where $b$ is the maximum node degree. Updates can be performed in $O(\log_{\frac b…
We study the problem of list ranking in the parallel external memory (PEM) model. We observe an interesting dual nature for the hardness of the problem due to limited information exchange among the processors about the structure of the…
Supervised learning algorithms generally assume the availability of enough memory to store data models during the training and test phases. However, this assumption is unrealistic when data comes in the form of infinite data streams, or…
A theoretical memory with limited processing power and internal connectivity at each element is proposed. This memory carries out parallel processing within itself to solve generic array problems. The applicability of this in-memory…
As well known the rotation distance D(S,T) between two binary trees S, T of n vertices is the minimum number of rotations of pairs of vertices to transform S into T. We introduce the new operation of chain rotation on a tree, involving two…
Deep neural networks (DNNs) depend on the storage of a large number of parameters, which consumes an important portion of the energy used during inference. This paper considers the case where the energy usage of memory elements can be…
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…
Given a digraph $D$, the Minimum Leaf Out-Branching problem (MinLOB) is the problem of finding in $D$ an out-branching with the minimum possible number of leaves, i.e., vertices of out-degree 0. We prove that MinLOB is polynomial-time…
Delay-tolerant networks (DTNs) are characterized by a possible absence of end-to-end communication routes at any instant. Still, connectivity can generally be established over time and space. The optimality of a temporal path (journey) in…
A \emph{tree-partition} of a graph $G$ is a proper partition of its vertex set into `bags', such that identifying the vertices in each bag produces a forest. The \emph{tree-partition-width} of $G$ is the minimum number of vertices in a bag…
We consider the worst-case load-shedding problem in electric power networks where a number of transmission lines are to be taken out of service. The objective is to identify a pre-specified number of line outage that leads to the maximum…
We propose a natural process for allocating n balls into n bins that are organized as the vertices of an undirected graph G. Each ball first chooses a vertex u in G uniformly at random. Then the ball performs a local search in G starting…
Recently, studying fundamental graph problems in the \emph{Massively Parallel Computation (MPC) framework, inspired by the MapReduce paradigm, has gained a lot of attention. An assumption common to a vast majority of approaches is to allow…
This paper describes a memory-efficient transformer model designed to drive a reduction in memory usage and execution time by substantial orders of magnitude without impairing the model's performance near that of the original model.…
Machine learning has an emerging critical role in high-performance computing to modulate simulations, extract knowledge from massive data, and replace numerical models with efficient approximations. Decision forests are a critical tool…