Related papers: Hypersuccinct Trees -- New universal tree source c…
Search trees on trees (STTs) generalize the fundamental binary search tree (BST) data structure: in STTs the underlying search space is an arbitrary tree, whereas in BSTs it is a path. An optimal BST of size $n$ can be computed for a given…
Many applications require data processing to be performed on individual pieces of data which are of finite sizes, e.g., files in cloud storage units and packets in data networks. However, traditional universal compression solutions would…
Alphabetic codes and binary search trees are combinatorial structures that abstract search procedures in ordered sets endowed with probability distributions. In this paper, we design new linear-time algorithms to construct alphabetic codes,…
Binary jumbled pattern matching asks to preprocess a binary string $S$ in order to answer queries $(i,j)$ which ask for a substring of $S$ that is of length $i$ and has exactly $j$ 1-bits. This problem naturally generalizes to…
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…
Many multivariate data such as social and biological data exhibit complex dependencies that are best characterized by graphs. Unlike sequential data, graphs are, in general, unordered structures. This means we can no longer use classic,…
We initiate the study of tree structures in the context of scenario-based robust optimization. Specifically, we study Binary Search Trees (BSTs) and Huffman coding, two fundamental techniques for efficiently managing and encoding data based…
Recently, the existence of considerable amount of redundancy in the Internet traffic has stimulated the deployment of several redundancy elimination techniques within the network. These techniques are often based on either packet-level…
We study the complexity of finding communication trees with the lowest possible completion time for rooted, irregular gather and scatter collective communication operations in fully connected, $k$-ported communication networks under a…
Efficient methods for storing and querying are critical for scaling high-order n-gram language models to large corpora. We propose a language model based on compressed suffix trees, a representation that is highly compact and can be easily…
The need for scalable concurrent ordered set data structures with linearizable range query support is increasing due to the rise of multicore computers, data processing platforms and in-memory databases. This paper presents a new concurrent…
We introduce a new compression scheme for labeled trees based on top trees. Our compression scheme is the first to simultaneously take advantage of internal repeats in the tree (as opposed to the classical DAG compression that only exploits…
The Binary Space Partitioning-Tree~(BSP-Tree) process was recently proposed as an efficient strategy for space partitioning tasks. Because it uses more than one dimension to partition the space, the BSP-Tree Process is more efficient and…
Many common sequential data sources, such as source code and natural language, have a natural tree-structured representation. These trees can be generated by fitting a sequence to a grammar, yielding a hierarchical ordering of the tokens in…
The problem of {\em efficiently} finding the best match for a query in a given set with respect to the Euclidean distance or the cosine similarity has been extensively studied in literature. However, a closely related problem of efficiently…
Implicit Neural Representations for Videos (NeRV) have emerged as a powerful paradigm for video representation, enabling direct mappings from frame indices to video frames. However, existing NeRV-based methods do not fully exploit temporal…
We study learning-augmented binary search trees (BSTs) via Treaps with carefully designed priorities. The result is a simple search tree in which the depth of each item $x$ is determined by its predicted weight $w_x$. Specifically, each…
Given an $n$-bit array $A$, the succinct rank data structure problem asks to construct a data structure using space $n+r$ bits for $r\ll n$, supporting rank queries of form $\mathtt{rank}(x)=\sum_{i=0}^{x-1} A[i]$. In this paper, we design…
We revisit tree compression with top trees (Bille et al, ICALP'13) and present several improvements to the compressor and its analysis. By significantly reducing the amount of information stored and guiding the compression step using a…
We present an algorithm for computing a maximum agreement subtree of two unrooted evolutionary trees. It takes O(n^{1.5} log n) time for trees with unbounded degrees, matching the best known time complexity for the rooted case. Our…