Related papers: Using statistical encoding to achieve tree succinc…
A simple linear-time algorithm for constructing a linear context-free tree grammar of size O(rg + r g log (n/r g))for a given input tree T of size n is presented, where g is the size of a minimal linear context-free tree grammar for T, and…
We give an algorithm to explicitly compute the largest subtree, in the local Bruhat-Tits tree for PSL_2(k), whose vertices correspond to orders containing a given suborder H, in terms of a set of generators for H. The shape of this subtree…
We describe an algorithm for compressing a partially ordered set, or \emph{poset}, so that it occupies space matching the information theory lower bound (to within lower order terms), in the worst case. Using this algorithm, we design a…
Given a string $T$, it is known that its suffix tree can be represented using the compact directed acyclic word graph (CDAWG) with $e_T$ arcs, taking overall $O(e_T+e_{{\overline{T}}})$ words of space, where ${\overline{T}}$ is the reverse…
Transformer-based models have demonstrated significant success in various source code representation tasks. Nonetheless, traditional positional embeddings employed by these models inadequately capture the hierarchical structure intrinsic to…
Phylogenetic (evolutionary) trees and networks are leaf-labeled graphs that are widely used to represent the evolutionary relationships between entities such as species, languages, cancer cells, and viruses. To reconstruct and analyze…
Most of the attention in statistical compression is given to the space used by the compressed sequence, a problem completely solved with optimal prefix codes. However, in many applications, the storage space used to represent the prefix…
Structural decomposition methods offer powerful theoretical guarantees for join evaluation, yet they are rarely used in real-world query optimizers. A major reason is the difficulty of combining cost-based plan search and structure-based…
Simulation of fermionic Hamiltonians with gate-based quantum computers requires the selection of an encoding from fermionic operators to quantum gates, the most widely used being the Jordan-Wigner transform. Many alternative encodings…
We study the compressed representation of a ranked tree by a (string) straight-line program (SLP) for its preorder traversal, and compare it with the well-studied representation by straight-line context free tree grammars (which are also…
Let tw(G) denote the treewidth of graph G. Given a graph G and a positive integer k such that tw(G) <= k + 1, we are to decide if tw(G) <= k. We give a certifying algorithm RTW ("R" for recursive) for this task: it returns one or more…
In this paper, we consider the problem of efficiently representing a set $S$ of $n$ items out of a universe $U=\{0,...,u-1\}$ while supporting a number of operations on it. Let $G=g_1...g_n$ be the gap stream associated with $S$, $gap$ its…
We present a succinct data structure for permutation graphs, and their superclass of circular permutation graphs, i.e., data structures using optimal space up to lower order terms. Unlike concurrent work on circle graphs (Acan et al. 2022),…
This paper is concerned with the approximation of tensors using tree-based tensor formats, which are tensor networks whose graphs are dimension partition trees. We consider Hilbert tensor spaces of multivariate functions defined on a…
Detecting all the strings that occur in a text more frequently or less frequently than expected according to an IID or a Markov model is a basic problem in string mining, yet current algorithms are based on data structures that are either…
Retrieval-Augmented Generation (RAG) has significantly enhanced Large Language Models' ability to access external knowledge, yet current graph-based RAG approaches face two critical limitations in managing hierarchical information: they…
The field of succinct data structures has flourished over the last 16 years. Starting from the compressed suffix array (CSA) by Grossi and Vitter (STOC 2000) and the FM-index by Ferragina and Manzini (FOCS 2000), a number of generalizations…
We present a family of encodings for sequence labeling dependency parsing, based on the concept of hierarchical bracketing. We prove that the existing 4-bit projective encoding belongs to this family, but it is suboptimal in the number of…
Tensor train (TT) decomposition is a powerful representation for high-order tensors, which has been successfully applied to various machine learning tasks in recent years. However, since the tensor product is not commutative, permutation of…
BERT based ranking models have achieved superior performance on various information retrieval tasks. However, the large number of parameters and complex self-attention operation come at a significant latency overhead. To remedy this, recent…