14 papers
LLCT: Learnable Linear Canonical Transform Family with Stability for Visual Feature Processing
Zunwei Fu, Zhen Wang, Dachun Yang +1
Visual structures are often characterized by directional geometry, local oscillation, and spatial--frequency coupling. To overcome the limitations of conventional spatial convoluti…
Faster Deterministic Approximation for Counting Knapsack
Ce Jin, Jaewoo Park, Barna Saha
Given nonnegative integer weights and an integer knapsack capacity , the Knapsack problem asks to count the number of subsets $I \subseteq \{1, 2, \do…
Almost Optimal Multiple Source Shortest Paths and Reachability
Barna Saha, Yinzhan Xu, Christopher Ye
Given a graph, computing distances and reachabilities from a small set of vertices to the whole graph is an important primitive both in theory and in practice. In undirected unweig…
Furthest Pair Requires Quadratic Time in Superconstant Dimension under SETH
Barna Saha, Yinzhan Xu, Christopher Ye
Several fundamental problems in computational geometry admit algorithms with running time for points in dimensions, making them among the most pro…
Deterministic Monotone Min-Plus Product and Convolution
Ce Jin, Jaewoo Park, Barna Saha +1
The Monotone Min-Plus Product problem is a useful primitive that has seen many algorithmic applications over the past decade. In this problem, we are given two integer…
On the Computational Hardness of Transformers
Barna Saha, Yinzhan Xu, Christopher Ye +1
The transformer has revolutionized modern AI across language, vision, and beyond. It consists of layers, each running attention heads in parallel and feeding the combined o…
Hardness of Dynamic Tree Edit Distance and Friends
Bingbing Hu, Jakob Nogler, Barna Saha
String Edit Distance is a more-than-classical problem whose behavior in the dynamic setting, where the strings are updated over time, is well studied. A single-character substituti…
Optimal Graph Reconstruction by Counting Connected Components in Induced Subgraphs
Hadley Black, Arya Mazumdar, Barna Saha +1
The graph reconstruction problem has been extensively studied under various query models. In this paper, we propose a new query model regarding the number of connected components,…
Subquadratic Algorithms and Hardness for Attention with Any Temperature
Shreya Gupta, Boyang Huang, Barna Saha +2
Despite the popularity of the Transformer architecture, the standard algorithm for computing Attention suffers from quadratic time complexity in context length . Alman and Song…
Average-Case Hardness of Parity Problems: Orthogonal Vectors, k-SUM and More
Mina Dalirrooyfard, Andrea Lincoln, Barna Saha +1
This work establishes conditional lower bounds for average-case {\em parity}-counting versions of the problems -XOR, -SUM, and -OV. The main contribution is a set of self-…
Faster Weighted and Unweighted Tree Edit Distance and APSP Equivalence
Jakob Nogler, Adam Polak, Barna Saha +3
The tree edit distance (TED) between two rooted ordered trees with nodes labeled from an alphabet is the minimum cost of transforming one tree into the other by a sequence…
Fine-Grained Optimality of Partially Dynamic Shortest Paths and More
Barna Saha, Virginia Vassilevska Williams, Yinzhan Xu +1
Single Source Shortest Paths () is among the most well-studied problems in computer science. In the incremental (resp. decremental) setting, the goal is to maintain…
The I/O Complexity of Attention, or How Optimal is Flash Attention?
Barna Saha, Christopher Ye
Self-attention is at the heart of the popular Transformer architecture, yet suffers from quadratic time and memory complexity. The breakthrough FlashAttention algorithm revealed I/…
Faster Approximate All Pairs Shortest Paths
Barna Saha, Christopher Ye
The all pairs shortest path problem (APSP) is one of the foundational problems in computer science. For weighted dense graphs on vertices, no truly sub-cubic algorithms exist t…