Related papers: New Techniques and Tighter Bounds for Local Comput…
In this work, we develop the low-space Massively Parallel Computation (MPC) complexity landscape for a family of fundamental graph problems on trees. We present a general method that solves most locally checkable labeling (LCL) problems…
A single-commodity congestion approximator for a graph is a compact data structure that approximately predicts the edge congestion required to route any set of single-commodity flow demands in a network. A hierarchical congestion…
Graph clustering has many important applications in computing, but due to growing sizes of graphs, even traditionally fast clustering methods such as spectral partitioning can be computationally expensive for real-world graphs of interest.…
Locally Checkable Labeling (LCL) problems include essentially all the classic problems of $\mathsf{LOCAL}$ distributed algorithms. In a recent enlightening revelation, Chang and Pettie [arXiv 1704.06297] showed that any LCL (on bounded…
We present an analysis of the Locally Competitive Algorithm (LCA), a Hopfield-style neural network that efficiently solves sparse approximation problems (e.g., approximating a vector from a dictionary using just a few non-zero…
We explore the use of local algorithms in the design of streaming algorithms for the Maximum Directed Cut problem. Specifically, building on the local algorithm of Buchbinder et al. (FOCS'12) and Censor-Hillel et al. (ALGOSENSORS'17), we…
We study the design of local algorithms for massive graphs. A local algorithm is one that finds a solution containing or near a given vertex without looking at the whole graph. We present a local clustering algorithm. Our algorithm finds a…
Deep neural networks are a promising solution for applications that solve problems based on learning data sets. DNN accelerators solve the processing bottleneck as a domain-specific processor. Like other hardware solutions, there must be…
Linear temporal logic (LTL) is a specification language for finite sequences (called traces) widely used in program verification, motion planning in robotics, process mining, and many other areas. We consider the problem of learning LTL…
We study the local complexity landscape of locally checkable labeling (LCL) problems on constant-degree graphs with a focus on complexities below $\log^* n$. Our contribution is threefold: Our main contribution is that we complete the…
We extend classical methods of computational complexity to the realm of distributed computing, where they sometimes prove more effective than in their original context. Our focus is on decision problems in the LOCAL model, a setting in…
This paper presents algorithms for local inversion of maps and shows how several important computational problems such as cryptanalysis of symmetric encryption algorithms, RSA algorithm and solving the elliptic curve discrete log problem…
The locally competitive algorithm (LCA) can solve sparse coding problems across a wide range of use cases. Recently, convolution-based LCA approaches have been shown to be highly effective for enhancing robustness for image recognition…
Local Search problem, which finds a local minimum of a black-box function on a given graph, is of both practical and theoretical importance to combinatorial optimization, complexity theory and many other areas in theoretical computer…
We investigate a zone based approach for the reachability problem in timed automata. The challenge is to alleviate the size explosion of the search space when considering networks of timed automata working in parallel. In the timed setting…
We investigate the space complexity of solving linear systems of equations. While all known deterministic or randomized algorithms solving a square system of $n$ linear equations in $n$ variables require $\Omega(\log^2 n)$ space, Ta-Shma…
This paper considers the problem of canonical-correlation analysis (CCA) (Hotelling, 1936) and, more broadly, the generalized eigenvector problem for a pair of symmetric matrices. These are two fundamental problems in data analysis and…
Transformer architectures have achieved remarkable success in various domains. While efficient alternatives to Softmax Attention have been widely studied, the search for more expressive mechanisms grounded in theoretical insight-even at…
We consider the distributed message-passing {LOCAL} model. In this model a communication network is represented by a graph where vertices host processors, and communication is performed over the edges. Computation proceeds in synchronous…
Canonical Correlation Analysis (CCA) is a widely used statistical tool with both well established theory and favorable performance for a wide range of machine learning problems. However, computing CCA for huge datasets can be very slow…