Related papers: Sublinear time algorithms in the theory of groups …
Graph coloring problems are a central topic of study in the theory of algorithms. We study the problem of partially coloring partially colorable graphs. For $\alpha \leq 1$ and $k \in \mathbb{Z}^+$, we say that a graph $G=(V,E)$ is…
Any graph with maximum degree $\Delta$ admits a proper vertex coloring with $\Delta + 1$ colors that can be found via a simple sequential greedy algorithm in linear time and space. But can one find such a coloring via a sublinear algorithm?…
We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions…
Many algorithms are designed to work well on average over inputs. When running such an algorithm on an arbitrary input, we must ask: Can we trust the algorithm on this input? We identify a new class of algorithmic problems addressing this,…
We provide linear-time algorithms for geometric graphs with sublinearly many crossings. That is, we provide algorithms running in O(n) time on connected geometric graphs having n vertices and k crossings, where k is smaller than n by an…
Monotonicity is a simple yet significant qualitative characteristic. We consider the problem of segmenting an array in up to K segments. We want segments to be as monotonic as possible and to alternate signs. We propose a quality metric for…
We consider the problem of testing graph cluster structure: given access to a graph $G=(V, E)$, can we quickly determine whether the graph can be partitioned into a few clusters with good inner conductance, or is far from any such graph?…
Graph coloring is one of the most famous computational problems with applications in a wide range of areas such as planning and scheduling, resource allocation, and pattern matching. So far coloring problems are mostly studied on static…
We present an algorithm for approximating semidefinite programs with running time that is sublinear in the number of entries in the semidefinite instance. We also present lower bounds that show our algorithm to have a nearly optimal running…
We initiate a systematic study of algorithms that are both differentially private and run in sublinear time for several problems in which the goal is to estimate natural graph parameters. Our main result is a differentially-private…
Lekkerkerker and Boland characterized the minimal forbidden induced subgraphs for the class of interval graphs. We give a linear-time algorithm to find one in any graph that is not an interval graph. Tucker characterized the minimal…
A locally testable semigroup S is a semigroup with the property that for some nonnegative integer k, called the order or level of local testability, two words u and v in some set of generators for semigroup S are equal in the semigroup if…
We present a new approach for solving (minimum disagreement) correlation clustering that results in sublinear algorithms with highly efficient time and space complexity for this problem. In particular, we obtain the following algorithms for…
Graph Neural Networks have gained huge interest in the past few years. These powerful algorithms expanded deep learning models to non-Euclidean space and were able to achieve state of art performance in various applications including…
We study which property testing and sublinear time algorithms can be transformed into graph streaming algorithms for random order streams. Our main result is that for bounded degree graphs, any property that is constant-query testable in…
Real-time analysis of graphs containing temporal information, such as social media streams, Q&A networks, and cyber data sources, plays an important role in various applications. Among them, detecting patterns is one of the fundamental…
Graphs are widely used in various fields of computer science. They have also found application in unrelated areas, leading to a diverse range of problems. These problems can be modeled as relationships between entities in various contexts,…
A right [left] locally testable language S is a language with the property that for some non negative integer k two words u and v in alphabet S are equal in the semi group if (1) the prefix and suffix of the words of length k coincide, (2)…
We investigate quantum algorithms for classification, a fundamental problem in machine learning, with provable guarantees. Given $n$ $d$-dimensional data points, the state-of-the-art (and optimal) classical algorithm for training…
Parameter testing algorithms are using constant number of queries to estimate the value of a certain parameter of a very large finite graph. It is well-known that graph parameters such as the independence ratio or the edit-distance from…