Related papers: New Techniques and Tighter Bounds for Local Comput…
A number of recent papers -- e.g. Brandt et al. (STOC 2016), Chang et al. (FOCS 2016), Ghaffari & Su (SODA 2017), Brandt et al. (PODC 2017), and Chang & Pettie (FOCS 2017) -- have advanced our understanding of one of the most fundamental…
We connect three distinct lines of research that have recently explored extensions of the classical LOCAL model of distributed computing: A. distributed quantum computing and non-signaling distributions [e.g. STOC 2024], B.…
Online algorithms make decisions based on past inputs. In general, the decision may depend on the entire history of inputs. If many computers run the same online algorithm with the same input stream but are started at different times, they…
We present a randomized Local Computation Algorithm (LCA) with query complexity $poly(\Delta) \cdot \log n$ for the Maximal Independent Set (MIS) problem. That is, the algorithm determines whether each node is in the computed MIS or not…
We study *non-adaptive* Local Computation Algorithms (LCA). A reduction of Parnas and Ron (TCS'07) turns any distributed algorithm into a non-adaptive LCA. Plugging known distributed algorithms, this leads to non-adaptive LCAs for constant…
Given a graph $G$ and a seed node $v_s$, the objective of local graph clustering (LGC) is to identify a subgraph $C_s \in G$ (a.k.a. local cluster) surrounding $v_s$ in time roughly linear with the size of $C_s$. This approach yields…
In this work, we present a fast distributed algorithm for local potential problems: these are graph problems where the task is to find a locally optimal solution where no node can unilaterally improve the utility in its local neighborhood…
We study the problem of multiway number partition optimization, which has a myriad of applications in the decision, learning and optimization literature. Even though the original multiway partitioning problem is NP-hard and requires…
In [Phys. Rev. A 69, 022316 (2004)] we presented a description of the action of local Clifford operations on graph states in terms of a graph transformation rule, known in graph theory as \emph{local complementation}. It was shown that two…
Common definitions of the "standard" LOCAL model tend to be sloppy and even self-contradictory on one point: do the nodes update their state using an arbitrary function or a computable function? So far, this distinction has been safe to…
The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…
This paper establishes several convergence results about flows of the dynamical system LCA (Locally Competitive Algorithm) to the mixed $\ell_2$-$\ell_1$ minimization problem LASSO and the constrained version, called CLASSO here, where the…
We introduce a generalized Spiking Locally Competitive Algorithm (LCA) that is biologically plausible and exhibits adaptability to a large variety of neuron models and network connectivity structures. In addition, we provide theoretical…
Error-correcting codes that admit local decoding and correcting algorithms have been the focus of much recent research due to their numerous theoretical and practical applications. An important goal is to obtain the best possible tradeoffs…
We introduce a method for sparsifying distributed algorithms and exhibit how it leads to improvements that go past known barriers in two algorithmic settings of large-scale graph processing: Massively Parallel Computation (MPC), and Local…
The landscape of the distributed time complexity is nowadays well-understood for subpolynomial complexities. When we look at deterministic algorithms in the LOCAL model and locally checkable problems (LCLs) in bounded-degree graphs, the…
We attempt to better understand randomization in local distributed graph algorithms by exploring how randomness is used and what we can gain from it: - We first ask the question of how much randomness is needed to obtain efficient…
The celebrated Time Hierarchy Theorem for Turing machines states, informally, that more problems can be solved given more time. The extent to which a time hierarchy-type theorem holds in the distributed LOCAL model has been open for many…
Longest common extension queries (LCE queries) and runs are ubiquitous in algorithmic stringology. Linear-time algorithms computing runs and preprocessing for constant-time LCE queries have been known for over a decade. However, these…
It is a well known fact that sequential algorithms which exhibit a strong "local" nature can be adapted to the distributed setting given a legal graph coloring. The running time of the distributed algorithm will then be at least the number…