Related papers: Fast Dynamic Programming in Trees in the MPC Model
We study the Weighted Min Cut problem in the Adaptive Massively Parallel Computation (AMPC) model. In 2019, Behnezhad et al. [3] introduced the AMPC model as an extension of the Massively Parallel Computation (MPC) model. In the past…
We prove that given a discrete space with $n$ points which is either embedded in a system of $k$ trees, or the Cartesian product of $k$ trees, we can compute all eccentricities in ${\cal O}(2^{{\cal O}(k\log{k})}(N+n)^{1+o(1)})$ time, where…
Cellular automata are synchronous discrete dynamical systems used to describe complex dynamic behaviors. The dynamic is based on local interactions between the components, these are defined by a finite graph with an initial node coloring…
We consider global problems, i.e. problems that take at least diameter time, even when the bandwidth is not restricted. We show that all problems considered admit efficient solutions in low-treewidth graphs. By ``efficient'' we mean that…
We revisit classic string problems considered in the area of parameterized complexity, and study them through the lens of dynamic data structures. That is, instead of asking for a static algorithm that solves the given instance efficiently,…
It is well known that many local graph problems, like Vertex Cover and Dominating Set, can be solved in 2^{O(tw)}|V|^{O(1)} time for graphs G=(V,E) with a given tree decomposition of width tw. However, for nonlocal problems, like the…
We study the Maximum Cardinality Matching (MCM) and the Maximum Weight Matching (MWM) problems, on trees and on some special classes of graphs, in the Online Preemptive and the Incremental Dynamic Graph models. In the {\em Online…
We present two algorithms for dynamically maintaining a spanning forest of a graph undergoing edge insertions and deletions. Our algorithms guarantee {\em worst-case update time} and work against an adaptive adversary, meaning that an edge…
We give the first algorithm that maintains an approximate decision tree over an arbitrary sequence of insertions and deletions of labeled examples, with strong guarantees on the worst-case running time per update request. For instance, we…
The randomized online-LOCAL model captures a number of models of computing; it is at least as strong as all of these models: - the classical LOCAL model of distributed graph algorithms, - the quantum version of the LOCAL model, - finitely…
We give a simple characterization of the functions that can be computed deterministically by anonymous processes in dynamic networks, depending on the number of leaders in the network. In addition, we provide efficient distributed…
This paper demonstrates the usefulness of distributed local verification of proofs, as a tool for the design of self-stabilizing algorithms.In particular, it introduces a somewhat generalized notion of distributed local proofs, and utilizes…
We prove several new tight distributed lower bounds for classic symmetry breaking graph problems. As a basic tool, we first provide a new insightful proof that any deterministic distributed algorithm that computes a $\Delta$-coloring on…
We provide a deterministic scheme for solving any decidable problem in the distributed {sleeping model}. The sleeping model is a generalization of the standard message-passing model, with an additional capability of network nodes to enter a…
Random forests and, more generally, (decision\nobreakdash-)tree ensembles are widely used methods for classification and regression. Recent algorithmic advances allow to compute decision trees that are optimal for various measures such as…
The success of modern parallel paradigms such as MapReduce, Hadoop, or Spark, has attracted a significant attention to the Massively Parallel Computation (MPC) model over the past few years, especially on graph problems. In this work, we…
Dynamic programming is widely used for exact computations based on tree decompositions of graphs. However, the space complexity is usually exponential in the treewidth. We study the problem of designing efficient dynamic programming…
Distributed algorithms for solving coupled semidefinite programs (SDPs) commonly require many iterations to converge. They also put high computational demand on the computational agents. In this paper we show that in case the coupled…
In this paper, we present a deterministic variant of Chan's randomized partition tree [Discret. Comput. Geom., 2012]. This result leads to numerous applications. In particular, for $d$-dimensional simplex range counting (for any constant $d…
Given a graph $G=(V,E)$, a $\beta$-ruling set is a subset $S\subseteq V$ that is i) independent, and ii) every node $v\in V$ has a node of $S$ within distance $\beta$. In this paper we present almost optimal distributed algorithms for…