Related papers: Towards True Work-Efficiency in Parallel Derandomi…
In the past few years, a successful line of research has lead to lower bounds for several fundamental local graph problems in the distributed setting. These results were obtained via a technique called round elimination. On a high level,…
This paper presents a novel meta algorithm, Partition-Merge (PM), which takes existing centralized algorithms for graph computation and makes them distributed and faster. In a nutshell, PM divides the graph into small subgraphs using our…
Randomized algorithms for very large matrix problems have received a great deal of attention in recent years. Much of this work was motivated by problems in large-scale data analysis, and this work was performed by individuals from many…
Previous parallel sorting algorithms do not scale to the largest available machines, since they either have prohibitive communication volume or prohibitive critical path length. We describe algorithms that are a viable compromise and…
Matching is a central problem in theoretical computer science, with a large body of work spanning the last five decades. However, understanding matching in the time-space bounded setting remains a longstanding open question, even in the…
We present two deterministic dynamic algorithms for the maximum matching problem. (1) An algorithm that maintains a $(2+\epsilon)$-approximate maximum matching in general graphs with $O(\text{poly}(\log n, 1/\epsilon))$ update time. (2) An…
We study parallel algorithms for the minimisation and equivalence checking of Deterministic Finite Automata (DFAs). Regarding DFA minimisation, we implement four different massively parallel algorithms on Graphics Processing Units~(GPUs).…
Recent works on the parallel complexity of Boosting have established strong lower bounds on the tradeoff between the number of training rounds $p$ and the total parallel work per round $t$. These works have also presented highly non-trivial…
We reexamine the classical subset sum problem: given a set $X$ of $n$ positive integers and a number $t$, decide whether there exists a subset of $X$ that sums to $t$; or more generally, compute the set $\mbox{out}$ of all numbers…
We propose a general methodology for testing whether a given polynomial with integer coefficients is identically zero. The methodology evaluates the polynomial at efficiently computable approximations of suitable irrational points. In…
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 $n\times n$ integer matrices $A$ and $B$, where each row of $B$ is a monotone…
Approximating the set of reachable states of a dynamical system is an algorithmic yet mathematically rigorous way to reason about its safety. Although progress has been made in the development of efficient algorithms for affine dynamical…
We present a novel characterization of the mapping of multiple parallelism forms (e.g. data and model parallelism) onto hierarchical accelerator systems that is hierarchy-aware and greatly reduces the space of software-to-hardware mapping.…
In this paper, a derandomized algorithm for sampling decoding is proposed to achieve near-optimal performance in lattice decoding. By setting a probability threshold to sample candidates, the whole sampling procedure becomes deterministic,…
The Massive Parallel Computation (MPC) model is a theoretical framework for popular parallel and distributed platforms such as MapReduce, Hadoop, or Spark. We consider the task of computing a large matching or small vertex cover in this…
This paper considers the scheduling of stochastic jobs on parallel identical machines to minimize the expected total weighted completion time. While this is a classical problem with a significant body of research on approximation algorithms…
We revisit the problem of finding optimal strategies for deterministic Markov Decision Processes (DMDPs), and a closely related problem of testing feasibility of systems of $m$ linear inequalities on $n$ real variables with at most two…
The decomposition method which makes the parallel solution of the block-tridiagonal matrix systems possible is presented. The performance of the method is analytically estimated based on the number of elementary multiplicative operations…
We present a framework for deterministically rounding a dynamic fractional matching. Applying our framework in a black-box manner on top of existing fractional matching algorithms, we derive the following new results: (1) The first…
A random search algorithm intended to solve discrete optimization problems is considered. We outline the main components of the algorithm, and then describe it in more detail. We show how the algorithm can be implemented on parallel…