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Ragusa, Maria Alessandra (Ed.)We study scheduling mechanisms that explore the tradeoff between containing the spread of COVID19 and performing inperson activity in organizations. Our mechanisms, referred to as group scheduling , are based on partitioning the population randomly into groups and scheduling each group on appropriate days with possible gaps (when no one is working and all are quarantined). Each group interacts with no other group and, importantly, any person who is symptomatic in a group is quarantined. We show that our mechanisms effectively tradeoff inperson activity for more effective control of the COVID19 virus spread. In particular, we show that a mechanism which partitions the population into two groups that alternatively work inperson for five days each, flatlines the number of COVID19 cases quite effectively, while still maintaining inperson activity at 70% of preCOVID19 level. Other mechanisms that partitions into two groups with less continuous work days or more spacing or three groups achieve even more aggressive control of the virus at the cost of a somewhat lower inperson activity (about 50%). We demonstrate the efficacy of our mechanisms by theoretical analysis and extensive experimental simulations on various epidemiological models based on realworld data.Free, publiclyaccessible full text available September 15, 2023

Motivated by the increasing need to understand the distributed algorithmic foundations of largescale graph computations, we study some fundamental graph problems in a messagepassing model for distributed computing where k ≥ 2 machines jointly perform computations on graphs with n nodes (typically, n >> k). The input graph is assumed to be initially randomly partitioned among the k machines, a common implementation in many realworld systems. Communication is pointtopoint, and the goal is to minimize the number of communication rounds of the computation. Our main contribution is the General Lower Bound Theorem , a theorem that can be used to show nontrivial lower bounds on the round complexity of distributed largescale data computations. This result is established via an informationtheoretic approach that relates the round complexity to the minimal amount of information required by machines to solve the problem. Our approach is generic, and this theorem can be used in a “cookbook” fashion to show distributed lower bounds for several problems, including nongraph problems. We present two applications by showing (almost) tight lower bounds on the round complexity of two fundamental graph problems, namely, PageRank computation and triangle enumeration . These applications show that our approach can yield lower boundsmore »

We study the communication cost (or message complexity) of fundamental distributed symmetry breaking problems, namely, coloring and MIS. While significant progress has been made in understanding and improving the running time of such problems, much less is known about the message complexity of these problems. In fact, all known algorithms need at least Ω(m) communication for these problems, where m is the number of edges in the graph. We addressthe following question in this paper: can we solve problems such as coloring and MIS using sublinear, i.e., o(m) communication, and if sounder what conditions? In a classical result, Awerbuch, Goldreich, Peleg, and Vainish [JACM 1990] showed that fundamental global problems such asbroadcast and spanning tree construction require at least o(m) messages in the KT1 Congest model (i.e., Congest model in which nodes have initial knowledge of the neighbors' ID's) when algorithms are restricted to be comparisonbased (i.e., algorithms inwhich node ID's can only be compared). Thirty five years after this result, King, Kutten, and Thorup [PODC 2015] showed that onecan solve the above problems using Õ(n) messages (n is the number of nodes in the graph) in Õ(n) rounds in the KT1 Congest model if noncomparisonbased algorithms are permitted. Anmore »

We study several fundamental problems in the kmachine model, a messagepassing model for largescale distributed computations where k ≥ 2 machines jointly perform computations on a large input of size N, (typically, N ≫ k). The input is initially partitioned (randomly or in a balanced fashion) among the k machines, a common implementation in many realworld systems. Communication is pointtopoint, and the goal is to minimize the number of communication rounds of the computation. Our main result is a general technique for designing efficient deterministic distributed algorithms in the kmachine model using PRAM algorithms. Our technique works by efficiently simulating PRAM algorithms in the kmachine model in a deterministic way. This simulation allows us to arrive at new algorithms in the kmachine model for some problems for which no efficient kmachine algorithms are known before and also improve on existing results in the kmachine model for some problems. While our simulation allows us to obtain kmachine algorithms for any problem with a known PRAM algorithm, we mainly focus on graph problems. For an input graph on n vertices and m edges, we obtain Õ(m/k 2 ) round 4 algorithms for various graph problems such as rconnectivity for r = 1,more »

Gilbert, Seth (Ed.)This paper concerns designing distributed algorithms that are singularly optimal, i.e., algorithms that are simultaneously time and message optimal, for the fundamental leader election problem in asynchronous networks. Kutten et al. (JACM 2015) presented a singularly near optimal randomized leader election algorithm for general synchronous networks that ran in O(D) time and used O(m log n) messages (where D, m, and n are the network’s diameter, number of edges and number of nodes, respectively) with high probability. Both bounds are near optimal (up to a logarithmic factor), since Ω(D) and Ω(m) are the respective lower bounds for time and messages for leader election even for synchronous networks and even for (MonteCarlo) randomized algorithms. On the other hand, for general asynchronous networks, leader election algorithms are only known that are either time or message optimal, but not both. Kutten et al. (DISC 2020) presented a randomized asynchronous leader election algorithm that is singularly near optimal for complete networks, but left open the problem for general networks. This paper shows that singularly near optimal (up to polylogarithmic factors) bounds can be achieved for general asynchronous networks. We present a randomized singularly near optimal leader election algorithm that runs in O(D + log²more »

Maximal Independent Set (MIS) is one of the fundamental problems in distributed computing. The round (time) complexity of distributed MIS has traditionally focused on the worstcase time for all nodes to finish. The bestknown (randomized) MIS algorithms take O(log n) worstcase rounds on general graphs (where n is the number of nodes). Breaking the O(log n) worstcase bound has been a longstanding open problem, while currently the bestknown lower bound is [EQUATION] rounds. Motivated by the goal to reduce total energy consumption in energyconstrained networks such as sensor and ad hoc wireless networks, we take an alternative approach to measuring performance. We focus on minimizing the total (or equivalently, the average) time for all nodes to finish. It is not clear whether the currently bestknown algorithms yield constantround (or even o(log n)) nodeaveraged round complexity for MIS in general graphs. We posit the sleeping model, a generalization of the traditional model, that allows nodes to enter either "sleep" or "waking" states at any round. While waking state corresponds to the default state in the traditional model, in sleeping state a node is "offline", i.e., it does not send or receive messages (and messages sent to it are dropped as well)more »

The Knearest neighbors is a basic problem in machine learning with numerous applications. In this problem, given a (training) set of n data points with labels and a query point q, we want to assign a label to q based on the labels of the Knearest points to the query. We study this problem in the kmachine model, a model for distributed largescale data. In this model, we assume that the n points are distributed (in a balanced fashion) among the k machines and the goal is to compute an answer given a query point to a machine using a small number of communication rounds. Our main result is a randomized algorithm in the kmachine model that runs in O(log K) communication rounds with high success probability (regardless of the number of machines k and the number of points n). The message complexity of the algorithm is small taking only O(k log K) messages. Our bounds are essentially the best possible for comparisonbased algorithms. We also implemented our algorithm and show that it performs well in practice.