John Augustine

We study the SUPPORTED model of distributed computing introduced by Schmid and Suomela [15], generalizing the LOCAL and CONGEST models. In this framework, multiple instances of the same problem, differing from each other by some problem specific input, recur over time, and need to be solved efficiently online. To do that, one may rely on an initial preprocessing phase for computing some useful information. This preprocessing phase makes it possible, in some cases, to obtain improved distributed algorithms, overcoming locality-based time lower bounds.We propose some natural recurrent variants of the dominating set problem and the coloring problem that are of interest particularly in the distributed setting. For these problems, we show that information about the topology can be used to overcome locality-based lower bounds. We also categorize the round complexity of Locally Checkable Labellings in the SUPPORTED model for the simple case of paths. Finally we present some interesting open problems and some partial results towards resolving them.

We study graph realization problems from a distributed perspective. The problem is naturally applicable to the distributed construction of overlay networks that must satisfy certain degree or connectivity properties, and we study it in the node capacitated clique (NCC) model of distributed computing, recently introduced for representing peer-to-peer networks.We focus on two central variants, degree-sequence realization and minimum threshold-connectivity realization. In the degree sequence problem, each node v is associated with a degree d(v), and the resulting degree sequence is realizable if it is possible to construct an overlay network in which the degree of each node v is d(v). The minimum threshold-connectivity problem requires us to construct an overlay network that satisfies connectivity constraints specified between every pair of nodes.Overlay network realizations can be either explicit or implicit. Explicit realizations require both endpoints of any edge in the realized graph to be aware of the edge. In implicit realizations, on the other hand, at least one endpoint of each edge of the realized graph needs to be aware of the edge.The main realization algorithms we present are the following. (1) A O(□ m,Δ) time algorithm for implicit realization of a degree sequence. Here, Δ = maxv d(v) is the maximum degree and m = (1/2) v d(v) is the number of edges in the final realization. (2) A O (Δ) time algorithm for an explicit realization of a degree sequence. We first compute an implicit realization and then transform it into an explicit one in O (Δ) additional rounds. (3) A O (Δ) time algorithm for the threshold connectivity problem that obtains an explicit solution and an improved O (1) algorithm for implicit realization when all nodes know each other's IDs. These algorithms are 2-approximations w.r.t. the number of edges. Our algorithms are complemented by lower bounds showing tightness up to log n factors. Additionally, we provide algorithms for realizing trees and an O (1) round algorithm for approximate degree sequence realization.

This paper revisits the widely researched gathering problem for two robots without any agreement on the coordinate system in a scenario which allows randomization in the asynchronous scheduling model. The scheduler is considered to be the adversary which determines the activation schedule of the robots. The adversary comes in three flavors, namely, adaptive offline, adaptive online, and oblivious, based on the knowledge of the outcome of random bits. The robots follow wait-look-compute-move cycle. In this paper, we classify the problems based on the capability of the adversary to control the parameters such as wait time, computation delay and the speed of robots and check the feasibility of gathering in terms of adversarial knowledge and capabilities. First, we show the impossibility of gathering under an adaptive offline adversary with non-negative wait time and non-negative computation delay. Gradually relaxing the adversarial capabilities, we present impossibility of gathering for finite random choices and improbability for infinite random choices for an adaptive online adversary. Under an oblivious adversary, we establish the possibility of gathering with zero computation delay. We improve the runtime of the algorithm by restricting the oblivious adversary to choose wait time and computation delay such that the sum of wait time and computation delay is more than a positive constant. Finally, we also extend our algorithm for multiple robots with merging.

We study the classical Art Gallery Problem first proposed by Klee in 1973 from a mobile multi-agents perspective. Specifically, we require an optimally small number of agents (also called guards) to navigate and position themselves in the interior of an unknown simple polygon with n vertices such that the collective view of all the agents covers the polygon. We consider the visibly connected setting wherein agents must remain connected through line of sight links – a requirement particularly relevant to multi-agent systems. We first provide a centralized algorithm for the visibly connected setting that runs in time O(n), which is of course optimal. We then provide algorithms for two different distributed settings. In the first setting, agents can only perceive relative proximity (i.e., can tell which of a pair of objects is closer) whereas they can perceive exact distances in the second setting. Our distributed algorithms work despite agents having no prior knowledge of the polygon. Furthermore, we provide lower bounds to show that our distributed algorithms are near optimal. Our visibly connected guarding ensures that (i) the guards form a connected network and (ii) the polygon is fully guarded. Consequently, this guarding provides the distributed infrastructure to execute any geometric algorithm for this polygon.

We will present the fundamentals of Byzantine agreement and leader election problems from a modern perspective. Byzantine fault tolerant protocols are at the heart of secure and robust protocols that can tolerate the presence of malicious nodes in a distributed system, such as a Peer-to-Peer (P2P) network, which allows a large number of peers to enter the network with little or no admission control. Such malicious peers acting alone or in collaboration can cause disruption of service in P2P systems. Our tutorial is largely inspired by recent P2P applications like Blockchain and cryptocurrencies that espouse permissionless settings whereby peers can anonymously and dynamically join and leave the network at will. Our presentation will be in three parts. In the first part, we will present the historic foundations of Byzantine agreement and leader election and describe the fundamentals that underlie our modern understanding of these problems. Much of the classical results focus on complete networks where nodes have global knowledge. In the second part, motivated by real-world distributed networks such as P2P networks which are typically sparse and bounded degree with nodes having only local knowledge, we focus on Byzantine protocols for sparse networks. While the first two parts will focus on static settings, motivated by modern applications such as blockchains and cryptocurrencies which operate on dynamic P2P networks, the third part will delve into Byzantine procotols for dynamic networks where nodes continuously join and leave the system. The tutorial will cover various tools and techniques that are useful in designing Byzantine protocols in sparse and dynamic networks and will discuss key open problems in the area.

We study the problem of gathering k anonymous mobile agents on a ring with n nodes. Importantly, f out of the k anonymous agents are Byzantine. The agents operate synchronously and in an autonomous fashion. In each round, each agent can communicate with other agents co-located with it by broadcasting a message. After receiving all the messages, each agent decides to either move to a neighbouring node or stay put. We begin with the k agents placed arbitrarily on the ring, and the task is to gather all the good agents in a single node. The task is made harder by the presence of Byzantine agents, which are controlled by a single Byzantine adversary. Byzantine agents can deviate arbitrarily from the protocol. The Byzantine adversary is computationally unbounded. Additionally, the Byzantine adversary is adaptive in the sense that it can capitalize on information gained over time (including the current round) to choreograph the actions of Byzantine agents. Specifically, the entire state of the system, which includes messages sent by all the agents and any random bits generated by the agents, is known to the Byzantine adversary before all the agents move. Thus the Byzantine adversary can compute the positioning of good agents across the ring and choreograph the movement of Byzantine agents accordingly. Moreover, we consider two settings: standard and visual tracking setting. With visual tracking, agents have the ability to track other agents that are moving along with them. In the standard setting, agents do not have such an ability. In the standard setting we can achieve gathering in O(n log n log k) rounds with high probability1 and can handle O (log kk number of Byzantine agents. With visual tracking, we can achieve gathering faster in O(n log n) rounds whp and can handle any constant fraction of the total number of agents being Byzantine.

We study the problem of rank aggregation where the goal is to obtain a global ranking by aggregating pair-wise comparisons of voters over a set of objects. We consider an adversarial setting where the voters are partitioned into two sets. The first set votes in a stochastic manner according to the popular score-based Bradley-Terry-Luce (BTL) model for pairwise comparisons. The second set comprises malicious Byzantine voters trying to deteriorate the ranking. We consider a strongly-adversarial scenario where the Byzantine voters know the BTL scores, the votes of the good voters, the algorithm, and can collude with each other. We first show that the popular spectral ranking based Rank-Centrality algorithm, though optimal for the BTL model, does not perform well even when a small constant fraction of the voters are Byzantine. We introduce the Byzantine Spectral Ranking Algorithm (and a faster variant of it), which produces a reliable ranking when the number of good voters exceeds the number of Byzantine voters. We show that no algorithm can produce a satisfactory ranking with probability > 1/2 for all BTL weights when there are more Byzantine voters than good voters, showing that our algorithm works for all possible population fractions. We support our theoretical results with experimental results on synthetic and real datasets to demonstrate the failure of the Rank-Centrality algorithm under several adversarial scenarios and how the proposed Byzantine Spectral Ranking algorithm is robust in obtaining good rankings.

We introduce a communication model for hybrid networks, where nodes have access to two different communication modes: a local mode where (like in traditional networks) communication is only possible between specific pairs of nodes, and a global mode where (like in overlay networks) communication between any pair of nodes is possible. Typically, communication over short-range connections is cheaper and can be done at a much higher rate than communication via the overlay network. Therefore, we are focusing on the LOCAL model for the local connections where nodes can exchange an unbounded amount of information per round. For the global communication we assume the so-called node-capacitated clique model, where in each round every node can exchange O(log n)-bit messages with O(log n) arbitrary nodes. We explore the impact of hybrid communication on the complexity of distributed algorithms by studying the problem of computing shortest paths in the graph given by the local connections. We present the following results. For the all-pairs shortest paths problem, we show that an exactapproximatesolutionsolutionscan be computedcan be computedin timeinÕtime (n2/3Θ ) (and √n)thatbut not faster. For the single-source shortest paths problem an exact solution can be computed in time Õ(√SPD), where SPD denotes the shortest path diameter. Furthermore, a ( Õ1+ (n1o/(1) 3). )-approximate Finally we show solution that can for every be computed constantinε >time 0 it is possible to compute an O(1)-approximate solution in time Õ(nε).

Load balancing is a well-studied problem, with balls-in-bins being the primary framework. The greedy algorithm Greedy[d] of Azar et al. [SIAM J. Comput., 29 (1999), pp. 180-200] places each ball by probing d > 1 random bins and placing the ball in the least loaded of them. With high probability, the maximum load under Greedy[d] is exponentially lower than the result when balls are placed uniformly randomly. Vöcking [J. ACM, 50 (2003), pp. 568-589] showed that a slightly asymmetric variant, Left[d], provides a further significant improvement. However, this improvement comes at the additional computational cost of imposing structure on the bins. Here, we present a fully decentralized and easy-to-implement algorithm called FirstDiff[d] that combines the simplicity of Greedy[d] and the improved balance of Left[d]. The key idea in FirstDiff[d] is to probe until a different bin size from the first observation is located and then place the ball. Although the number of probes could be quite large for some of the balls, we show that FirstDiff[d] requires only at most d probes on average per ball (in both the standard and the heavily loaded settings). Thus the number of probes is no greater than that of either Greedy[d] or Left[d]. More importantly, we show that FirstDiff[d] closely matches the improved maximum load ensured by Left[d] in both the standard and heavily loaded settings. We further provide a tight lower bound on the maximum load up to O(log log log n) terms. We additionally give experimental data that FirstDiff[d] is indeed as good as Left[d], if not better, in practice.

—We study the cost of distributed MST construction in the setting where each edge has a latency and a capacity, along with the weight. Edge latencies capture the delay on the links of the communication network, while capacity captures their throughput (the rate at which messages can be sent). Depending on how the edge latencies relate to the edge weights, we provide several tight bounds on the time and messages required to construct an MST. When edge weights exactly correspond with the latencies, we show that, perhaps interestingly, the bottleneck parameter in determining the running time of an algorithm is the total weight W of the MST (rather than the total number of nodes n, as in the standard CONGEST model). That is, we show a tight bound of T( D + W/c) rounds, where D refers to the latency diameter of the graph, W refers to the total weight of the constructed MST and edges have capacity c. The proposed algorithm sends Õ(m + W) messages, where m, the total number of edges in the network graph under consideration, is a known lower bound on message complexity for MST construction. We also show that O(W) is a lower bound for fast MST constructions. When the edge latencies and the corresponding edge weights are unrelated, and either can take arbitrary values, we show that (unlike the sub-linear time algorithms in the standard CONGEST model, on small diameter graphs), the best time complexity that can be achieved is T( D + n/c). However, if we restrict all edges to have equal latency and capacity c while having possibly different weights (weights could deviate arbitrarily from ), we give an algorithm that constructs an MST in Õ(D + n/c) time. In each case, we provide nearly matching upper and lower bounds.