Distributed Queuing in Dynamic Networks

We consider the problem of forming a distributed queue in the adversarial dynamic network model of Kuhn, Lynch, and Oshman (STOC 2010) in which the network topology changes from round to round but the network stays connected. This is a synchronous model in which network nodes are assumed to be fixed, the communication links for each round are chosen by an adversary, and nodes do not know who their neighbors are for the current round before they broadcast their messages. Queue requests may arrive over rounds at arbitrary nodes and the goal is to eventually enqueue them in a distributed queue. We present two algorithms that give a total distributed ordering of queue requests in this model. We measure the performance of our algorithms through round complexity, which is the total number of rounds needed to solve the distributed queuing problem. We show that in 1-interval connected graphs, where the communication links change arbitrarily between every round, it is possible to solve the distributed queueing problem in O(nk) rounds using O(log n) size messages, where n is the number of nodes in the network and k <= n is the number of queue requests. Further, we show that for more stable graphs, e.g. T-interval connected graphs where the communication links change in every T rounds, the distributed queuing problem can be solved in O(n+ (nk/min(alpha,T))) rounds using the same O(log n) size messages, where alpha > 0 is the concurrency level parameter that captures the minimum number of active queue requests in the system in any round. These results hold in any arbitrary (sequential, one-shot concurrent, or dynamic) arrival of k queue requests in the system. Moreover, our algorithms ensure correctness in the sense that each queue request is eventually enqueued in the distributed queue after it is issued and each queue request is enqueued exactly once. We also provide an impossibility result for this distributed queuing problem in this model. To the best of our knowledge, these are the first solutions to the distributed queuing problem in adversarial dynamic networks.Comment: In Proceedings FOMC 2013, arXiv:1310.459

Scheduling in Transactional Memory Systems: Models, Algorithms, and Evaluations

Transactional memory provides an alternative synchronization mechanism that removes many limitations of traditional lock-based synchronization so that concurrent program writing is easier than lock-based code in modern multicore architectures. The fundamental module in a transactional memory system is the transaction which represents a sequence of read and write operations that are performed atomically to a set of shared resources; transactions may conflict if they access the same shared resources. A transaction scheduling algorithm is used to handle these transaction conflicts and schedule appropriately the transactions. In this dissertation, we study transaction scheduling problem in several systems that differ through the variation of the intra-core communication cost in accessing shared resources. Symmetric communication costs imply tightly-coupled systems, asymmetric communication costs imply large-scale distributed systems, and partially asymmetric communication costs imply non-uniform memory access systems. We made several theoretical contributions providing tight, near-tight, and/or impossibility results on three different performance evaluation metrics: execution time, communication cost, and load, for any transaction scheduling algorithm. We then complement these theoretical results by experimental evaluations, whenever possible, showing their benefits in practical scenarios. To the best of our knowledge, the contributions of this dissertation are either the first of their kind or significant improvements over the best previously known results

A Constant-Factor Approximation Algorithm for Online Coverage Path Planning with Energy Constraint

In this paper, we study the problem of coverage planning by a mobile robot with a limited energy budget. The objective of the robot is to cover every point in the environment while minimizing the traveled path length. The environment is initially unknown to the robot. Therefore, it needs to avoid the obstacles in the environment on-the-fly during the exploration. As the robot has a specific energy budget, it might not be able to cover the complete environment in one traversal. Instead, it will need to visit a static charging station periodically in order to recharge its energy. To solve the stated problem, we propose a budgeted depth-first search (DFS)-based exploration strategy that helps the robot to cover any unknown planar environment while bounding the maximum path length to a constant-factor of the shortest-possible path length. Our $O(1)$-approximation guarantee advances the state-of-the-art of log-approximation for this problem. Simulation results show that our proposed algorithm outperforms the current state-of-the-art algorithm both in terms of the traveled path length and run time in all the tested environments with concave and convex obstacles

Near-Optimal Dispersion on Arbitrary Anonymous Graphs

Given an undirected, anonymous, port-labeled graph of n memory-less nodes, m edges, and degree ?, we consider the problem of dispersing k ? n robots (or tokens) positioned initially arbitrarily on one or more nodes of the graph to exactly k different nodes of the graph, one on each node. The objective is to simultaneously minimize time to achieve dispersion and memory requirement at each robot. If all k robots are positioned initially on a single node, depth first search (DFS) traversal solves this problem in O(min{m,k?}) time with ?(log(k+?)) bits at each robot. However, if robots are positioned initially on multiple nodes, the best previously known algorithm solves this problem in O(min{m,k?}? log ?) time storing ?(log(k+?)) bits at each robot, where ? ? k/2 is the number of multiplicity nodes in the initial configuration. In this paper, we present a novel multi-source DFS traversal algorithm solving this problem in O(min{m,k?}) time with ?(log(k+?)) bits at each robot, improving the time bound of the best previously known algorithm by O(log ?) and matching asymptotically the single-source DFS traversal bounds. This is the first algorithm for dispersion that is optimal in both time and memory in arbitrary anonymous graphs of constant degree, ? = O(1). Furthermore, the result holds in both synchronous and asynchronous settings

Weighted Reservoir Sampling from Distributed Streams

We consider message-efficient continuous random sampling from a distributed stream, where the probability of inclusion of an item in the sample is proportional to a weight associated with the item. The unweighted version, where all weights are equal, is well studied, and admits tight upper and lower bounds on message complexity. For weighted sampling with replacement, there is a simple reduction to unweighted sampling with replacement. However, in many applications the stream has only a few heavy items which may dominate a random sample when chosen with replacement. Weighted sampling \textit{without replacement} (weighted SWOR) eludes this issue, since such heavy items can be sampled at most once. In this work, we present the first message-optimal algorithm for weighted SWOR from a distributed stream. Our algorithm also has optimal space and time complexity. As an application of our algorithm for weighted SWOR, we derive the first distributed streaming algorithms for tracking \textit{heavy hitters with residual error}. Here the goal is to identify stream items that contribute significantly to the residual stream, once the heaviest items are removed. Residual heavy hitters generalize the notion of $\ell_1$ heavy hitters and are important in streams that have a skewed distribution of weights. In addition to the upper bound, we also provide a lower bound on the message complexity that is nearly tight up to a $\log(1/\epsilon)$ factor. Finally, we use our weighted sampling algorithm to improve the message complexity of distributed $L_1$ tracking, also known as count tracking, which is a widely studied problem in distributed streaming. We also derive a tight message lower bound, which closes the message complexity of this fundamental problem.Comment: To appear in PODS 201

Collisionless Pattern Discovery in Robot Swarms Using Deep Reinforcement Learning

We present a deep reinforcement learning-based framework for automatically discovering patterns available in any given initial configuration of fat robot swarms. In particular, we model the problem of collision-less gathering and mutual visibility in fat robot swarms and discover patterns for solving them using our framework. We show that by shaping reward signals based on certain constraints like mutual visibility and safe proximity, the robots can discover collision-less trajectories leading to well-formed gathering and visibility patterns