An Introduction to the Topological Theory of Distributed Computing with Safe-consensus

AbstractThe theory of distributed computing shares a deep and fascinating connection with combinatorial and algebraic topology. One of the key ideas that facilitates the development of the topological theory of distributed computing is the use of iterated shared memory models. In such a model processes communicate through a sequence of shared objects. Processes access the sequence of objects, one-by-one, in the same order and asynchronously. Each process accesses each shared object only once. In the most basic form of an iterated model, any number of processes can crash, and the shared objects are snapshot objects. A process can write a value to such an object, and gets back a snapshot of its contents.The purpose of this paper is to give an introduction to this research area, using an iterated model based on the safe-consensus task (Afek, Gafni and Lieber, DISCʼ09). In a safe-consensus task, the validity condition of consensus is weakened as follows. If the first process to invoke an object solving a safe-consensus task returns before any other process invokes it, then the process gets back its own input; otherwise the value returned by the task can be arbitrary. As with consensus, the agreement requirement is that always the same value is returned to all processes.A safe-consensus-based iterated model is described in detail. It is explained how its runs can be described with simplicial complexes. The usefulness of the iterated memory model for the topological theory of distributed computing is exhibited by presenting some new results (with very clean and well structured proofs) about the solvability of the (n,k)-set agreement task. Throughout the paper, the main ideas are explained with figures and intuitive examples

The solvability of consensus in iterated models extended with safe-consensus

The safe-consensus task was introduced by Afek, Gafni and Lieber (DISC'09) as a weakening of the classic consensus. When there is concurrency, the consensus output can be arbitrary, not even the input of any process. They showed that safe-consensus is equivalent to consensus, in a wait-free system. We study the solvability of consensus in three shared memory iterated models extended with the power of safe-consensus black boxes. In the first model, for the $i$-th iteration, processes write to the memory, invoke safe-consensus boxes and finally they snapshot the memory. We show that in this model, any wait-free implementation of consensus requires $\binom{n}{2}$ safe-consensus black-boxes and this bound is tight. In a second iterated model, the processes write to memory, then they snapshot it and finally they invoke safe-consensus boxes. We prove that in this model, consensus cannot be implemented. In the last iterated model, processes first invoke safe-consensus, then they write to memory and finally they snapshot it. We show that this model is equivalent to the previous model and thus consensus cannot be implemented.Comment: 49 pages, A preliminar version of the main results appeared in the SIROCCO 2014 proceeding

Distributed Computing with Adaptive Heuristics

We use ideas from distributed computing to study dynamic environments in which computational nodes, or decision makers, follow adaptive heuristics (Hart 2005), i.e., simple and unsophisticated rules of behavior, e.g., repeatedly "best replying" to others' actions, and minimizing "regret", that have been extensively studied in game theory and economics. We explore when convergence of such simple dynamics to an equilibrium is guaranteed in asynchronous computational environments, where nodes can act at any time. Our research agenda, distributed computing with adaptive heuristics, lies on the borderline of computer science (including distributed computing and learning) and game theory (including game dynamics and adaptive heuristics). We exhibit a general non-termination result for a broad class of heuristics with bounded recall---that is, simple rules of behavior that depend only on recent history of interaction between nodes. We consider implications of our result across a wide variety of interesting and timely applications: game theory, circuit design, social networks, routing and congestion control. We also study the computational and communication complexity of asynchronous dynamics and present some basic observations regarding the effects of asynchrony on no-regret dynamics. We believe that our work opens a new avenue for research in both distributed computing and game theory.Comment: 36 pages, four figures. Expands both technical results and discussion of v1. Revised version will appear in the proceedings of Innovations in Computer Science 201

Randomized Two-Process Wait-Free Test-and-Set

We present the first explicit, and currently simplest, randomized algorithm for 2-process wait-free test-and-set. It is implemented with two 4-valued single writer single reader atomic variables. A test-and-set takes at most 11 expected elementary steps, while a reset takes exactly 1 elementary step. Based on a finite-state analysis, the proofs of correctness and expected length are compressed into one table.Comment: 9 pages, 4 figures, LaTeX source; Submitte

Past, Present, and Future of Simultaneous Localization And Mapping: Towards the Robust-Perception Age

Simultaneous Localization and Mapping (SLAM)consists in the concurrent construction of a model of the environment (the map), and the estimation of the state of the robot moving within it. The SLAM community has made astonishing progress over the last 30 years, enabling large-scale real-world applications, and witnessing a steady transition of this technology to industry. We survey the current state of SLAM. We start by presenting what is now the de-facto standard formulation for SLAM. We then review related work, covering a broad set of topics including robustness and scalability in long-term mapping, metric and semantic representations for mapping, theoretical performance guarantees, active SLAM and exploration, and other new frontiers. This paper simultaneously serves as a position paper and tutorial to those who are users of SLAM. By looking at the published research with a critical eye, we delineate open challenges and new research issues, that still deserve careful scientific investigation. The paper also contains the authors' take on two questions that often animate discussions during robotics conferences: Do robots need SLAM? and Is SLAM solved

Detecting Topology Variations in Dynamical Networks

This paper considers the problem of detecting topology variations in dynamical networks. We consider a network whose behavior can be represented via a linear dynamical system. The problem of interest is then that of finding conditions under which it is possible to detect node or link disconnections from prior knowledge of the nominal network behavior and on-line measurements. The considered approach makes use of analysis tools from switching systems theory. A number of results are presented along with examples