Rendezvous of Two Robots with Constant Memory

We study the impact that persistent memory has on the classical rendezvous problem of two mobile computational entities, called robots, in the plane. It is well known that, without additional assumptions, rendezvous is impossible if the entities are oblivious (i.e., have no persistent memory) even if the system is semi-synchronous (SSynch). It has been recently shown that rendezvous is possible even if the system is asynchronous (ASynch) if each robot is endowed with O(1) bits of persistent memory, can transmit O(1) bits in each cycle, and can remember (i.e., can persistently store) the last received transmission. This setting is overly powerful. In this paper we weaken that setting in two different ways: (1) by maintaining the O(1) bits of persistent memory but removing the communication capabilities; and (2) by maintaining the O(1) transmission capability and the ability to remember the last received transmission, but removing the ability of an agent to remember its previous activities. We call the former setting finite-state (FState) and the latter finite-communication (FComm). Note that, even though its use is very different, in both settings, the amount of persistent memory of a robot is constant. We investigate the rendezvous problem in these two weaker settings. We model both settings as a system of robots endowed with visible lights: in FState, a robot can only see its own light, while in FComm a robot can only see the other robot's light. We prove, among other things, that finite-state robots can rendezvous in SSynch, and that finite-communication robots are able to rendezvous even in ASynch. All proofs are constructive: in each setting, we present a protocol that allows the two robots to rendezvous in finite time.Comment: 18 pages, 3 figure

Improving the benefits of multicast prioritization algorithms

The final publication is available at Springer via http://dx.doi.org/10.1007/s11227-014-1087-zPrioritized atomic multicast consists in delivering messages in total order while ensuring that the priorities of the messages are considered; i.e., messages with higher priorities are delivered first. That service can be used in multiple applications. An example is the usage of prioritization algorithms for reducing the transaction abort rates in applications that use a replicated database system. To this end, transaction messages get priorities according to their probability of violating the existing integrity constraints. This paper evaluates how that abort reduction may be improved varying the message sending rate and the bounds set on the length of the priority reordering queue being used by those multicast algorithms.This work has been partially supported by EU FEDER and Spanish MICINN under research Grants TIN2009-14460-C03-01 and TIN2010-17193.Miedes De Elías, EP.; Muñoz Escoí, FD. (2014). Improving the benefits of multicast prioritization algorithms. Journal of Supercomputing. 68(3):1280-1301. doi:10.1007/s11227-014-1087-zS12801301683Amir Y, Danilov C, Stanton JR (2000) A low latency, loss tolerant architecture and protocol for wide area group communication. In: International Conference on Dependable Systems and Networks (DSN), IEEE-CS, Washington, DC, USA, pp 327–336Chockler G, Keidar I, Vitenberg R (2001) Group communication specifications: a comprehensive study. ACM Comput Surv 33(4):427–469CiA (2001) About CAN in Automation (CiA). http://www.can-cia.org/index.php?id=aboutciaDéfago X, Schiper A, Urbán P (2004) Total order broadcast and multicast algorithms: taxonomy and survey. ACM Comput Surv 36(4):372–421Dolev D, Dwork C, Stockmeyer L (1987) On the minimal synchronism needed for distributed consensus. J ACM 34(1):77–97International Organization for Standardization (ISO) (1993) Road vehicles—interchange of digital information—controller area network (CAN) for high-speed communication. Revised by ISO 11898-1:2003JBoss (2011) The Netty project 3.2 user guide. http://docs.jboss.org/netty/3.2/guide/html/Kaashoek MF, Tanenbaum AS (1996) An evaluation of the Amoeba group communication system. In: International conference on distributed computing system (ICDCS), IEEE-CS, Washington, DC, USA, pp 436–448Miedes E, Muñoz-Escoí FD (2008) Managing priorities in atomic multicast protocols. In: International conference on availability, reliability and security (ARES), Barcelona, Spain, pp 514–519Miedes E, Muñoz-Escoí FD (2010) Dynamic switching of total-order broadcast protocols. In: International conference on parallel and distributed processing techniques and applications (PDPTA), CSREA Press, Las Vegas, Nevada, USA, pp 457–463Miedes E, Muñoz-Escoí FD, Decker H (2008) Reducing transaction abort rates with prioritized atomic multicast protocols. In: International European conference on parallel and distributed computing (Euro-Par), Springer, Las Palmas de Gran Canaria, Spain, Lecture notes in computer science, vol 5168, pp 394–403Mocito J, Rodrigues L (2006) Run-time switching between total order algorithms. In: International European conference on parallel and distributed computing (Euro-Par), Springer, Dresden, Germany, Lecture Notes in Computer Science, vol 4128, pp 582–591Moser LE, Melliar-Smith PM, Agarwal DA, Budhia R, Lingley-Papadopoulos C (1996) Totem: a fault-tolerant multicast group communication system. Commun ACM 39(4):54–63Nakamura A, Takizawa M (1992) Priority-based total and semi-total ordering broadcast protocols. In: International conference on distributed computing systems (ICDCS), Yokohama, Japan, pp 178–185Nakamura A, Takizawa M (1993) Starvation-prevented priority based total ordering broadcast protocol on high-speed single channel network. In: 2nd International symposium on high performance distributed computing (HPDC), pp 281–288Rodrigues L, Veríssimo P, Casimiro A (1995) Priority-based totally ordered multicast. In: Workshop on algorithms and architectures for real-time control (AARTC), Ostend, BelgiumRütti O, Wojciechowski P, Schiper A (2006) Structural and algorithmic issues of dynamic protocol update. In: 20th International parallel and distributed processing symposium (IPDPS), IEEE-CS Press, Rhodes Island, GreeceTindell K, Clark J (1994) Holistic schedulability analysis for distributed hard real-time systems. Microprocess Microprogr 40(2–3):117–134Tully A, Shrivastava SK (1990) Preventing state divergence in replicated distributed programs. In: International symposium on reliable distributed systems (SRDS), Huntsville, Alabama, USA, pp 104–113Wiesmann M, Schiper A (2005) Comparison of database replication techniques based on total order broadcast. IEEE Trans Knowl Data Eng 17(4):551–56

Rendezvous on a Line by Location-Aware Robots Despite the Presence of Byzantine Faults

A set of mobile robots is placed at points of an infinite line. The robots are equipped with GPS devices and they may communicate their positions on the line to a central authority. The collection contains an unknown subset of "spies", i.e., byzantine robots, which are indistinguishable from the non-faulty ones. The set of the non-faulty robots need to rendezvous in the shortest possible time in order to perform some task, while the byzantine robots may try to delay their rendezvous for as long as possible. The problem facing a central authority is to determine trajectories for all robots so as to minimize the time until the non-faulty robots have rendezvoused. The trajectories must be determined without knowledge of which robots are faulty. Our goal is to minimize the competitive ratio between the time required to achieve the first rendezvous of the non-faulty robots and the time required for such a rendezvous to occur under the assumption that the faulty robots are known at the start. We provide a bounded competitive ratio algorithm, where the central authority is informed only of the set of initial robot positions, without knowing which ones or how many of them are faulty. When an upper bound on the number of byzantine robots is known to the central authority, we provide algorithms with better competitive ratios. In some instances we are able to show these algorithms are optimal

Byzantine Gathering in Networks

This paper investigates an open problem introduced in [14]. Two or more mobile agents start from different nodes of a network and have to accomplish the task of gathering which consists in getting all together at the same node at the same time. An adversary chooses the initial nodes of the agents and assigns a different positive integer (called label) to each of them. Initially, each agent knows its label but does not know the labels of the other agents or their positions relative to its own. Agents move in synchronous rounds and can communicate with each other only when located at the same node. Up to f of the agents are Byzantine. A Byzantine agent can choose an arbitrary port when it moves, can convey arbitrary information to other agents and can change its label in every round, in particular by forging the label of another agent or by creating a completely new one. What is the minimum number M of good agents that guarantees deterministic gathering of all of them, with termination? We provide exact answers to this open problem by considering the case when the agents initially know the size of the network and the case when they do not. In the former case, we prove M=f+1 while in the latter, we prove M=f+2. More precisely, for networks of known size, we design a deterministic algorithm gathering all good agents in any network provided that the number of good agents is at least f+1. For networks of unknown size, we also design a deterministic algorithm ensuring the gathering of all good agents in any network but provided that the number of good agents is at least f+2. Both of our algorithms are optimal in terms of required number of good agents, as each of them perfectly matches the respective lower bound on M shown in [14], which is of f+1 when the size of the network is known and of f+2 when it is unknown

Pattern formation

The Pattern Formation problem is one of the most important coordination problem for robotic systems. Initially the entities are in arbitrary positions; within finite time they must arrange themselves in the space so to form a pattern given in input. In this chapter, we will mainly deal with the problem in the OBLOT model

Self-stabilizing Deterministic Gathering

In this paper, we investigate the possibility to deterministically solve the gathering problem (GP) with weak robots (anonymous, autonomous, disoriented, deaf and dumb, and oblivious). We introduce strong multiplicity detection as the ability for the robots to detect the exact number of robots located at a given position. We show that with strong multiplicity detection, there exists a deterministic self-stabilizing algorithm solving GP for n robots if, and only if, n is odd

Solving atomic multicast when groups crash

In this paper, we study the atomic multicast problem, a fundamental abstraction for building faulttolerant systems. In the atomic multicast problem, the system is divided into non-empty and disjoint groups of processes. Multicast messages may be addressed to any subset of groups, each message possibly being multicast to a different subset. Several papers previously studied this problem either in local area networks [3, 9, 20] or wide area networks [13, 21]. However, none of them considered atomic multicast when groups may crash. We present two atomic multicast algorithms that tolerate the crash of groups. The first algorithm tolerates an arbitrary number of failures, is genuine (i.e., to deliver a message m, only addressees of m are involved in the protocol), and uses the perfect failures detector P. We show that among realistic failure detectors, i.e., those that do not predict the future, P is necessary to solve genuine atomic multicast if we do not bound the number of processes that may fail. Thus, P is the weakest realistic failure detector for solving genuine atomic multicast when an arbitrary number of processes may crash. Our second algorithm is non-genuine and less resilient to process failures than the first algorithm but has several advantages: (i) it requires perfect failure detection within groups only, and not across the system, (ii) as we show in the paper it can be modified to rely on unreliable failure detection at the cost of a weaker liveness guarantee, and (iii) it is fast, messages addressed to multiple groups may be delivered within two inter-group message delays only

Scalability approaches for causal multicast: a survey

The final publication is available at Springer via http://dx.doi.org/10.1007/s00607-015-0479-0Many distributed services need to be scalable: internet search, electronic commerce, e-government... In order to achieve scalability, high availability and fault tolerance, such applications rely on replicated components. Because of the dynamics of growth and volatility of customer markets, applications need to be hosted by adaptive, highly scalable systems. In particular, the scalability of the reliable multicast mechanisms used for supporting the consistency of replicas is of crucial importance. Reliable multicast might propagate updates in a pre-determined order (e.g., FIFO, total or causal). Since total order needs more communication rounds than causal order, the latter appears to be the preferable candidate for achieving multicast scalability, although the consistency guarantees based on causal order are weaker than those of total order. 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