Synchronous Rounds Research Articles

Deterministic Network Exploration by Anonymous Silent Agents with Local Traffic Reports

A team consisting of an unknown number of mobile agents starting from different nodes of an unknown network, possibly at different times, have to explore the network: Every node must be visited by at least one agent, and all agents must eventually stop. Agents are anonymous (identical), execute the same deterministic algorithm, and move in synchronous rounds along links of the network. They are silent: They cannot send any messages to other agents or mark visited nodes in any way. In the absence of any additional information, exploration with termination of an arbitrary network in this model, devoid of any means of communication between agents, is impossible. Our aim is to solve the exploration problem by giving to agents very restricted local traffic reports . Specifically, an agent that is at a node v in a given round is provided with three bits of information answering the following questions: Am I alone at v ? Did any agent enter v in this round? Did any agent exit v in this round? We show that this small amount of information permits us to solve the exploration problem in arbitrary networks. More precisely, we give a deterministic terminating exploration algorithm working in arbitrary networks for all initial configurations that are not perfectly symmetric ; that is, in which there are agents with different views of the network. The algorithm works in polynomial time in the (unknown) size of the network. A deterministic terminating exploration algorithm working for all initial configurations in arbitrary networks does not exist.

Gathering Despite Mischief

A team consisting of an unknown number of mobile agents, starting from different nodes of an unknown network, have to meet at the same node. Agents move in synchronous rounds. Each agent has a different label. Up to f of the agents are Byzantine. We consider two levels of Byzantine behavior. A strongly Byzantine agent can choose an arbitrary port when it moves and it can convey arbitrary information to other agents, while a weakly Byzantine agent can do the same, except changing its label. What is the minimum number of good agents that guarantees deterministic gathering of all of them, with termination? We solve exactly this Byzantine gathering problem in arbitrary networks for weakly Byzantine agents and give approximate solutions for strongly Byzantine agents, both when the size of the network is known and when it is unknown. It turns out that both the strength versus the weakness of Byzantine behavior and the knowledge of network size significantly impact the results. For weakly Byzantine agents, we show that any number of good agents permits solving the problem for networks of known size. If the size is unknown, then this minimum number is f +2. More precisely, we show a deterministic polynomial algorithm that gathers all good agents in an arbitrary network, provided that there are at least f +2 of them. We also provide a matching lower bound: we prove that if the number of good agents is at most f +1, then they are not able to gather deterministically with termination in some networks. For strongly Byzantine agents, we give a lower bound of f +1, even when the graph is known: we show that f good agents cannot gather deterministically in the presence of f Byzantine agents even in a ring of known size. On the positive side, we give deterministic gathering algorithms for at least 2 f +1 good agents when the size of the network is known and for at least 4 f +2 good agents when it is unknown.

Guard Beacon: An Energy-Efficient Beacon Strategy for Time Synchronization in Wireless Sensor Networks

In this paper, we present Guard Beacon, which is a beacon strategy to reduce the energy consumption of time synchronization in wireless sensor networks (WSNs). In a low duty-cycled sensor network, a node may miss incoming synchronization beacons because of wrong active/sleep mode due to clock drift. Therefore, it is critical to guarantee that beacons arrive at the receiver at the right time. The proposed method, i.e., Guard Beacon, can reduce the overall power consumption of synchronization while guaranteeing a very high probability that the synchronization packet is received, by sending multiple beacons within a synchronization round. By investigating on the energy tradeoff between sending and receiving beacons, we find an optimal iterative solution as well as a suboptimal analytical solution as to how many beacons should be sent and when to send them. The strategy is implemented in a real-world testbed for experiment validation. The results show that the proposed Guard Beacon may save more than 40% synchronization power consumption compared with the existed Single Beacon strategy and is also more energy efficient than RTSP in multihop networks.

Time versus space trade-offs for rendezvous in trees

Two identical (anonymous) mobile agents start from arbitrary nodes of an unknown tree and have to meet at some node. Agents move in synchronous rounds: in each round an agent can either stay at the current node or move to one of its neighbors. We consider deterministic algorithms for this rendezvous task. The main result of this paper is a tight trade-off between the optimal time of completing rendezvous and the size of memory of the agents. For agents with $$k$$ memory bits, we show that optimal rendezvous time is $$\Theta (n+n^2/k)$$ in $$n$$ -node trees. More precisely, if $$k \ge c\log n$$ , for some constant $$c$$ , we design agents accomplishing rendezvous in arbitrary trees of size $$n$$ (unknown to the agents) in time $$O(n+n^2/k)$$ , starting with arbitrary delay. We also show that no pair of agents can accomplish rendezvous in time $$o(n+n^2/k)$$ , even in the class of lines of known length and even with simultaneous start. Finally, we prove that at least logarithmic memory is necessary for rendezvous, even for agents starting simultaneously in a $$n$$ -node line.

On the complexity of distributed BFS in ad hoc networks with non-spontaneous wake-ups

Distributed Computing and Networking We study time and message complexity of the problem of building a BFS tree by a spontaneously awaken node in ad hoc network. Computation is in synchronous rounds, and messages are sent via point-to-point bi-directional links. Network topology is modeled by a graph. Each node knows only its own id and the id's of its neighbors in the network and no pre-processing is allowed; therefore the solutions to the problem of spanning a BFS tree in this setting must be distributed. We deliver a deterministic distributed solution that trades time for messages, mainly, with time complexity O(D . min(D; n=f(n)) . logD . log n) and with the number of point-to-point messages sent O(n. (min(D; n=f(n))+f(n)) . logD. log n), for any n-node network with diameter D and for any monotonically non-decreasing sub-linear integer function f. Function f in the above formulas come from the threshold value on node degrees used by our algorithms, in the sense that nodes with degree at most f(n) are treated differently that the other nodes. This yields the first BFS-finding deterministic distributed algorithm in ad hoc networks working in time o(n) and with o(n2) message complexity, for some suitable functions f(n) = o(n= log2 n), provided D = o(n= log4 n).

Tolerating permanent and transient value faults

Transmission faults allow us to reason about permanent and transient value faults in a uniform way. However, all existing solutions to consensus in this model are either in the synchronous system, or require strong conditions for termination, that exclude the case where all messages of a process can be corrupted. In this paper we introduce eventual consistency in order to overcome this limitation. Eventual consistency denotes the existence of rounds in which processes receive the same set of messages. We show how eventually consistent rounds can be simulated from eventually synchronous rounds, and how eventually consistent rounds can be used to solve consensus. Depending on the nature and number of permanent and transient transmission faults, we obtain different conditions on $$n$$ , the number of processes, in order to solve consensus in our weak model.

Delays Induce an Exponential Memory Gap for Rendezvous in Trees

The aim of rendezvous in a graph is meeting of two mobile agents at some node of an unknown anonymous connected graph. In this article, we focus on rendezvous in trees, and, analogously to the efforts that have been made for solving the exploration problem with compact automata, we study the size of memory of mobile agents that permits to solve the rendezvous problem deterministically. We assume that the agents are identical, and move in synchronous rounds. We first show that if the delay between the starting times of the agents is arbitrary , then the lower bound on memory required for rendezvous is Ω (log n ) bits, even for the line of length n . This lower bound meets a previously known upper bound of O (log n ) bits for rendezvous in arbitrary graphs of size at most n . Our main result is a proof that the amount of memory needed for rendezvous with simultaneous start depends essentially on the number ℓ of leaves of the tree, and is exponentially less impacted by the number n of nodes. Indeed, we present two identical agents with O (log ℓ + log log n ) bits of memory that solve the rendezvous problem in all trees with at most n nodes and at most ℓ leaves. Hence, for the class of trees with polylogarithmically many leaves, there is an exponential gap in minimum memory size needed for rendezvous between the scenario with arbitrary delay and the scenario with delay zero. Moreover, we show that our upper bound is optimal by proving that Ω (log ℓ + log log n ) bits of memory are required for rendezvous, even in the class of trees with degrees bounded by 3.

Liver regeneration

In this ‘Snapshot’ article, we take a fresh look at the fundamentals of liver regeneration in light of recent technical innovations. While the mammalian response to partial hepatectomy (PH) has been studied for decades [1,2], in recent years the use of new experimental techniques has not only lead to a re-affirmation of basic principles of regeneration initially described by Nancy Bucher and others [3]; it also highlights remaining questions. PH leads to tightly synchronous rounds of replication, and given that the remaining liver is uninjured, it offers a physiological way to study both proliferative pathways in normal hepatocytes and abnormal regeneration in genetically modified mice.

Modeling and performance analysis of optical WDM node architecture using SRR protocol

In order to enhance the data transport capability and overall throughput of an optical wavelength division multiplexing (WDM) system, a proper node architecture design is necessary. In the present paper a simple node architecture model based on media access control protocols for bursty data traffic of variable time slot duration and data rate has been proposed to decrease the packet loss probability and to increase the efficiency of an optical WDM system using synchronous round robin (SRR) protocol. An appropriate mathematical model has been derived to evaluate performance of the proposed node architecture. It has been observed that the network performance is well controlled through implemented model and the corresponding network design parameters.

Of Choices, Failures and Asynchrony: The Many Faces of Set Agreement

Set agreement is a fundamental problem in distributed computing in which processes collectively choose a small subset of values from a larger set of proposals. The impossibility of fault-tolerant set agreement in asynchronous networks is one of the seminal results in distributed computing. In synchronous networks, too, the complexity of set agreement has been a significant research challenge that has now been resolved. Real systems, however, are neither purely synchronous nor purely asynchronous. Rather, they tend to alternate between periods of synchrony and periods of asynchrony. Nothing specific is known about the complexity of set agreement in such a “partially synchronous” setting. In this paper, we address this challenge, presenting the first (asymptotically) tight bound on the complexity of set agreement in such systems. We introduce a novel technique for simulating, in a fault-prone asynchronous shared memory, executions of an asynchronous and failure-prone message-passing system in which some fragments appear synchronous to some processes. We use this simulation technique to derive a lower bound on the round complexity of set agreement in a partially synchronous system by a reduction from asynchronous wait-free set agreement. Specifically, we show that every set agreement protocol requires at least $\lfloor\frac{t}{k}\rfloor + 2$ synchronous rounds to decide. We present an (asymptotically) matching algorithm that relies on a distributed asynchrony detection mechanism to decide as soon as possible during periods of synchrony. From these two results, we derive the size of the minimal window of synchrony needed to solve set agreement. By relating synchronous, asynchronous and partially synchronous environments, our simulation technique is of independent interest. In particular, it allows us to obtain a new lower bound on the complexity of early deciding k-set agreement complementary to that of Gafni et al. (in SIAM J. Comput. 40(1):63–78, 2011), and to re-derive the combinatorial topology lower bound of Guerraoui et al. (in Theor. Comput. Sci. 410(6–7):570–580, 2009) in an algorithmic way.

A Theory of Synchronous Relational Interfaces

Compositional theories are crucial when designing large and complex systems from smaller components. In this work we propose such a theory for synchronous concurrent systems. Our approach follows so-called interface theories, which use game-theoretic interpretations of composition and refinement. These are appropriate for systems with distinct inputs and outputs, and explicit conditions on inputs that must be enforced during composition. Our interfaces model systems that execute in an infinite sequence of synchronous rounds. At each round, a contract must be satisfied. The contract is simply a relation specifying the set of valid input/output pairs. Interfaces can be composed by parallel, serial or feedback composition. A refinement relation between interfaces is defined, and shown to have two main properties: (1) it is preserved by composition, and (2) it is equivalent to substitutability, namely, the ability to replace an interface by another one in any context. Shared refinement and abstraction operators, corresponding to greatest lower and least upper bounds with respect to refinement, are also defined. Input-complete interfaces, that impose no restrictions on inputs, and deterministic interfaces, that produce a unique output for any legal input, are discussed as special cases, and an interesting duality between the two classes is exposed. A number of illustrative examples are provided, as well as algorithms to compute compositions, check refinement, and so on, for finite-state interfaces.

Average long-lived binary consensus: Quantifying the stabilizing role played by memory

Consider a system composed of n sensors operating in synchronous rounds. In each round an input vector of sensor readings x is produced, where the i -th entry of x is a binary value produced by the i -th sensor. The sequence of input vectors is assumed to be smooth: exactly one entry of the vector changes from one round to the next one. The system implements a fault-tolerant averaging consensus function f . This function returns, in each round, a representative output value v of the sensor readings x . Assuming that at most t entries of the vector can be erroneous, f is required to return a value that appears at least t + 1 times in x . We introduce the definition of instability of the system, which consists in the number of output changes over a random sequence of input vectors. We first design optimal (with respect to the instability measure) consensus systems: D 0 without memory, and D 1 with memory. Then we quantify the gain factor due to memory by computing c n ( t ) , the number of decision changes performed by D 0 per decision change performed by D 1 .

Privacy-preserving distributed network troubleshooting—bridging the gap between theory and practice

Today, there is a fundamental imbalance in cybersecurity. While attackers act more and more globally and coordinated, network defense is limited to examine local information only due to privacy concerns. To overcome this privacy barrier, we use secure multiparty computation (MPC) for the problem of aggregating network data from multiple domains. We first optimize MPC comparison operations for processing high volume data in near real-time by not enforcing protocols to run in a constant number of synchronization rounds. We then implement a complete set of basic MPC primitives in the SEPIA library. For parallel invocations, SEPIA's basic operations are between 35 and several hundred times faster than those of comparable MPC frameworks. Using these operations, we develop four protocols tailored for distributed network monitoring and security applications: the entropy, distinct count, event correlation, and top-k protocols. Extensive evaluation shows that the protocols are suitable for near real-time data aggregation. For example, our top-k protocol PPTKS accurately aggregates counts for 180,000 distributed IP addresses in only a few minutes. Finally, we use SEPIA with real traffic data from 17 customers of a backbone network to collaboratively detect, analyze, and mitigate distributed anomalies. Our work follows a path starting from theory, going to system design, performance evaluation, and ending with measurement. Along this way, it makes a first effort to bridge two very disparate worlds: MPC theory and network monitoring and security practices.

Node discovery in networks

This paper abstracts the problem of network nodes discovering one another in a network of unknown size using all-to-all gossip. The problem is studied in terms of evolving directed graphs where each vertex represents a participating node and each edge represents one node’s knowledge about another. Ideally, such a graph has diameter one, i.e., each node knows all others. Nodes share their knowledge by sending gossip messages. Gossip among the nodes allows them to discover one another, decreasing the diameter of the graph. Here this problem is considered in several synchronous settings under different assumptions about the ability of the participating nodes to communicate. Specifically, the following aspects of communication are considered: (1) the ability of the nodes to multicast gossip messages, and (2) the size of the messages. The results describe the lower and upper bounds on the number of synchronous rounds required for the participants to discover each other. A particular question of interest is: if the network size is unknown, how does a node know that it has discovered all other nodes? Given a weakly-connected graph describing the initial knowledge of the nodes, every node in our algorithm can stop the discovery process knowing that there are no unknown nodes—this is done without any prior knowledge of the total number of nodes participating in the computation.

Control of cell cycle entry and exiting from the second mitotic wave in the Drosophiladeveloping eye

BackgroundIn the morphogenetic furrow (MF) of the Drosophila developing eye, all cells arrest in G1 and photoreceptor cell differentiation initiates. As the cells exit the MF, Notch signaling is required for the uncommitted cells to enter a synchronous round of cell division referred to as the "second mitotic wave" (SMW). How cell cycle entry and exit in SMW is regulated remains unclear. Recent studies have suggested that Notch signaling controls S phase in the SMW by regulating Cyclin A and the E2F transcription factor independent of Cyclin E. In this manuscript, we investigate the developmental regulation of cell cycle entry into and exit from SMW.ResultsWe demonstrate here that Cyclin E-dependent kinase activity is required for S phase entry in SMW. We show that removal of Su(H), a key transcription factor downstream of Notch signaling, blocks G1/S transition in SMW with strong upregulation of the Cyclin E/Cdk2 inhibitor Dacapo (Dap). We further show that the upregulation of Dap, which is mediated by bHLH protein Daughterless (Da), is important for cell cycle arrest of Su(H) mutant cells in SMW. Finally we show that removal of Dap leads to additional cell proliferation and an accumulation of the non-photoreceptor cells in the Drosophila developing eye.ConclusionOur data demonstrate that Cyclin E/Cdk2 kinase activity is absolutely required for S phase in SMW, and that Dap is required for the proper cell cycle arrest of cells exiting the SMW. In addition, our results suggest that the G1 arrest of notch and Su(H) mutant cells in the SMW are regulated by distinct mechanisms, and that the upregulation of Dap contributes the G1 arrest of Su(H) mutant cells.

Feasible Reactivity for Synchronous Cooperative Threads

We are concerned with programs composed of cooperative threads whose execution proceeds in synchronous rounds called instants. We develop static analysis methods to guarantee that each instant terminates in time polynomial in the size of the parameters of the program at the beginning of the computation.

Resource control for synchronous cooperative threads

We develop new methods to statically bound the resources needed for the execution of systems of concurrent, interactive threads. Our study is concerned with a synchronous model of interaction based on cooperative threads whose execution proceeds in synchronous rounds called instants. Our contribution is a system of compositional static analyses to guarantee that each instant terminates and to bound the size of the values computed by the system as a function of the size of its parameters at the beginning of the instant. Our method generalises an approach designed for first-order functional languages that relies on a combination of standard termination techniques for term rewriting systems and an analysis of the size of the computed values based on the notion of quasi-interpretation. We show that these two methods can be combined to obtain an explicit polynomial bound on the resources needed for the execution of the system during an instant. As a second contribution, we introduce a virtual machine and a related bytecode thus producing a precise description of the resources needed for the execution of a system. In this context, we present a suitable control flow analysis that allows to formulate the static analyses for resource control at bytecode level.

Extracellular Signals Responsible for Spatially Regulated Proliferation in the Differentiating Drosophila Eye

Spatially and temporally choreographed cell cycles accompany the differentiation of the Drosophila retina. The extracellular signals that control these patterns have been identified through mosaic analysis of mutations in signal transduction pathways. All cells arrest in G1 prior to the start of neurogenesis. Arrest depends on Dpp and Hh, acting redundantly. Most cells then go through a synchronous round of cell division before fate specification and terminal cell cycle exit. Cell cycle entry is induced by Notch signaling and opposed in subsets of cells by EGF receptor activity. Unusually, Cyclin E levels are not limiting for retinal cell cycles. Rbf/E2F and the Cyclin E antagonist Dacapo are important, however. All retinal cells, including the postmitotic photoreceptor neurons, continue dividing when rbf and dacapo are mutated simultaneously. These studies identify the specific extracellular signals that pattern the retinal cell cycles and show how differentiation can be uncoupled from cell cycle exit.

Replication of simian virus 40 (SV40) DNA in virus-infected CV1 cells selectively permeabilized for small molecules by Staphylococcus aureus alpha-toxin: involvement of mitochondria in the fast O2-dependent regulation of SV40 DNA replication.

SV40 (simian virus 40)-infected CV1 cells were permeabilized with Staphylococcus aureus alpha-toxin for small molecules (<2 kDa) in a medium that supports DNA replication. Incorporation of [alpha-32P]dATP was shown to proceed at an essentially constant rate for at least 1 h. 32P-labelled DNA replication intermediates and products were analysed by alkaline sucrose density centrifugation. The results suggested that SV40 DNA replication in alpha-toxin-permeabilized CV1 cells occurred essentially as in vivo. After bromodeoxyuridine 5'-triphosphate-labelling and isopycnic banding, significant amounts of DNA density-labelled in both strands were detected from 110 min of permeabilization onwards, indicating repeated rounds of viral DNA replication in the permeabilized cells. Incubation of permeabilized SV40-infected cells under hypoxic culture conditions caused inhibition of SV40 DNA replication. As seen in unpermeabilized cells, SV40 DNA replication was inhibited at the stage of initiation. The inhibition of DNA replication induced by hypoxia was mimicked by AA (antimycin A), an inhibitor of mitochondrial respiration, and also by the replacement of glutamate, a substrate of mitochondrial respiration, by Hepes in the permeabilization medium. Inhibition of DNA replication was not mediated by intracellular ATP depletion. AA also inhibited SV40 DNA replication in unpermeabilized, normoxically incubated cells. Moreover, as in hypoxically incubated cells, the addition of glucose to SV40-infected cells incubated for several hours with AA induced a burst of new initiations followed by a nearly synchronous round of viral DNA replication. Taken together, these results indicate that mitochondria are involved in the oxygen-dependent regulation of SV40 DNA replication.

Joint Base Station Scheduling

Consider a scenario where radio base stations need to send data to users with wireless devices. Time is discrete and slotted into synchronous rounds. Transmitting a data item from a base station to a user takes one round. A user can receive the data item from any of the base stations. The positions of the base stations and users are modeled as points in Euclidean space. If base station b transmits to user u in a certain round, no other user within distance at most kb􀀀uk2 from b can receive data in the same round due to interference phenomena. The goal is to minimize, given the positions of the base stations and users, the number of rounds until all users have received their data.We call this problem the Joint Base Station Scheduling Problem (JBS) and consider it on the line (1D-JBS) and in the plane (2D-JBS). For 1D-JBS, we give an efcient 2-approximation algorithm and polynomial time optimal algorithms for special cases. We model transmissions from base stations to users as arrows (intervals with a distinguished endpoint) and show that their conict graphs, which we call arrow graphs, are a subclass of the class of perfect graphs. For 2D-JBS, we prove NP-hardness and show that some natural greedy heuristics do not achieve approximation ratio better than O(log n), where n is the number of users.