arXiv subjects

Bogdan S. Chlebus

Publications and source records attributed to Bogdan S. Chlebus.

At least 19 recordsLinked to original sources

arXiv2024

Broadcasting on Adversarial Multiple Access Channels

We study deterministic distributed algorithms for broadcasting on multiple-access channels. Packet injection is modeled by leaky-bucket adversaries. There is a fixed set of stations attached to a channel. Additional features of the model of communication include an upper bound on the number of stations activated in a round, an individual injection rate, and randomness in generating and injecting packets. We demonstrate that some broadcast algorithms designed for ad-hoc channels have bounded latency for increased ranges of injection rates than in ad-hoc channels when executed on channels with a fixed number of stations against adversaries that can activate at most one station per round. Individual injection rates are shown to impact latency, as compared to the model of general leaky bucket adversaries. Outcomes of experiments are given that compare the performance of broadcast algorithms against randomized adversaries. The experiments include deterministic algorithms and randomized backoff algorithms.

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arXiv2023

Disconnected Agreement in Networks Prone to Link Failures

We consider deterministic distributed algorithms for reaching agreement in synchronous networks of arbitrary topologies. Links are bi-directional and prone to failures while nodes stay non-faulty at all times. A faulty link may omit messages. Agreement among nodes is understood as holding in each connected component of a network obtained by removing faulty links. We call ``disconnected agreement'' the algorithmic problem of reaching such agreement. We introduce the concept of stretch, which is the number of connected components of a network, obtained by removing faulty links, minus~$1$ plus the sum of diameters of connected components. We define the concepts of ``fast'' and ``early-stopping'' algorithms for disconnected agreement by referring to stretch. A network has $n$ nodes and $m$ links. Nodes are normally assumed to know their own names and ability to associate communication with local ports. If we additionally assume that a bound~$Λ$ on stretch is known to all nodes, then there is an algorithm for disconnected agreement working in time $O(Λ)$ using messages of $O(\log n)$ bits. We give a general disconnected agreement algorithm operating in~$n+1$ rounds that uses messages of $O(\log n)$ bits. Let~$λ$ be an unknown stretch occurring in an execution; we give an algorithm working in time~$(λ+2)^3$ and using messages of $O(n\log n)$ bits. We show that disconnected agreement can be solved in the optimal $O(λ)$ time, but at the cost of increasing message size to~$O(m\log n)$. We also design an algorithm that uses only~$O(n)$ non-faulty links and works in time~$O(n m)$, while nodes start with their ports mapped to neighbors and messages carry $O(m\log n)$ bits. We prove lower bounds on the performance of disconnected-agreement solutions that refer to the parameters of evolving network topologies and the knowledge available to nodes.

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arXiv2023

Deterministic Fault-Tolerant Distributed Computing in Linear Time and Communication

We develop deterministic algorithms for the problems of consensus, gossiping and checkpointing with nodes prone to failing. Distributed systems are modeled as synchronous complete networks. Failures are represented either as crashes or authenticated Byzantine faults. The algorithmic goal is to have both linear running time and linear amount of communication for as large an upper bound $t$ on the number of faults as possible, with respect to the number of nodes~$n$. For crash failures, these bounds of optimality are $t=\mathcal{O}(\frac{n}{\log n})$ for consensus and $t=\mathcal{O}(\frac{n}{\log^2 n})$ for gossiping and checkpointing, while the running time for each algorithm is $Θ(t+\log n)$. For the authenticated Byzantine model of failures, we show how to accomplish both linear running time and communication for $t=\mathcal{O}(\sqrt{n})$. We show how to implement the algorithms in the single-port model, in which a node may choose only one other node to send/receive a message to/from in a round, such as to preserve the range of running time and communication optimality. We prove lower bounds to show the optimality of some performance bounds.

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arXiv2022

Stable Scheduling in Transactional Memory

We study computer systems with transactions executed on a set of shared objects. Transactions arrive continually subjects to constrains that are framed as an adversarial model and impose limits on the average rate of transaction generation and the number of objects that transactions use. We show that no deterministic distributed scheduler in the queue-free model of transaction autonomy can provide stability for any positive rate of transaction generation. Let a system consist of $m$ shared objects and an adversary be constrained such that each transaction may access at most $k$ shared objects. We prove that no scheduler can be stable if a generation rate is greater than $\max\bigl\{\frac{2}{k+1},\frac{2}{\lfloor \sqrt{2m} \rfloor}\bigr\}$. We develop a centralized scheduler that is stable if a transaction generation rate is at most $\max\bigl\{\frac{1}{4k}, \frac{1}{4\lceil\sqrt{m}\rceil} \bigr\}$. We design a distributed scheduler in the queue-based model of transaction autonomy, in which a transaction is assigned to an individual processor, that guarantees stability if the rate of transaction generation is less than $\max\bigl\{ \frac{1}{6k},\frac{1}{6\lceil\sqrt{m}\rceil}\bigr\}$. For each of the schedulers we give upper bounds on the queue size and transaction latency in the range of rates of transaction generation for which the scheduler is stable.

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arXiv2021

Asynchronous Exclusive Selection

We consider the task of assigning unique integers to a group of processes in an asynchronous distributed system of a total of $n$ processes prone to crashes that communicate through shared read-write registers. In the Renaming problem, an arbitrary group of $k\le n$ processes that hold the original names from a range $[N]=\{1,\ldots,N\}$, contend to acquire unique integers in a smaller range $[M]$ as new names using some $r$ auxiliary shared registers. We give number of wait-free renaming algorithms, in particular an adaptive one having $M=8k-\lg k-1$ as a bound on the range of new names that operates in $O(k)$ local steps and uses $r=O(n^2)$ registers. As a lower bound, we show that a wait-free solution to Renaming requires $1+\min\{k-2,\lfloor\log_{2r} \frac{N}{M+k-1}\rfloor\}$ steps in the worst case. We apply renaming algorithms to obtain solutions to Store&Collect problem, which is about a group of $k\le n$ processes with the original names in a range $[N]$ proposing individual values (operation Store) and returning a view of all proposed values (operation Collect), while using some $r$ auxiliary shared read-write registers. We consider a problem Mining-Names, in which processes may repeatedly request positive integers as new names subject to the constraints that no integer can be assigned to different processes and the number of integers never acquired as names is finite in an infinite execution. We give two solutions to Mining-Names in a distributed system in which there are infinitely many shared read-write registers available. A non-blocking solution leaves at most $2n-2$ nonnegative integers never assigned as names, and a wait-free algorithm leaves at most $(n+2)(n-1)$ nonnegative integers never assigned as names.

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arXiv2021

Distributed Bare-Bones Communication in Wireless Networks

We consider wireless networks operating under the SINR model of interference. Nodes have limited individual knowledge and capabilities: they do not know their positions in a coordinate system in the plane, further they do not know their neighborhoods, nor do they know the size of the network $n$, and finally they cannot sense collisions resulting from simultaneous transmissions by at least two neighbors. Each node is equipped with a unique integer name, where $N$ as an upper bound on the a range of names. We refer as a backbone to a subnetwork induced by a diameter-preserving dominating set of nodes. Let $Δ$ denote a maximum number of nodes that can successfully receive a message transmitted by a node when no other nodes transmit concurrently. We study distributed algorithms for communication problems in three settings. In the single-node-start case, when one node starts an execution and other nodes are awoken by receiving messages from already awoken nodes, we present a randomized broadcast algorithm that wakes up all nodes in $O(n \log^2 N)$ rounds with high probability. For the synchronized-start case, when all nodes start an execution simultaneously, we give a randomized algorithm computing a backbone in $O(Δ\log^{7} N)$ rounds with high probability. In the partly-coordinated-start case, when a number of nodes start an execution together and other nodes are awoken by receiving messages from the already awoken nodes, we develop an algorithm that creates a backbone in time $O(n\log^2 N +Δ\log^{7} N)$ with high probability.

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arXiv2019

Energy Efficient Adversarial Routing in Shared Channels

We investigate routing on networks modeled as multiple access channels, when packets are injected continually. There is an energy cap understood as a bound on the number of stations that can be switched on simultaneously. Each packet is injected into some station and needs to be delivered to its destination station via the channel. A station has to be switched on in order to receive a packet when it is heard on the channel. Each station manages when it is switched on and off by way of a programmable wakeup mechanism, which is scheduled by a routing algorithm. Packet injection is governed by adversarial models that determine upper bounds on injection rates and burstiness. We develop deterministic distributed routing algorithms and assess their performance in the worst-case sense. One of the algorithms maintains bounded queues for the maximum injection rate 1 subject only to the energy cap 3. This energy cap is provably optimal, in that obtaining the same throughput with the energy cap 2 is impossible. We give algorithms subject to the minimum energy cap 2 that have latency polynomial in the total number of stations n for each fixed adversary of injection rate less than 1. An algorithm is k-energy-oblivious if at most k stations are switched on in a round and for each station the rounds when it will be switched on are determined in advance. We give a k-energy-oblivious algorithm that has packet delay O(n) for adversaries of injection rates less than (k-1)/(n-1), and show that there is no k-energy-oblivious stable algorithm against adversaries with injection rates greater than k/n. We give a k-energy-oblivious algorithm routing directly that has latency O(n^2/k) for adversaries of sufficiently small injection rates that are O(k^2/n^2). We show that no k-energy-oblivious algorithm routing directly can be stable against adversaries with injection rates greater than k(k-1)/n(n-1).

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arXiv2018

Stability of Adversarial Routing with Feedback

We consider the impact of scheduling disciplines on performance of routing in the framework of adversarial queuing. We propose an adversarial model which reflects stalling of packets due to transient failures and explicitly incorporates feedback produced by a network when packets are stalled. This adversarial model provides a methodology to study stability of routing protocols when flow-control and congestion-control mechanisms affect the volume of traffic. We show that any scheduling policy that is universally stable, in the regular model of routing that additionally allows packets to have two priorities, remains stable in the proposed adversarial model.

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arXiv2018

Naming a Channel with Beeps

We consider a communication channel in which the only possible communication mode is transmitting beeps, which reach all the nodes instantaneously. Nodes are anonymous, in that they do not have any individual identifiers. The algorithmic goal is to randomly assign names to the nodes in such a manner that the names make a contiguous segment of positive integers starting from $1$. We give a Las Vegas naming algorithm for the case when the number of nodes $n$ is known, and a Monte Carlo algorithm for the case when the number of nodes $n$ is not known. The algorithms are provably optimal with respect to the expected time $O(n\log n)$, the number of used random bits $O(n\log n)$, and the probability of error.

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arXiv2018

Scalable Wake-up of Multi-Channel Single-Hop Radio Networks

We consider single-hop radio networks with multiple channels as a model of wireless networks. There are $n$ stations connected to $b$ radio channels that do not provide collision detection. A station uses all the channels concurrently and independently. Some $k$ stations may become active spontaneously at arbitrary times. The goal is to wake up the network, which occurs when all the stations hear a successful transmission on some channel. Duration of a waking-up execution is measured starting from the first spontaneous activation. We present a deterministic algorithm for the general problem that wakes up the network in $O(k\log^{1/b} k\log n)$ time, where $k$ is unknown. We give a deterministic scalable algorithm for the special case when $b>d \log \log n$, for some constant $d>1$, which wakes up the network in $O(\frac{k}{b}\log n\log(b\log n))$ time, with $k$ unknown. This algorithm misses time optimality by at most a factor of $O(\log n(\log b +\log\log n))$, because any deterministic algorithm requires $Ω(\frac{k}{b}\log \frac{n}{k})$ time. We give a randomized algorithm that wakes up the network within $O(k^{1/b}\ln \frac{1}ε)$ rounds with a probability that is at least $1-ε$, for any $0<ε<1$, where $k$ is known. We also consider a model of jamming, in which each channel in any round may be jammed to prevent a successful transmission, which happens with some known parameter probability $p$, independently across all channels and rounds. For this model, we give two deterministic algorithms for unknown~$k$: one wakes up the network in time $O(\log^{-1}(\frac{1}{p})\, k\log n\log^{1/b} k)$, and the other in time $O(\log^{-1}(\frac{1}{p}) \, \frac{k}{b} \log n\log(b\log n))$ but assuming the inequality $b>\log(128b\log n)$, both with a probability that is at least $1-1/\mbox{poly}(n)$.

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arXiv2018

Routing in Wireless Networks with Interferences

We consider dynamic routing in multi-hop wireless networks with adversarial traffic. The model of wireless communication incorporates interferences caused by packets' arrivals into the same node that overlap in time. We consider two classes of adversaries: balanced and unbalanced. We demonstrate that, for each routing algorithm and an unbalanced adversary, the algorithm is unstable against this adversary in some networks. We develop a routing algorithm that has bounded packet latency against each balanced adversary.

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arXiv2018

Doing-it-All with Bounded Work and Communication

We consider the Do-All problem, where $p$ cooperating processors need to complete $t$ similar and independent tasks in an adversarial setting. Here we deal with a synchronous message passing system with processors that are subject to crash failures. Efficiency of algorithms in this setting is measured in terms of work complexity (also known as total available processor steps) and communication complexity (total number of point-to-point messages). When work and communication are considered to be comparable resources, then the overall efficiency is meaningfully expressed in terms of effort defined as work + communication. We develop and analyze a constructive algorithm that has work $O( t + p \log p\, (\sqrt{p\log p}+\sqrt{t\log t}\, ) )$ and a nonconstructive algorithm that has work $O(t +p \log^2 p)$. The latter result is close to the lower bound $Ω(t + p \log p/ \log \log p)$ on work. The effort of each of these algorithms is proportional to its work when the number of crashes is bounded above by $c\,p$, for some positive constant $c < 1$. We also present a nonconstructive algorithm that has effort $O(t + p ^{1.77})$.

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arXiv2018

Adversarial Multiple Access Channels with Individual Injection Rates

We study deterministic distributed broadcasting in synchronous multiple-access channels. Packets are injected into $n$ nodes by a window-type adversary that is constrained by a window $w$ and injection rates individually assigned to all nodes. We investigate what queue size and packet latency can be achieved with the maximum aggregate injection rate of one packet per round, depending on properties of channels and algorithms. We give a non-adaptive algorithm for channels with collision detection and an adaptive algorithm for channels without collision detection that achieve $O(\min(n+w,w\log n))$ packet latency. We show that packet latency has to be either $Ω(w \max (1,\log_w n))$, when $w\le n$, or $Ω(w+n)$, when $w>n$, as a matching lower bound to these algorithms. We develop a non-adaptive algorithm for channels without collision detection that achieves $O(n+w)$ queue size and $O(nw)$ packet latency. This is in contrast with the adversarial model of global injection rates, in which non-adaptive algorithms with bounded packet latency do not exist (Chlebus et al. Distributed Computing 22(2): 93 - 116, 2009). Our algorithm avoids collisions produced by simultaneous transmissions; we show that any algorithm with this property must have $Ω(nw)$ packet latency.

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arXiv2018

Broadcasting in Ad Hoc Multiple Access Channels

We study broadcast in multiple access channels in dynamic adversarial settings. There is an unbounded supply of anonymous stations attached to a synchronous channel. There is an adversary who injects packets into stations to be broadcast on the channel. The adversary is restricted by injection rate, burstiness, and by how many passive stations can be simultaneously activated by providing them with packets. We consider deterministic distributed broadcast algorithms, which are further categorized by their properties. We investigate for which injection rates can algorithms attain bounded packet latency, when adversaries are restricted to be able to activate at most one station per round. The rates of algorithms we present make the increasing sequence consisting of $\frac{1}{3}$, $\frac{3}{8}$ and $\frac{1}{2}$, reflecting the additional features of algorithms. We show that injection rate $\frac{3}{4}$ cannot be handled with bounded packet latency.

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arXiv2018

Packet Latency of Deterministic Broadcasting in Adversarial Multiple Access Channels

We study broadcasting in multiple access channels with dynamic packet arrivals and jamming. Communication environments are represented by adversarial models that specify constraints on packet arrivals and jamming. We consider deterministic distributed broadcast algorithms and give upper bounds on the worst-case packet latency and the number of queued packets in relation to the parameters defining adversaries. Packet arrivals are determined by a rate of injections and a number of packets that can be generated in one round. Jamming is constrained by a rate with which an adversary can jam rounds and by a number of consecutive rounds that can be jammed.

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arXiv2018

Deterministic Computations on a PRAM with Static Processor and Memory Faults

We consider Parallel Random Access Machine (PRAM) which has some processors and memory cells faulty. The faults considered are static, i.e., once the machine starts to operate, the operational/faulty status of PRAM components does not change. We develop a deterministic simulation of a fully operational PRAM on a similar faulty machine which has constant fractions of faults among processors and memory cells. The simulating PRAM has $n$ processors and $m$ memory cells, and simulates a PRAM with $n$ processors and a constant fraction of $m$ memory cells. The simulation is in two phases: it starts with preprocessing, which is followed by the simulation proper performed in a step-by-step fashion. Preprocessing is performed in time $O((\frac{m}{n}+ \log n)\log n)$. The slowdown of a step-by-step part of the simulation is $O(\log m)$.

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arXiv2017

Broadcasting Spanning Forests on a Multiple-Access Channel

The problem of finding a spanning forest of a graph in a distributed-processing environment is studied. If an input graph is weighted, then the goal is to find a minimum-weight spanning forest. The processors communicate by broadcasting. The output consists of the edges that make a spanning forest and have been broadcast on the network. Input edges are distributed among the processors, with each edge held by one processor. The underlying broadcast network is implemented as a multiple-access channel. If exactly one processor attempts to perform a broadcast, then the broadcast is successful. A message broadcast successfully is delivered to all the processors in one step. If more than one processors broadcast simultaneously, then the messages interfere with each other and no processor can receive any of them. Optimality of algorithmic solutions is investigated, by way of comparing deterministic with randomized algorithms, and adaptive with oblivious ones. Lower bounds are proved that either justify the optimality of specific algorithms or show that the optimal performance depends on a class of algorithms.

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arXiv2017

Randomized Communication in Radio Networks

A communication network is called a radio network if its nodes exchange messages in the following restricted way. First, a send operation performed by a node delivers copies of the same message to all directly reachable nodes. Secondly, a node can successfully receive an incoming message only if exactly one of its neighbors sent a message in that step. It is this semantics of how ports at nodes send and receive messages that defines the networks rather than the fact that only radio waves are used as a medium of communication; but if that is the case then just a single frequency is used. We discuss algorithmic aspects of exchanging information in such networks, concentrating on distributed randomized protocols. Specific problems and solutions depend a lot on the topology of the underlying reachability graph and how much the nodes know about it. In single-hop networks each pair of nodes can communicate directly. This kind of networks is also known as the multiple access channel. Popular broadcasting protocols used on such channels are Aloha and the exponential backoff. Multi-hop networks may have arbitrary topology and packets need to be routed hopping through a sequence of adjacent nodes. Distributed protocols run by such networks are usually robust enough not to expect the nodes to know their neighbors. These ad-hoc networks and protocols model the situation when nodes are mobile and do not rely on a fixed infrastructure.

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