arXiv subjects

Dariusz R. Kowalski

Publications and source records attributed to Dariusz R. Kowalski.

At least 55 records · Page 3Linked to original sources

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

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

Ordered and Delayed Adversaries and How to Work against Them on a Shared Channel

In this work we define a class of ordered adversaries causing distractions according to some partial order fixed by the adversary before the execution, and study how they affect performance of algorithms. We focus on the Do-All problem of performing t tasks on a shared channel consisting of p crash-prone stations. The channel restricts communication: no message is delivered to the alive stations if more than one station transmits at the same time. The performance measure for the Do-All problem is work: the total number of available processor steps during the whole execution. We address the question of how the ordered adversaries controlling crashes of stations influence work performance of Do-All algorithms. The first presented algorithm solves Do-All with work O(t+p\sqrt{t}\log p) against the Linearly-Ordered adversary, restricted by some pre-defined linear order of crashing stations. Another algorithm runs against the Weakly-Adaptive adversary, restricted by some pre-defined set of f crash-prone stations (it can be seen as restricted by the order being an anti-chain of crashing stations). The work done by this algorithm is O(t+p\sqrt{t}+p\min{p/(p-f),t}\log p). Both results are close to the corresponding lower bounds from [CKL]. We generalize this result to the class of adversaries restricted by a partial order with a maximum anti-chain of size k and complement with the lower bound. We also consider a class of delayed adaptive adversaries, who could see random choices with some delay. We give an algorithm that runs against the 1-RD adversary (seeing random choices of stations with one round delay), achieving close to optimal O(t+p\sqrt{t}\log^2 p) work complexity. This shows that restricting adversary by even 1 round delay results in (almost) optimal work on a shared channel.

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arXiv2018

Fault-tolerant parallel scheduling of arbitrary length jobs on a shared channel

We study the problem of scheduling jobs on fault-prone machines communicating via a shared channel, also known as multiple-access channel. We have $n$ arbitrary length jobs to be scheduled on $m$ identical machines, $f$ of which are prone to crashes by an adversary. A machine can inform other machines when a job is completed via the channel without collision detection. Performance is measured by the total number of available machine steps during the whole execution. Our goal is to study the impact of preemption (i.e., interrupting the execution of a job and resuming later in the same or different machine) and failures on the work performance of job processing. The novelty is the ability to identify the features that determine the complexity (difficulty) of the problem. We show that the problem becomes difficult when preemption is not allowed, by showing corresponding lower and upper bounds, the latter with algorithms reaching them. We also prove that randomization helps even more, but only against a non-adaptive adversary; in the presence of more severe adaptive adversary, randomization does not help in any setting. Our work has extended from previous work that focused on settings including: scheduling on multiple-access channel without machine failures, complete information about failures, or incomplete information about failures (like in this work) but with unit length jobs and, hence, without considering preemption.

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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

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 Digital Clustering of Wireless Ad Hoc Networks

We consider deterministic distributed communication in wireless ad hoc networks of identical weak devices under the SINR model without predefined infrastructure. Most algorithmic results in this model rely on various additional features or capabilities, e.g., randomization, access to geographic coordinates, power control, carrier sensing with various precision of measurements, and/or interference cancellation. We study a pure scenario, when no such properties are available. As a general tool, we develop a deterministic distributed clustering algorithm. Our solution relies on a new type of combinatorial structures (selectors), which might be of independent interest. Using the clustering, we develop a deterministic distributed local broadcast algorithm accomplishing this task in $O(Δ\log^*N \log N)$ rounds, where $Δ$ is the density of the network. To the best of our knowledge, this is the first solution in pure scenario which is only polylog$(n)$ away from the universal lower bound $Ω(Δ)$, valid also for scenarios with randomization and other features. Therefore, none of these features substantially helps in performing the local broadcast task. Using clustering, we also build a deterministic global broadcast algorithm that terminates within $O(D(Δ+ \log^* N) \log N)$ rounds, where $D$ is the diameter of the network. This result is complemented by a lower bound $Ω(D Δ^{1-1/α})$, where $α> 2$ is the path-loss parameter of the environment. This lower bound shows that randomization or knowledge of own location substantially help (by a factor polynomial in $Δ$) in the global broadcast. Therefore, unlike in the case of local broadcast, some additional model features may help in global broadcast.

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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

Maximum Throughput of Multiple Access Channels in Adversarial Environments

We consider deterministic distributed broadcasting on multiple access channels in the framework of adversarial queuing. Packets are injected dynamically by an adversary that is constrained by the injection rate and the number of packets that may be injected simultaneously; the latter we call burstiness. The maximum injection rate that an algorithm can handle in a stable manner is called the throughput of the algorithm. We develop an algorithm that achieves throughput $1$ for any number of stations against leaky-bucket adversaries. The algorithm has $O(n^2+\text{burstiness})$ packets queued simultaneously at any time, where $n$ is the number of stations; this upper bound is proved to be best possible. An algorithm is called fair when each packet is eventually broadcast. We show that no algorithm can be both stable and fair for a system of at least two stations against leaky-bucket adversaries. We study in detail small systems of exactly two and three stations against window adversaries to exhibit differences in quality of broadcast among classes of algorithms. For two stations, we show that fair latency can be achieved by a full sensing algorithm, while there is no stable acknowledgment based algorithm. For three stations, we show that fair latency can be achieved by a general algorithm, while no full sensing algorithm can be stable. Finally, we show that algorithms that either are fair or do not have the queue sizes affect the order of transmissions cannot be stable in systems of at least four stations against window adversaries.

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arXiv2017

Polynomial Counting in Anonymous Dynamic Networks with Applications to Anonymous Dynamic Algebraic Computations

Starting with Michail, Chatzigiannakis, and Spirakis work, the problem of Counting the number of nodes in Anonymous Dynamic Networks has attracted a lot of attention. The problem is challenging because nodes are indistinguishable (they lack identifiers and execute the same program) and the topology may change arbitrarily from round to round of communication, as long as the network is connected in each round. The problem is central in distributed computing as the number of participants is frequently needed to make important decisions, such as termination, agreement, synchronization, and many others. A variety of algorithms built on top of mass-distribution techniques have been presented, analyzed, and also experimentally evaluated; some of them assumed additional knowledge of network characteristics, such as bounded degree or given upper bound on the network size. However, the question of whether Counting can be solved deterministically in sub-exponential time remained open. In this work, we answer this question positively by presenting Methodical Counting, which runs in polynomial time and requires no knowledge of network characteristics. Moreover, we also show how to extend Methodical Counting to compute the sum of input values and more complex functions without extra cost. Our analysis leverages previous work on random walks in evolving graphs, combined with carefully chosen alarms in the algorithm that control the process and its parameters. To the best of our knowledge, our Counting algorithm and its extensions to other algebraic and Boolean functions are the first that can be implemented in practice with worst-case guarantees.

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arXiv2017

Lightweight Robust Framework for Workload Scheduling in Clouds

Reliability, security and stability of cloud services without sacrificing too much resources have become a desired feature in the area of workload management in clouds. The paper proposes and evaluates a lightweight framework for scheduling a workload which part could be unreliable. This unreliability could be caused by various types of failures or attacks. Our framework for robust workload scheduling efficiently combines classic fault-tolerant and security tools, such as packet/job scanning, with workload scheduling, and it does not use any heavy resource-consuming tools, e.g., cryptography or non-linear optimization. More specifically, the framework uses a novel objective function to allocate jobs to servers and constantly decides which job to scan based on a formula associated with the objective function. We show how to set up the objective function and the corresponding scanning procedure to make the system provably stable, provided it satisfies a specific stability condition. As a result, we show that our framework assures cloud stability even if naive scanning-all and scanning-none strategies are not stable. We extend the framework to decentralized scheduling and evaluate it under several popular routing procedures.

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arXiv2017

Ad-hoc Affectance-selective Families for Layer Dissemination

Information dissemination protocols for ad-hoc wireless networks frequently use a minimal subset of the available communication links, defining a rooted "broadcast" tree. In this work, we focus on the core challenge of disseminating from one layer to the next one of such tree. We call this problem Layer Dissemination. We study Layer Dissemination under a generalized model of interference, called affectance. The affectance model subsumes previous models, such as Radio Network and Signal to Inteference-plus-Noise Ratio. We present randomized and deterministic protocols for Layer Dissemination. These protocols are based on a combinatorial object that we call Affectance-selective Families. Our approach combines an engineering solution with theoretical guarantees. That is, we provide a method to characterize the network with a global measure of affectance based on measurements of interference in the specific deployment area. Then, our protocols distributedly produce an ad-hoc transmissions schedule for dissemination. In the randomized protocol only the network characterization is needed, whereas the deterministic protocol requires full knowledge of affectance. Our theoretical analysis provides guarantees on schedule length. We also present simulations of a real network-deployment area contrasting the performance of our randomized protocol, which takes into account affectance, against previous work for interference models that ignore some physical constraints. The striking improvement in performance shown by our simulations show the importance of utilizing a more physically-accurate model of interference that takes into account other effects beyond distance to transmitters.

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arXiv2017

Deterministic Backbone Creation in an SINR Network without Knowledge of Location

For a given network, a backbone is an overlay network consisting of a connected dominating set with additional accessibility properties. Once a backbone is created for a network, it can be utilized for fast communication amongst the nodes of the network. The Signal-to-Interference-plus-Noise-Ratio (SINR) model has become the standard for modeling communication among devices in wireless networks. For this model, the community has pondered what the most realistic solutions for communication problems in wireless networks would look like. Such solutions would have the characteristic that they would make the least number of assumptions about the availability of information about the participating nodes. Solving problems when nothing at all is known about the network and having nodes just start participating would be ideal. However, this is quite challenging and most likely not feasible. The pragmatic approach is then to make meaningful assumptions about the available information and present efficient solutions based on this information. We present a solution for creation of backbone in the SINR model, when nodes do not have access to their physical coordinates or the coordinates of other nodes in the network. This restriction models the deployment of nodes in various situations for sensing hurricanes, cyclones, and so on, where only information about nodes prior to their deployment may be known but not their actual locations post deployment. We assume that nodes have access to knowledge of their label, the labels of nodes within their neighborhood, the range from which labels are taken $[N]$ and the total number of participating nodes $n$. We also assume that nodes wake up spontaneously. We present an efficient deterministic protocol to create a backbone with a round complexity of $O(Δ\lg^2 N)$.

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arXiv2016

Universal Routing in Multi-hop Radio Networks

In this article we introduce a new model to study stability in multi-hop wireless networks in the framework of adversarial queueing. In such a model, a routing protocol consists of three components: a transmission policy, a scheduling policy to select the packet to transmit form a set of packets parked at a node, and a hearing control mechanism to coordinate transmissions with scheduling. For such a setting, we propose a definition of universal stability that takes into account not only the scheduling policies (as in the standard wireline adversarial model), but also the transmission policies. First, we show that any scheduling policy that is unstable in the classical wireline adversarial model remains unstable in the multi-hop radio network model, even in scenarios free of inter- ferences. Then, we show that both SIS and LIS (two well-known universally stable scheduling policies in the wireline adversarial model) remain stable in the multi-hop radio network model, provided a proactive hearing control is used. In contrast, such scheduling policies turn out to be unstable when using a reactive hearing control. However, the scheduling policy LIS can be enforced to be universally stable provided ties are resolved in a permanent manner. Such a situation doesn't hold in the case of SIS, which remains unstable regardless of how ties are resolved. Furthermore, for some transmission policies which we call regular, we also show that all scheduling policies that are universally stable when using proactive hearing control (which include SIS and LIS) remain universally stable when using reactive hearing control.

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arXiv2015

Dynamic Multiple-Message Broadcast: Bounding Throughput in the Affectance Model

We study a dynamic version of the Multiple-Message Broadcast problem, where packets are continuously injected in network nodes for dissemination throughout the network. Our performance metric is the ratio of the throughput of such protocol against the optimal one, for any sufficiently long period of time since startup. We present and analyze a dynamic Multiple-Message Broadcast protocol that works under an affectance model, which parameterizes the interference that other nodes introduce in the communication between a given pair of nodes. As an algorithmic tool, we develop an efficient algorithm to schedule a broadcast along a BFS tree under the affectance model. To provide a rigorous and accurate analysis, we define two novel network characteristics based on the network topology and the affectance function. The combination of these characteristics influence the performance of broadcasting with affectance (modulo a logarithmic function). We also carry out simulations of our protocol under affectance. To the best of our knowledge, this is the first dynamic Multiple-Message Broadcast protocol that provides throughput guarantees for continuous injection of messages and works under the affectance model.

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arXiv2015

Multi-Broadcasting under the SINR Model

We study the multi-broadcast problem in multi-hop wireless networks under the SINR model deployed in the 2D Euclidean plane. In multi-broadcast, there are $k$ initial rumours, potentially belonging to different nodes, that must be forwarded to all $n$ nodes of the network. Furthermore, in each round a node can only transmit a small message that could contain at most one initial rumor and $O(\log n)$ control bits. In order to be successfully delivered to a node, transmissions must satisfy the (Signal-to-Inference-and-Noise-Ratio) SINR condition and have sufficiently strong signal at the receiver. We present deterministic algorithms for multi-broadcast for different settings that reflect the different types of knowledge about the topology of the network available to the nodes: (i) the whole network topology (ii) their own coordinates and coordinates of their neighbors (iii) only their own coordinates, and (iv) only their own ids and the ids of their neighbors. For the former two settings, we present solutions that are scalable with respect to the diameter of the network and the polylogarithm of the network size, i.e., $\log^c n$ for some constant $c> 0$, while the solutions for the latter two have round complexity that is superlinear in the number of nodes. The last result is of special significance, as it is the first result for the SINR model that does not require nodes to know their coordinates in the plane (a very specialized type of knowledge), but intricately exploits the understanding that nodes are implanted in the 2D Euclidean plane.

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arXiv2014

Information Gathering in Ad-Hoc Radio Networks with Tree Topology

We study the problem of information gathering in ad-hoc radio networks without collision detection, focussing on the case when the network forms a tree, with edges directed towards the root. Initially, each node has a piece of information that we refer to as a rumor. Our goal is to design protocols that deliver all rumors to the root of the tree as quickly as possible. The protocol must complete this task within its allotted time even though the actual tree topology is unknown when the computation starts. In the deterministic case, assuming that the nodes are labeled with small integers, we give an O(n)-time protocol that uses unbounded messages, and an O(n log n)-time protocol using bounded messages, where any message can include only one rumor. We also consider fire-and-forward protocols, in which a node can only transmit its own rumor or the rumor received in the previous step. We give a deterministic fire-and- forward protocol with running time O(n^1.5), and we show that it is asymptotically optimal. We then study randomized algorithms where the nodes are not labelled. In this model, we give an O(n log n)-time protocol and we prove that this bound is asymptotically optimal.

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