arXiv subjects

Dariusz R. Kowalski

Publications and source records attributed to Dariusz R. Kowalski.

At least 37 records · Page 2Linked to original sources

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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arXiv2022

Optimal Algorithms for Free Order Multiple-Choice Secretary

Suppose we are given integer $k \leq n$ and $n$ boxes labeled $1,\ldots, n$ by an adversary, each containing a number chosen from an unknown distribution. We have to choose an order to sequentially open these boxes, and each time we open the next box in this order, we learn its number. If we reject a number in a box, the box cannot be recalled. Our goal is to accept the $k$ largest of these numbers, without necessarily opening all boxes. This is the free order multiple-choice secretary problem. Free order variants were studied extensively for the secretary and prophet problems. Kesselheim, Kleinberg, and Niazadeh KKN (STOC'15) initiated a study of randomness-efficient algorithms (with the cheapest order in terms of used random bits) for the free order secretary problems. We present an algorithm for free order multiple-choice secretary, which is simultaneously optimal for the competitive ratio and used amount of randomness. I.e., we construct a distribution on orders with optimal entropy $Θ(\log\log n)$ such that a deterministic multiple-threshold algorithm is $1-O(\sqrt{\log k/k})$-competitive. This improves in three ways the previous best construction by KKN, whose competitive ratio is $1 - O(1/k^{1/3}) - o(1)$. Our competitive ratio is (near)optimal for the multiple-choice secretary problem; it works for exponentially larger parameter $k$; and our algorithm is a simple deterministic multiple-threshold algorithm, while that in KKN is randomized. We also prove a corresponding lower bound on the entropy of optimal solutions for the multiple-choice secretary problem, matching entropy of our algorithm, where no such previous lower bound was known. We obtain our algorithmic results with a host of new techniques, and with these techniques we also improve significantly the previous results of KKN about constructing entropy-optimal distributions for the classic free order secretary.

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arXiv2022

Efficient Deterministic Quantitative Group Testing for Precise Information Retrieval

The Quantitative Group Testing (QGT) is about learning a (hidden) subset $K$ of some large domain $N$ using a sequence of queries, where a result of a query provides information about the size of the intersection of the query with the unknown subset $K$. Almost all previous work focused on randomized algorithms minimizing the number of queries; however, in case of large domains $N$, randomization may result in a significant deviation from the expected precision. Others assumed unlimited computational power (existential results) or adaptiveness of queries. In this work we propose efficient non-adaptive deterministic QGT algorithms for constructing queries and deconstructing a hidden set $K$ from the results of the queries, without using randomization, adaptiveness or unlimited computational power. The efficiency is three-fold. First, in terms of almost-optimal number of queries - we improve it by factor nearly $|K|$ comparing to previous constructive results. Second, our algorithms construct the queries and reconstruct set $K$ in polynomial time. Third, they work for any hidden set $K$, as well as multi-sets, and even if the results of the queries are capped at $\sqrt{|K|}$. We also analyze how often elements occur in queries and its impact to parallelization and fault-tolerance of the query system.

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arXiv2022

Efficient Algorithm for Deterministic Search of Hot Elements

When facing a very large stream of data, it is often desirable to extract most important statistics online in a short time and using small memory. For example, one may want to quickly find the most influential users generating posts online or check if the stream contains many identical elements. In this paper, we study streams containing insertions and deletions of elements from a possibly large set $N$ of size $|N| = n$, that are being processed by online deterministic algorithms. At any point in the stream the algorithm may be queried to output elements of certain frequency in the already processed stream. More precisely, the most frequent elements in the stream so far. The output is considered correct if the returned elements it contains all elements with frequency greater than a given parameter $φ$ and no element with frequency smaller than $φ-ε$. We present an efficient online deterministic algorithm for solving this problem using $O(\min(n, \frac{polylog(n)}ε))$ memory and $O(polylog(n))$ time per processing and outputting an element. It is the first such algorithm as the previous algorithms were either randomized, or processed elements in substantially larger time $Ω(\min(n, \frac{\log n}ε))$, or handled only insertions and required two passes over the stream (i.e., were not truly online). Our solution is almost-optimally scalable (with only a polylogarithmic overhead) and does not require randomness or scanning twice through the stream. We complement the algorithm analysis with a lower bound $Ω(\min(n, \frac{1}ε))$ on required memory.

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arXiv2022

Improved Communication Complexity of Fault-Tolerant Consensus

Consensus is one of the most thoroughly studied problems in distributed computing, yet there are still complexity gaps that have not been bridged for decades. In particular, in the classical message-passing setting with processes' crashes, since the seminal works of Bar-Joseph and Ben-Or [1998] \cite{Bar-JosephB98} and Aspnes and Waarts [1996, 1998] \cite{AspnesW-SICOMP-96,Aspnes-JACM-98} in the previous century, there is still a fundamental unresolved question about communication complexity of fast randomized Consensus against a (strong) adaptive adversary crashing processes arbitrarily online. The best known upper bound on the number of communication bits is $Θ(\frac{n^{3/2}}{\sqrt{\log{n}}})$ per process, while the best lower bound is $Ω(1)$. This is in contrast to randomized Consensus against a (weak) oblivious adversary, for which time-almost-optimal algorithms guarantee amortized $O(1)$ communication bits per process \cite{GK-SODA-10}. We design an algorithm against adaptive adversary that reduces the communication gap by nearly linear factor to $O(\sqrt{n}\cdot\text{polylog } n)$ bits per process, while keeping almost-optimal (up to factor $O(\log^3 n)$) time complexity $O(\sqrt{n}\cdot\log^{5/2} n)$. More surprisingly, we show this complexity indeed can be lowered further, but at the expense of increasing time complexity, i.e., there is a {\em trade-off} between communication complexity and time complexity. More specifically, our main Consensus algorithm allows to reduce communication complexity per process to any value from $\text{polylog } n$ to $O(\sqrt{n}\cdot\text{polylog } n)$, as long as Time $\times$ Communication $= O(n\cdot \text{polylog } n)$. Similarly, reducing time complexity requires more random bits per process, i.e., Time $\times$ Randomness $=O(n\cdot \text{polylog } n)$.

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arXiv2022

Efficient Distributed Computations in Anonymous Dynamic Congested Systems with Opportunistic Connectivity

In this work we address the question of efficiency of distributed computing in anonymous, congested and highly dynamic and not-always-connected networks/systems. More precisely, the system consists of an unknown number of anonymous nodes with congestion on links and local computation. Links can change arbitrarily from round to round, with only limitation that the union of any T consecutive networks must form a temporarily connected (multi-)graph on all nodes (knowledge of T is the only information the nodes require, otherwise the communication would not be feasible). Nodes do not have any IDs, only some number l of them have a bit distinguishing them from nodes without such a bit. In each round a node can send and receive messages from its current neighbors. Links and nodes are congested, in the sense that the length of messages and local cache memory for local computation is (asymptotically) logarithmic. All-to-all communication is a fundamental principle in distributed computing - it assumes that each node has an input message to be delivered to all other nodes. Without loss of generality, the size of each input message is logarithmic to fit in the link and node congestion assumption; otherwise, they could be split in logarithmic batches and considered one-by-one. Because of anonymity, each node needs to receive only a set of all input messages, each accompanied by a number of initiating nodes (message multiplicity). We prove that this task can be done in time polynomial in the (initially unknown) number of nodes n and in the lower bound on the isoperimetric numbers of dynamically evolving graphs. This allows to efficiently emulate a popular Congested Clique model on top of Anonymous Dynamic Congested Systems (ADCS) with Opportunistic Connectivity, even if the number of nodes may arbitrarily change in the beginning of emulation.

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arXiv2021

Tree exploration in dual-memory model

We study the problem of online tree exploration by a deterministic mobile agent. Our main objective is to establish what features of the model of the mobile agent and the environment allow linear exploration time. We study agents that, upon entering to a node, do not receive as input the edge via which they entered. In such a model, deterministic memoryless exploration is infeasible, hence the agent needs to be allowed to use some memory. The memory can be located at the agent or at each node. The existing lower bounds show that if the memory is either only at the agent or only at the nodes, then the exploration needs superlinear time. We show that tree exploration in dual-memory model, with constant memory at the agent and logarithmic at each node is possible in linear time when one of two additional features is present: fixed initial state of the memory at each node (so called clean memory) or a single movable token. We present two algorithms working in linear time for arbitrary trees in these two models. On the other hand, in our lower bound we show that if the agent has a single bit of memory and one bit is present at each node, then exploration may require quadratic time on paths, if the initial memory at nodes could be set arbitrarily (so called dirty memory). This shows that having clean node memory or a token allows linear exploration of trees in the model with two types of memory, but having neither of those features may lead to quadratic exploration time even on a simple path.

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arXiv2021

Generalized Framework for Group Testing: Queries, Feedbacks and Adversaries

In the Group Testing problem, the objective is to learn a subset K of some much larger domain N, using the shortest-possible sequence of queries Q. A feedback to a query provides some information about the intersection between the query and subset K. Several specific feedbacks have been studied in the literature, often proving different formulas for the estimate of the query complexity of the problem, defined as the shortest length of queries' sequence solving Group Testing problem with specific feedback. In this paper we study what are the properties of the feedback that influence the query complexity of Group Testing and what is their measurable impact. We propose a generic framework that covers a vast majority of relevant settings considered in the literature, which depends on two fundamental parameters of the feedback: input capacity $α$ and output expressiveness $β$. They upper bound the logarithm of the size of the feedback function domain and image, respectively. To justify the value of the framework, we prove upper bounds on query complexity of non adaptive, deterministic Group Testing under some "efficient" feedbacks, for minimum, maximum and general expressiveness, and complement them with a lower bound on all feedbacks with given parameters $α,β$. Our upper bounds also hold if the feedback function could get an input twisted by a malicious adversary, in case the intersection of a query and the hidden set is bigger than the feedback capacity $α$. We also show that slight change in the feedback function may result in substantial worsening of the query complexity. Additionally, we analyze explicitly constructed randomized counterparts of the deterministic results. Our results provide some insights to what are the most useful bits of information an output-restricted feedback could provide, and open a number of challenging research directions.

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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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arXiv2021

Polynomial Anonymous Dynamic Distributed Computing without a Unique Leader

Counting the number of nodes in Anonymous Dynamic Networks is enticing from an algorithmic perspective: an important computation in a restricted platform with promising applications. Starting with Michail, Chatzigiannakis, and Spirakis [19], a flurry of papers sped up the running time guarantees from doubly-exponential to polynomial [16]. There is a common theme across all those works: a distinguished node is assumed to be present, because Counting cannot be solved deterministically without at least one. In the present work we study challenging questions that naturally follow: how to efficiently count with more than one distinguished node, or how to count without any distinguished node. More importantly, what is the minimal information needed about these distinguished nodes and what is the best we can aim for (count precision, stochastic guarantees, etc.) without any. We present negative and positive results to answer these questions. To the best of our knowledge, this is the first work that addresses them.

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arXiv2021

Time and Communication Complexity of Leader Election in Anonymous Networks

We study the problem of randomized Leader Election in synchronous distributed networks with indistinguishable nodes. We consider algorithms that work on networks of arbitrary topology in two settings, depending on whether the size of the network, i.e., the number of nodes, is known or not. In the former setting, we present a new Leader Election protocol that improves over previous work by lowering message complexity and making it close to a lower bound by a factor of $\tilde{O}(\sqrt{t_{mix}\sqrtΦ})$, where $Φ$ is the conductance and $t_{mix}$ is the mixing time of the network graph. We then show that lacking the network size no Leader Election algorithm can guarantee that the election is final with constant probability, even with unbounded communication. Hence, we further classify the problem as Irrevocable Leader Election (the classic one, requiring knowledge of n - as is our first protocol) or Revocable Leader Election, and present a new polynomial time and message complexity Revocable Leader Election algorithm in the setting without knowledge of network size. We analyze time and message complexity of our protocols in the Congest model of communication.

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arXiv2020

Contention resolution on a restrained channel

We examine deterministic broadcasting on multiple-access channels for a scenario when packets are injected continuously by an adversary to the buffers of the devices at rate $ρ$ packages per round. The aim is to maintain system stability, that is, bounded queues. In contrast to previous work we assume that there is a strict limit of available power, defined as the total number of stations allowed to transmit or listen to the channel at a given time, that can never be exceeded. We study how this constraint influences the quality of services with particular focus on stability. We show that in the regime of deterministic algorithms, the significance of energy restriction depends strongly on communication capabilities of broadcasting protocols. For the adaptive and full-sensing protocols, wherein stations may substantially adopt their behavior to the injection pattern, one can construct efficient algorithms using very small amounts of power without sacrificing throughput or stability of the system. In particular, we construct constant-energy adaptive and full sensing protocols stable for $ρ=1$ and any $ρ<1$, respectively, even for worst case (adversarial) injection patterns. Surprisingly, for the case of acknowledgment based algorithms that cannot adopt to the situation on the channel (i.e., their transmitting pattern is fixed in advance), limiting power leads to reducing the throughput. That is, for this class of protocols in order to preserve stability we need to reduce injection rate significantly. We support our theoretical analysis by simulation results of algorithms constructed in the paper. We depict how they work for systems of moderate, realistic sizes. We also provide a comprehensive simulation to compare our algorithms with backoff algorithms, which are common in real-world implementations, in terms of queue sizes and energy consumption.

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arXiv2020

Optimal Packet-oblivious Stable Routing in Multi-hop Wireless Networks

Stability is an important issue in order to characterize the performance of a network, and it has become a major topic of study in the last decade. Roughly speaking, a communication network system is said to be stable if the number of packets waiting to be delivered (backlog) is finitely bounded at any one time. In this paper, we introduce a new family of combinatorial structures, which we call universally strong selectors, that are used to provide a set of transmission schedules. Making use of these structures, combined with some known queuing policies, we propose a packet-oblivious routing algorithm which is working without using any global topological information, and guarantees stability for certain injection rates. We show that this protocol is asymptotically optimal regarding the injection rate for which stability is guaranteed. Furthermore, we also introduce a packet-oblivious routing algorithm that guarantees stability for higher traffic. This algorithm is optimal regarding the injection rate for which stability is guaranteed. However, it needs to use some global information of the system topology.

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arXiv2019

Deterministic coloring algorithms in the LOCAL model

We study the problem of bi-chromatic coloring of hypergraphs in the LOCAL distributed model of computation. This problem can easily be solved by a randomized local algorithm with no communication. However, it is not known how to solve it deterministically with only a polylogarithmic number of communication rounds. In this paper we indeed design such a deterministic algorithm that solves this problem with polylogarithmic number of communication rounds. This is an almost exponential improvement on the previously known deterministic local algorithms for this problem. Because the bi-chromatic coloring of hypergraphs problem is known to be complete in the class of all locally checkable graph problems, our result implies deterministic local algorithms with polylogarithmic number of communication rounds for all such problems for which an efficient randomized algorithm exists. This solves one of the fundamental open problems in the area of local distributed graph algorithms. By reductions due to Ghaffari, Kuhn and Maus [STOC 2017] this implies such polylogarithmically efficient deterministic local algorithms for many graph problems.

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arXiv2019

On the complexity of fault-tolerant consensus

The paper studies the problem of reaching agreement in a distributed message-passing system prone to crash failures. Crashes are generated by \constrained\ adversaries - a \wadapt\ adversary, who has to fix in advance the set of $f$ crash-prone processes, or a \chainadapt\ adversary, who orders all the processes into $k$ disjoint chains and has to follow this pattern when crashing them. Apart from these constraints, both of them may crash processes in an adaptive way at any time. While commonly used \sadapt\ adversaries model attacks and \noadapt\ ones -- pre-defined faults, the constrained adversaries model more realistic scenarios when there are fault-prone dependent processes, e.g., in hierarchical or dependable software/hardware systems. We propose time-efficient consensus algorithms against such adversaries and also show how to improve the message complexity of proposed solutions. Finally, we show how to reach consensus against a \kthick\ adversary, limited by an arbitrary partial order \dk{with a maximal anti-chain of length $k$}. We complement our algorithmic results with (almost) tight lower bounds, and extend the one for \wadapt\ adversaries to hold also for (syntactically) weaker \noadapt\ adversaries. Together with the consensus algorithm against \wadapt\ adversaries (which automatically translates to \noadapt\ adversaries), these results extend the state-of-the-art of the popular class of \noadapt\ adversaries, in particular the result of Chor, Meritt and Shmoys~\cite{CMS}, and prove general separation between \sadapt\ and the constrained adversaries (including \noadapt) analyzed by Bar-Joseph and Ben-Or~\cite{BB} and others.

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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

Randomized Rumor Spreading in Ad Hoc Networks with Buffers

The randomized rumor spreading problem generates a big interest in the area of distributed algorithms due to its simplicity, robustness and wide range of applications. The two most popular communication paradigms used for spreading the rumor are Push and Pull algorithms. The former protocol allows nodes to send the rumor to a randomly selected neighbor at each step, while the latter is based on sending a request and downloading the rumor from a randomly selected neighbor, provided the neighbor has it. Previous analysis of these protocols assumed that every node could process all such push/pull operations within a single step, which could be unrealistic in practical situations. Therefore we propose a new framework for analysis rumor spreading accommodating buffers, in which a node can process only one push/pull message or push request at a time. We develop upper and lower bounds for randomized rumor spreading time in the new framework, and compare the results with analogous in the old framework without buffers.

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