arXiv subjects

Dariusz R. Kowalski

Publications and source records attributed to Dariusz R. Kowalski.

At least 19 recordsLinked to original sources

arXiv2026

Weighted Beeping Networks

Beeping Networks (BN) have become an established model of wireless communication and computation. They assume, however, that the communication interference caused by beeping nodes is binary (OR channel), while both artificial and nature-driven networks are based on varied signal strength and receiving thresholds. This work naturally extends the classic beeping networks to weighted beeping networks (WBN), by modeling signal strengths by weights on graph edges and receiving a beep if the accumulative signal strengths of transmitting neighbors are above receiving threshold. Under this generalized model, we study the fundamental Local Broadcast (LB) problem. Since edges with low weights may not even accumulate to a received beep, we only require that messages are delivered along sufficiently heavy edges, with weights above some given threshold $σ$. We design an LB algorithm that completes its task in $O(I_σ\log n \cdot (\mathcal{M}+\log n))$ beeping rounds, whp, where $n$ is the number of nodes, $I_σ$ is the maximum local interference on heavy edges, and $\mathcal{M}$ is the maximum length of messages sent locally. This result is nearly optimal, as, with probability $1$, $Ω(I_σ)$ beeping rounds are necessary to solve LB. Finally, we show that any algorithm designed for the classic beeping networks and terminating in polynomial number of beeping rounds, can be emulated on any WBN with a logarithmic overhead, that is, it returns the same output as working on the classic beeping network isomorphic to the sub-graph of heavy edges.

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arXiv2026

Towards Efficient Data Structures for Approximate Search with Range Queries

Range queries are simple and popular types of queries used in data retrieval. However, extracting exact and complete information using range queries is costly. As a remedy, some previous work proposed a faster principle, {\em approximate} search with range queries, also called single range cover (SRC) search. It can, however, produce some false positives. In this work we introduce a new SRC search structure, a $c$-DAG (Directed Acyclic Graph), which provably decreases the average number of false positives by logarithmic factor while keeping asymptotically same time and memory complexities as a classic tree structure. A $c$-DAG is a tunable augmentation of the 1D-Tree with denser overlapping branches ($c \geq 3$ children per node). We perform a competitive analysis of a $c$-DAG with respect to 1D-Tree and derive an additive constant time overhead and a multiplicative logarithmic improvement of the false positives ratio, on average. We also provide a generic framework to extend our results to empirical distributions of queries, and demonstrate its effectiveness for Gowalla dataset. Finally, we quantify and discuss security and privacy aspects of SRC search on $c$-DAG vs 1D-Tree, mainly mitigation of structural leakage, which makes $c$-DAG a good data structure candidate for deployment in privacy-preserving systems (e.g., searchable encryption) and multimedia retrieval.

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arXiv2025

Near-Optimal Stability for Distributed Transaction Processing in Blockchain Sharding

In blockchain sharding, $n$ processing nodes are divided into $s$ shards, and each shard processes transactions in parallel. A key challenge in such a system is to ensure system stability for any ``tractable'' pattern of generated transactions; this is modeled by an adversary generating transactions with a certain rate of at most $ρ$ and burstiness $b$. This model captures worst-case scenarios and even some attacks on transactions' processing, e.g., DoS. A stable system ensures bounded transaction queue sizes and bounded transaction latency. It is known that the absolute upper bound on the maximum injection rate for which any scheduler could guarantee bounded queues and latency of transactions is $\max\left\{ \frac{2}{k+1}, \frac{2}{ \left\lfloor\sqrt{2s}\right\rfloor}\right\}$, where $k$ is the maximum number of shards that each transaction accesses. Here, we first provide a single leader scheduler that guarantees stability under injection rate $ρ\leq \max\left\{ \frac{1}{16k}, \frac{1}{16\lceil \sqrt{s} \rceil}\right\}$. Moreover, we also give a distributed scheduler with multiple leaders that guarantees stability under injection rate $ρ\leq \frac{1}{16c_1 \log D \log s}\max\left\{ \frac{1}{k}, \frac{1}{\lceil \sqrt{s} \rceil} \right\}$, where $c_1$ is some positive constant and $D$ is the diameter of shard graph $G_s$. This bound is within a poly-log factor from the optimal injection rate, and significantly improves the best previous known result for the distributed setting by Adhikari et al., SPAA 2024.

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arXiv2025

Ultra-Resilient Superimposed Codes: Near-Optimal Construction and Applications

A superimposed code is a collection of binary vectors (codewords) with the property that no vector is contained in the Boolean sum of any $k$ others, enabling unique identification of codewords within any group of $k$. Superimposed codes are foundational combinatorial tools with applications in areas ranging from distributed computing and data retrieval to fault-tolerant communication. However, classical superimposed codes rely on strict alignment assumptions, limiting their effectiveness in asynchronous and fault-prone environments, which are common in modern systems and applications. We introduce Ultra-Resilient Superimposed Codes (URSCs), a new class of codes that extends the classic superimposed framework by ensuring a stronger codewords' isolation property and resilience to two types of adversarial perturbations: arbitrary cyclic shifts and partial bitwise corruption (flips). Additionally, URSCs exhibit universality, adapting seamlessly to any number $k$ of concurrent codewords without prior knowledge. This is a combination of properties not achieved in any previous construction. We provide the first polynomial-time construction of URSCs with near-optimal length, significantly outperforming previous constructions with less general features, all without requiring prior knowledge of the number of concurrent codewords, $k$. % We demonstrate that our URSCs significantly advance the state of the art in multiple applications, including uncoordinated beeping networks, where our codes reduce time complexity for local broadcast by nearly two orders of magnitude, and generalized contention resolution in multi-access channel communication.

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arXiv2025

Deterministic Fault-Tolerant Local Load Balancing and its Applications against Adaptive Adversaries

Load balancing is among the basic primitives in distributed computing. In this paper, we consider this problem when executed locally on a network with nodes prone to failures. We show that there exist lightweight network topologies that are immune to message delivery failures incurred by (at most) a constant fraction of all nodes. More precisely, we design a novel deterministic fault-tolerant local load balancing (LLB) algorithm, which, similarly to their classical counterparts working in fault-free networks, has a relatively simple structure and guarantees exponentially fast convergence to the average value despite crash and omission failures. As the second part of our contribution, we show three applications of the newly developed fault-tolerant local load balancing protocol. We give a randomized consensus algorithm, working against $t < n / 3$ crash failures, that improves over the best-known consensus solution by Hajiaghayi et al. with respect to communication complexity, yet with an arguable simpler technique of combining a randomly and locally selected virtual communication graph with a deterministic fault-tolerant local load balancing on this graph. We also give a new solution for consensus for networks with omission failures. Our solution works against $t < \frac{n}{C\log{n} (\log\log n)^2}$ omissions, for some constant $C$, is nearly optimal in terms of time complexity, but most notably -- it has communication complexity $O((t^2 + n)\text{ polylog } {n})$, matching, within a polylogarithmic factor, the lower bound by Abraham et. al. with respect to both terms depending on $t$ and $n$. Ours is the first algorithm in the literature that is simultaneously nearly optimal, in terms of $n,t$, with respect to both complexity measures, against the adaptive omission-causing adversary.

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arXiv2025

Beeping Deterministic CONGEST Algorithms in Graphs

The Beeping Network (BN) model captures important properties of biological processes. Paradoxically, the extremely limited communication capabilities of such nodes has helped BN become one of the fundamental models for networks. Since in each round, a node may transmit at most one bit, it is useful to treat the communications in the network as distributed coding and design it to overcome the interference. We study both non-adaptive and adaptive codes. Some communication and graph problems already studied in BN admit fast randomized algorithms. On the other hand, all known deterministic algorithms for non-trivial problems have time complexity at least polynomial in the maximum node-degree $Δ$. We improve known results for deterministic algorithms showing that beeping out a single round of any congest algorithm in any network can be done in $O(Δ^2 \log^{O(1)} n)$ beeping rounds, even if the nodes intend to send different messages to different neighbors. This upper bound reduces polynomially the time for a deterministic simulation of congest in a BN, comparing to the best known algorithms, and nearly matches the time obtained recently using. Our simulator allows us to implement any efficient algorithm designed for the congest networks in BN, with $O(Δ^2 \log^{O(1)} n)$ overhead. This $O(Δ^2 \log^{O(1)} n)$ implementation results in a polynomial improvement upon the best-to-date $Θ(Δ^3)$-round beeping MIS algorithm. Using a more specialized transformer and some additional machinery, we constructed various other efficient deterministic Beeping algorithms for other commonly used building blocks, such as Network Decomposition. For $h$-hop simulations, we prove a lower bound $Ω(Δ^{h+1})$, and we design a nearly matching algorithm that is able to ``pipeline'' the information in a faster way than working layer by layer.

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arXiv2025

Beating Competitive Ratio 4 for Graphic Matroid Secretary

One of the classic problems in online decision-making is the *secretary problem* where to goal is to maximize the probability of choosing the largest number from a randomly ordered sequence. A natural extension allows selecting multiple values under a combinatorial constraint. Babaioff, Immorlica, Kempe, and Kleinberg (SODA'07, JACM'18) introduced the *matroid secretary conjecture*, suggesting an $O(1)$-competitive algorithm exists for matroids. Many works since have attempted to obtain algorithms for both general matroids and specific classes of matroids. The ultimate goal is to obtain an $e$-competitive algorithm, and the *strong matroid secretary conjecture* states that this is possible for general matroids. A key class of matroids is the *graphic matroid*, where a set of graph edges is independent if it contains no cycle. The rich combinatorial structure of graphs makes them a natural first step towards solving a problem for general matroids. Babaioff et al. (SODA'07, JACM'18) first studied the graphic matroid setting, achieving a $16$-competitive algorithm. Subsequent works have improved the competitive ratio, most recently to 4 by Soto, Turkieltaub, and Verdugo (SODA'18). We break this $4$-competitive barrier, presenting a new algorithm with a competitive ratio of $3.95$. For simple graphs, we further improve this to $3.77$. Intuitively, solving the problem for simple graphs is easier since they lack length-two cycles. A natural question is whether a ratio arbitrarily close to $e$ can be achieved by assuming sufficiently large girth. We answer this affirmatively, showing a competitive ratio arbitrarily close to $e$ even for constant girth values, supporting the strong matroid secretary conjecture. We also prove this bound is tight: for any constant $g$, no algorithm can achieve a ratio better than $e$ even when the graph has girth at least $g$.

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arXiv2024

Dynamic Metric Embedding into $\ell_p$ Space

We give the first non-trivial decremental dynamic embedding of a weighted, undirected graph $G$ into $\ell_p$ space. Given a weighted graph $G$ undergoing a sequence of edge weight increases, the goal of this problem is to maintain a (randomized) mapping $ϕ: (G,d) \to (X,\ell_p)$ from the set of vertices of the graph to the $\ell_p$ space such that for every pair of vertices $u$ and $v$, the expected distance between $ϕ(u)$ and $ϕ(v)$ in the $\ell_p$ metric is within a small multiplicative factor, referred to as the \emph{distortion}, of their distance in $G$. Our main result is a dynamic algorithm with expected distortion $O(\log^3 n)$ and total update time $O\left((m^{1+o(1)} \log^2 W + Q \log n)\log(nW) \right)$, where $W$ is the maximum weight of the edges, $Q$ is the total number of updates and $n, m$ denote the number of vertices and edges in $G$ respectively. This is the first result of its kind, extending the seminal result of Bourgain to the growing field of dynamic algorithms. Moreover, we demonstrate that in the fully dynamic regime, where we tolerate edge insertions as well as deletions, no algorithm can explicitly maintain an embedding into $\ell_p$ space that has a low distortion with high probability.

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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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arXiv2024

Nearly-Optimal Consensus Tolerating Adaptive Omissions: Why is a Lot of Randomness Needed?

We study the problem of reaching agreement in a synchronous distributed system by $n$ autonomous parties, when the communication links from/to faulty parties can omit messages. The faulty parties are selected and controlled by an adaptive, full-information, computationally unbounded adversary. We design a randomized algorithm that works in $O(\sqrt{n}\log^2 n)$ rounds and sends $O(n^2\log^3 n)$ communication bits, where the number of faulty parties is $Θ(n)$. Our result is simultaneously tight for both these measures within polylogarithmic factors: due to the $Ω(n^2)$ lower bound on communication by Abraham et al. (PODC'19) and $Ω(\sqrt{n/\log n})$ lower bound on the number of rounds by Bar-Joseph and Ben-Or (PODC'98). We also quantify how much randomness is necessary and sufficient to reduce time complexity to a certain value, while keeping the communication complexity (nearly) optimal. We prove that no MC algorithm can work in less than $Ω(\frac{n^2}{\max\{R,n\}\log n})$ rounds if it uses less than $O(R)$ calls to a random source, assuming a constant fraction of faulty parties. This can be contrasted with a long line of work on consensus against an {\em adversary limited to polynomial computation time}, thus unable to break cryptographic primitives, culminating in a work by Ghinea et al. (EUROCRYPT'22), where an optimal $O(r)$-round solution with probability $1-(cr)^{-r}$ is given. Our lower bound strictly separates these two regimes, by excluding such results if the adversary is computationally unbounded. On the upper bound side, we show that for $R\in\tilde{O}(n^{3/2})$ there exists an algorithm solving consensus in $\tilde{O}(\frac{n^2}{R})$ rounds with high probability, where tilde notation hides a polylogarithmic factor. The communication complexity of the algorithm does not depend on the amount of randomness $R$ and stays optimal within polylogarithmic factor.

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arXiv2024

Online Sampling and Decision Making with Low Entropy

Consider the problem: we are given $n$ boxes, labeled $\{1,2,\ldots, n\}$ by an adversary, each containing a single number chosen from an unknown distribution; these $n$ distributions are not necessarily identical. We are also given an integer $k \leq n$. We have to choose an order in which we will sequentially open these boxes, and each time we open the next box in this order, we learn the number in the box. Once we reject a number in a box, the box cannot be recalled. Our goal is to accept $k$ of these numbers, without necessarily opening all boxes, such that the accepted numbers are the $k$ largest numbers in the boxes (thus their sum is maximized). A natural approach to solve such problems is to use randomness to sample randomly ordered elements, however, as indicated in several sources, e.g., Turan et al. NIST'15, Bierhorst et al. Nature'18, pure randomness is hard to get in reality. We present an algorithm for this problem, which is provably and simultaneously near-optimal with respect to the achieved competitive ratio and the used amount of randomness. In particular, we construct a distribution on the orders with entropy $Θ(\log\log n)$ such that a deterministic multiple-threshold algorithm gives a competitive ratio $1-O(\sqrt{\log k/k})$, for $k < \log n/\log \log n$. Our competitive ratio is simultaneously optimal and uses optimal entropy $Θ(\log\log n)$, improving in three ways the previous best known algorithm, whose competitive ratio is $1 - O(1/k^{1/3}) - o(1)$.

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arXiv2024

Stable Blockchain Sharding under Adversarial Transaction Generation

Sharding is used to improve the scalability and performance of blockchain systems. We investigate the stability of blockchain sharding, where transactions are continuously generated by an adversarial model. The system consists of $n$ processing nodes that are divided into $s$ shards. Following the paradigm of classical adversarial queuing theory, transactions are continuously received at injection rate $ρ\leq 1$ and burstiness $b > 0$. We give an absolute upper bound $\max\{ \frac{2}{k+1}, \frac{2}{ \left\lfloor\sqrt{2s}\right\rfloor}\}$ on the maximum injection rate for which any scheduler could guarantee bounded queues and latency of transactions, where $k$ is the number of shards that each transaction accesses. We next give a basic distributed scheduling algorithm for uniform systems where shards are equally close to each other. To guarantee stability, the injection rate is limited to $ρ\leq \max\{ \frac{1}{18k}, \frac{1}{\lceil 18 \sqrt{s} \rceil} \}$. We then provide a fully distributed scheduling algorithm for non-uniform systems where shards are arbitrarily far from each other. By using a hierarchical clustering of the shards, stability is guaranteed with injection rate $ρ\leq \frac{1}{c_1d \log^2 s} \cdot \max\{ \frac{1}{k}, \frac{1}{\sqrt{s}} \}$, where $d$ is the worst distance of any transaction to the shards it will access, and $c_1$ is some positive constant. We also conduct simulations to evaluate the algorithms and measure the average queue sizes and latency throughout the system. To our knowledge, this is the first adversarial stability analysis of sharded blockchain systems.

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arXiv2024

Byzantine-Resilient Population Protocols

Population protocols model information spreading and computation in network systems where pairwise node exchanges are determined by an external random scheduler and nodes have small memory. Most of the population protocols in the literature assume that the participating $n$ nodes are honest. Such an assumption may not be, however, accurate for large-scale systems of small devices. Hence, in this work, we study population protocols in a setting where up to $f$ nodes can be Byzantine. We examine the majority (binary) consensus problem against different levels of adversary strengths, ranging from the Full Byzantine adversary that has complete knowledge of all the node states to the Weak Content-Oblivious Byzantine adversary that has only knowledge about which exchanges take place. We also take into account Dynamic vs Static node corruption by the adversary. We give lower bounds that require any algorithm solving the majority consensus to have initial difference $d = Ω(f + 1)$ for the tally between the two proposed values, which holds for both the Full Static and Weak Dynamic adversaries. We then present an algorithm that solves the majority consensus problem and tolerates $f \leq n / c$ Byzantine nodes, for some constant $c>0$, with $d = Ω(f + \sqrt{n \log n})$ and $O(\log^3 n)$ parallel time steps, using $O(\log^3 n)$ states per node. We also give an alternative algorithm, with the same asymptotic performance, for $d = Ω(\min\{f \log^2 n + 1,n\})$. Finally, we combine both algorithms into one using a new robust distributed common coin. The only other known previous work on Byzantine-resilient population protocols tolerates up to $f = o(\sqrt n)$ faulty nodes and was analyzed against a Static adversary; hence, our protocols significantly improve fault-tolerance by an $ω(\sqrt n)$ factor and all of them work correctly against a stronger Dynamic adversary.

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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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arXiv2023

Fault-Tolerant Consensus in Quantum Networks

Fault-tolerant consensus is about reaching agreement on some of the input values in a limited time by non-faulty autonomous processes, despite of failures of processes or communication medium. This problem is particularly challenging and costly against an adaptive adversary with full information. Bar-Joseph and Ben-Or (PODC'98) were the first who proved an absolute lower bound $Ω(\sqrt{n/\log n})$ on expected time complexity of consensus in any classic (i.e., randomized or deterministic) message-passing network with $n$ processes succeeding with probability $1$ against such a strong adaptive adversary crashing processes. Seminal work of Ben-Or and Hassidim (STOC'05) broke the $Ω(\sqrt{n/\log n})$ barrier for consensus in classic (deterministic and randomized) networks by employing quantum computing. They showed an (expected) constant-time quantum algorithm for a linear number of crashes $t<n/3$. In this paper, we improve upon that seminal work by reducing the number of quantum and communication bits to an arbitrarily small polynomial, and even more, to a polylogarithmic number -- though, the latter in the cost of a slightly larger polylogarithmic time (still exponentially smaller than the time lower bound $Ω(\sqrt{n/\log n})$ for classic computation).

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arXiv2022

Deterministic non-adaptive contention resolution on a shared channel

In a multiple access channel, autonomous stations are able to transmit and listen to a shared device. A fundamental problem, called \textit{contention resolution}, is to allow any station to successfully deliver its message by resolving the conflicts that arise when several stations transmit simultaneously. Despite a long history on such a problem, most of the results deal with the static setting when all stations start simultaneously, while many fundamental questions remain open in the realistic scenario when stations can join the channel at arbitrary times. In this paper, we explore the impact that three major channel features (asynchrony among stations, knowledge of the number of contenders and possibility of switching off stations after a successful transmission) can have on the time complexity of non-adaptive deterministic algorithms. We establish upper and lower bounds allowing to understand which parameters permit time-efficient contention resolution and which do not.

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arXiv2022

Time and Energy Efficient Contention Resolution in Asynchronous Shared Channels

A number of stations, independently activated over time, is able to communicate by transmitting and listening to a shared channel in discrete time slots, and a message is successfully delivered to all stations if and only if its source station is the only transmitter at a time. Despite a vast amount of work in the last decades, many fundamental questions remain open in the realistic situation where stations do not start synchronously but are awaken in arbitrary times. In this work we present a broad picture of results for the fundamental problem of Contention resolution, in which each of the contending stations needs to broadcast successfully its message. We show that adaptive algorithms or algorithms with the knowledge of the contention size $k$ achieve a linear $O(k)$ message latency even if the channel feedback is restricted to simple acknowledgements in case of successful transmissions and in the absence of synchronization. This asymptotically optimal performance cannot be extended to other settings: we prove that there is no non-adaptive algorithm without the knowledge of contention size $k$ admitting latency $o(k\log k/(\log\log k)^2)$. This means, in particular, that coding (even random) with acknowledgements is not very efficient on a shared channel without synchronization or an estimate of the contention size. We also present a non-adaptive algorithm with no knowledge of contention size that almost matches the lower bound on latency. Finally, despite the absence of a collision detection mechanism, we show that our algorithms are also efficient in terms of energy, understood as the total number of transmissions performed by the stations during the execution.

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