# Bernhard Haeupler

## Contact Details

NameBernhard Haeupler |
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## Pubs By Year |
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## Pub CategoriesComputer Science - Data Structures and Algorithms (34) Computer Science - Distributed; Parallel; and Cluster Computing (21) Mathematics - Information Theory (10) Computer Science - Information Theory (10) Mathematics - Combinatorics (5) Computer Science - Discrete Mathematics (5) Computer Science - Networking and Internet Architecture (3) Quantitative Biology - Quantitative Methods (1) Computer Science - Computational Complexity (1) Physics - Physics and Society (1) Quantitative Biology - Molecular Networks (1) |

## Publications Authored By Bernhard Haeupler

We consider the problem of making distributed computations robust to noise, in particular to worst-case (adversarial) corruptions of messages. We give a general distributed interactive coding scheme which simulates any asynchronous distributed protocol while tolerating an optimal corruption of a $\Theta(1/n)$ fraction of all messages while incurring a moderate blowup of $O(n\log^2 n)$ in the communication complexity. Our result is the first fully distributed interactive coding scheme in which the topology of the communication network is not known in advance. Read More

Distributed optimization algorithms are frequently faced with solving sub-problems on disjoint connected parts of a network. Unfortunately, the diameter of these parts can be significantly larger than the diameter of the underlying network, leading to slow running times. Recent work by [Ghaffari and Hauepler; SODA'16] showed that this phenomenon can be seen as the broad underlying reason for the pervasive $\Omega(\sqrt{n} + D)$ lower bounds that apply to most optimization problems in the CONGEST model. Read More

We study the communication rate of coding schemes for interactive communication that transform any two-party interactive protocol into a protocol that is robust to noise. Recently, Haeupler (FOCS '14) showed that if an $\epsilon > 0$ fraction of transmissions are corrupted, adversarially or randomly, then it is possible to achieve a communication rate of $1 - \widetilde{O}(\sqrt{\epsilon})$. Furthermore, Haeupler conjectured that this rate is optimal for general input protocols. Read More

The Lovasz Local Lemma (LLL) is a cornerstone principle in the probabilistic method of combinatorics, and a seminal algorithm of Moser & Tardos (2010) provided an efficient randomized algorithm to implement it. This algorithm could be parallelized to give an algorithm that uses polynomially many processors and $O(\log^3 n)$ time, stemming from $O(\log n)$ adaptive computations of a maximal independent set (MIS). Chung et. Read More

We provide tight upper and lower bounds on the noise resilience of interactive communication over noisy channels with feedback. In this setting, we show that the maximal fraction of noise that any robust protocol can resist is 1/3. Additionally, we provide a simple and efficient robust protocol that succeeds as long as the fraction of noise is at most 1/3 - \epsilon. Read More

Document sketching using Jaccard similarity has been a workable effective technique in reducing near-duplicates in Web page and image search results, and has also proven useful in file system synchronization, compression and learning applications. Min-wise sampling can be used to derive an unbiased estimator for Jaccard similarity and taking a few hundred independent consistent samples leads to compact sketches which provide good estimates of pairwise-similarity. Subsequent works extended this technique to weighted sets and show how to produce samples with only a constant number of hash evaluations for any element, independent of its weight. Read More

We provide the first capacity approaching coding schemes that robustly simulate any interactive protocol over an adversarial channel that corrupts any $\epsilon$ fraction of the transmitted symbols. Our coding schemes achieve a communication rate of $1 - O(\sqrt{\epsilon \log \log 1/\epsilon})$ over any adversarial channel. This can be improved to $1 - O(\sqrt{\epsilon})$ for random, oblivious, and computationally bounded channels, or if parties have shared randomness unknown to the channel. Read More

We introduce collision free layerings as a powerful way to structure radio networks. These layerings can replace hard-to-compute BFS-trees in many contexts while having an efficient randomized distributed construction. We demonstrate their versatility by using them to provide near optimal distributed algorithms for several multi-message communication primitives. Read More

We present a randomized distributed algorithm that in radio networks with collision detection broadcasts a single message in $O(D + \log^6 n)$ rounds, with high probability. This time complexity is most interesting because of its optimal additive dependence on the network diameter $D$. It improves over the currently best known $O(D\log\frac{n}{D}\,+\,\log^2 n)$ algorithms, due to Czumaj and Rytter [FOCS 2003], and Kowalski and Pelc [PODC 2003]. Read More

Gossip algorithms spread information by having nodes repeatedly forward information to a few random contacts. By their very nature, gossip algorithms tend to be distributed and fault tolerant. If done right, they can also be fast and message-efficient. Read More

We study coding schemes for error correction in interactive communications. Such interactive coding schemes simulate any $n$-round interactive protocol using $N$ rounds over an adversarial channel that corrupts up to $\rho N$ transmissions. Important performance measures for a coding scheme are its maximum tolerable error rate $\rho$, communication complexity $N$, and computational complexity. Read More

We consider the task of interactive communication in the presence of adversarial errors and present tight bounds on the tolerable error-rates in a number of different settings. Most significantly, we explore adaptive interactive communication where the communicating parties decide who should speak next based on the history of the interaction. Braverman and Rao [STOC'11] show that non-adaptively one can code for any constant error rate below 1/4 but not more. Read More

Distributed computing models typically assume reliable communication between processors. While such assumptions often hold for engineered networks, e.g. Read More

We consider the well-studied radio network model: a synchronous model with a graph G=(V,E) with |V|=n where in each round, each node either transmits a packet, with length B=Omega(log n) bits, or listens. Each node receives a packet iff it is listening and exactly one of its neighbors is transmitting. We consider the problem of k-message broadcast, where k messages, each with Theta(B) bits, are placed in an arbitrary nodes of the graph and the goal is to deliver all messages to all the nodes. Read More

We present distributed randomized leader election protocols for multi-hop radio networks that elect a leader in almost the same time $T_{BC}$ required for broadcasting a message. For the setting without collision detection, our algorithm runs with high probability in $O(D \log \frac{n}{D} + \log^3 n) \min\{\log\log n,\log \frac{n}{D}\}$ rounds on any $n$-node network with diameter $D$. Since $T_{BC} = \Theta(D \log \frac{n}{D} + \log^2 n)$ is a lower bound, our upper bound is optimal up to a factor of at most $\log \log n$ and the extra $\log n$ factor on the additive term. Read More

We study gossip algorithms for the rumor spreading problem which asks each node to deliver a rumor to all nodes in an unknown network. Gossip algorithms allow nodes only to call one neighbor per round and have recently attracted attention as message efficient, simple and robust solutions to the rumor spreading problem. Recently, non-uniform random gossip schemes were devised to allow efficient rumor spreading in networks with bottlenecks. Read More

Efficient communication in wireless networks is typically challenged by the possibility of interference among several transmitting nodes. Much important research has been invested in decreasing the number of collisions in order to obtain faster algorithms for communication in such networks. This paper proposes a novel approach for wireless communication, which embraces collisions rather than avoiding them, over an additive channel. Read More

We study lower bounds on information dissemination in adversarial dynamic networks. Initially, k pieces of information (henceforth called tokens) are distributed among n nodes. The tokens need to be broadcast to all nodes through a synchronous network in which the topology can change arbitrarily from round to round provided that some connectivity requirements are satisfied. Read More

Gossip and in particular network coded algebraic gossip have recently attracted attention as a fast, bandwidth-efficient, reliable and distributed way to broadcast or multicast multiple messages. While the algorithms are simple, involved queuing approaches are used to study their performance. The most recent result in this direction shows that uniform algebraic gossip disseminates k messages in O({\Delta}(D + k + log n)) rounds where D is the diameter, n the size of the network and {\Delta} the maximum degree. Read More

We consider the problem of computing a maximal independent set (MIS) in an extremely harsh broadcast model that relies only on carrier sensing. The model consists of an anonymous broadcast network in which nodes have no knowledge about the topology of the network or even an upper bound on its size. Furthermore, it is assumed that an adversary chooses at which time slot each node wakes up. Read More

The local broadcast problem assumes that processes in a wireless network are provided messages, one by one, that must be delivered to their neighbors. In this paper, we prove tight bounds for this problem in two well-studied wireless network models: the classical model, in which links are reliable and collisions consistent, and the more recent dual graph model, which introduces unreliable edges. Our results prove that the Decay strategy, commonly used for local broadcast in the classical setting, is optimal. Read More

The broadcast throughput in a network is defined as the average number of messages that can be transmitted per unit time from a given source to all other nodes when time goes to infinity. Classical broadcast algorithms treat messages as atomic tokens and route them from the source to the receivers by making intermediate nodes store and forward messages. The more recent network coding approach, in contrast, prompts intermediate nodes to mix and code together messages. Read More

We study randomized gossip-based processes in dynamic networks that are motivated by discovery processes in large-scale distributed networks like peer-to-peer or social networks. A well-studied problem in peer-to-peer networks is the resource discovery problem. There, the goal for nodes (hosts with IP addresses) is to discover the IP addresses of all other hosts. Read More

We design and analyze gossip algorithms for networks with correlated data. In these networks, either the data to be distributed, the data already available at the nodes, or both, are correlated. This model is applicable for a variety of modern networks, such as sensor, peer-to-peer and content distribution networks. Read More

Given a network infrastructure (e.g., data-center or on-chip-network) and a distribution on the source-destination requests, the expected path (route) length is an important measure for the performance, efficiency and power consumption of the network. Read More

We consider the problem of finding a maximal independent set (MIS) in the discrete beeping model. At each time, a node in the network can either beep (i.e. Read More

We present two on-line algorithms for maintaining a topological order of a directed $n$-vertex acyclic graph as arcs are added, and detecting a cycle when one is created. Our first algorithm handles $m$ arc additions in $O(m^{3/2})$ time. For sparse graphs ($m/n = O(1)$), this bound improves the best previous bound by a logarithmic factor, and is tight to within a constant factor among algorithms satisfying a natural {\em locality} property. Read More

In this paper, we study the question of how efficiently a collection of interconnected nodes can perform a global computation in the widely studied GOSSIP model of communication. In this model, nodes do not know the global topology of the network, and they may only initiate contact with a single neighbor in each round. This model contrasts with the much less restrictive LOCAL model, where a node may simultaneously communicate with all of its neighbors in a single round. Read More

We use network coding to improve the speed of distributed computation in the dynamic network model of Kuhn, Lynch and Oshman [STOC '10]. In this model an adversary adaptively chooses a new network topology in every round, making even basic distributed computations challenging. Kuhn et al. Read More

We resolve the question of optimality for a well-studied packetized implementation of random linear network coding, called PNC. In PNC, in contrast to the classical memoryless setting, nodes store received information in memory to later produce coded packets that reflect this information. PNC is known to achieve order optimal stopping times for the many-to-all multicast problem in many settings. Read More

Random Linear Network Coding (RLNC) has emerged as a powerful tool for robust high-throughput multicast. Projection analysis - a recently introduced technique - shows that the distributed packetized RLNC protocol achieves (order) optimal and perfectly pipelined information dissemination in many settings. In the original approach to RNLC intermediate nodes code together all available information. Read More

We give a new technique to analyze the stopping time of gossip protocols that are based on random linear network coding (RLNC). Our analysis drastically simplifies, extends and strengthens previous results. We analyze RLNC gossip in a general framework for network and communication models that encompasses and unifies the models used previously in this context. Read More

Two planar graphs G1 and G2 sharing some vertices and edges are `simultaneously planar' if they have planar drawings such that a shared vertex [edge] is represented by the same point [curve] in both drawings. It is an open problem whether simultaneous planarity can be tested efficiently. We give a linear-time algorithm to test simultaneous planarity when the two graphs share a 2-connected subgraph. Read More

We determine the thresholds for the number of variables, number of clauses, number of clause intersection pairs and the maximum clause degree of a k-CNF formula that guarantees satisfiability under the assumption that every two clauses share at most $\alpha$ variables. More formally, we call these formulas $\alpha$-intersecting and define, for example, a threshold $\mu_i(k,\alpha)$ for the number of clause intersection pairs $i$, such that every $\alpha$-intersecting k-CNF formula in which at most $\mu_i(k,\alpha)$ pairs of clauses share a variable is satisfiable and there exists an unsatisfiable $\alpha$-intersecting k-CNF formula with $\mu_m(k,\alpha)$ such intersections. We provide a lower bound for these thresholds based on the Lovasz Local Lemma and a nearly matching upper bound by constructing an unsatisfiable k-CNF to show that $\mu_i(k,\alpha) = \tilde{\Theta}(2^{k(2+1/\alpha)})$. Read More

The van der Waerden number W(k,2) is the smallest integer n such that every 2-coloring of 1 to n has a monochromatic arithmetic progression of length k. The existence of such an n for any k is due to van der Waerden but known upper bounds on W(k,2) are enormous. Much effort was put into developing lower bounds on W(k,2). Read More

The Lov\'{a}sz Local Lemma (LLL) states that the probability that none of a set of "bad" events happens is nonzero if the probability of each event is small compared to the number of bad events it depends on. A series of results have provided algorithms to efficiently construct structures whose existence is (non-constructively) guaranteed by the full asymmetric LLL, culminating in the recent breakthrough of Moser & Tardos. We show that the output distribution of the Moser-Tardos procedure has sufficient randomness, leading to two classes of algorithmic applications. Read More

The Lovasz Local Lemma (LLL) is a powerful result in probability theory that states that the probability that none of a set of bad events happens is nonzero if the probability of each event is small compared to the number of events that depend on it. It is often used in combination with the probabilistic method for non-constructive existence proofs. A prominent application is to k-CNF formulas, where LLL implies that, if every clause in the formula shares variables with at most d <= 2^k/e other clauses then such a formula has a satisfying assignment. Read More

One of the characteristic features of genetic networks is their inherent robustness, that is, their ability to retain functionality in spite of the introduction of random errors. In this paper, we seek to better understand how robustness is achieved and what functionalities can be maintained robustly. Our goal is to formalize some of the language used in biological discussions in a reasonable mathematical framework, where questions can be answered in a rigorous fashion. Read More

The heap is a basic data structure used in a wide variety of applications, including shortest path and minimum spanning tree algorithms. In this paper we explore the design space of comparison-based, amortized-efficient heap implementations. From a consideration of dynamic single-elimination tournaments, we obtain the binomial queue, a classical heap implementation, in a simple and natural way. Read More

We present an on-line algorithm for maintaining a topological order of a directed acyclic graph as arcs are added, and detecting a cycle when one is created. Our algorithm takes O(m^{1/2}) amortized time per arc, where m is the total number of arcs. For sparse graphs, this bound improves the best previous bound by a logarithmic factor and is tight to within a constant factor for a natural class of algorithms that includes all the existing ones. Read More

We consider the problem of finding a feasible single-commodity flow in a strongly connected network with fixed supplies and demands, provided that the sum of supplies equals the sum of demands and the minimum arc capacity is at least this sum. A fast algorithm for this problem improves the worst-case time bound of the Goldberg-Rao maximum flow method by a constant factor. Erlebach and Hagerup gave an linear-time feasible flow algorithm. Read More