Deterministic Symmetry Breaking in Ring Networks

We study a distributed coordination mechanism for uniform agents located on a circle. The agents perform their actions in synchronised rounds. At the beginning of each round an agent chooses the direction of its movement from clockwise, anticlockwise, or idle, and moves at unit speed during this round. Agents are not allowed to overpass, i.e., when an agent collides with another it instantly starts moving with the same speed in the opposite direction (without exchanging any information with the other agent). However, at the end of each round each agent has access to limited information regarding its trajectory of movement during this round. We assume that $n$ mobile agents are initially located on a circle unit circumference at arbitrary but distinct positions unknown to other agents. The agents are equipped with unique identifiers from a fixed range. The {\em location discovery} task to be performed by each agent is to determine the initial position of every other agent. Our main result states that, if the only available information about movement in a round is limited to %information about distance between the initial and the final position, then there is a superlinear lower bound on time needed to solve the location discovery problem. Interestingly, this result corresponds to a combinatorial symmetry breaking problem, which might be of independent interest. If, on the other hand, an agent has access to the distance to its first collision with another agent in a round, we design an asymptotically efficient and close to optimal solution for the location discovery problem.Comment: Conference version accepted to ICDCS 201

On the Impact of Geometry on Ad Hoc Communication in Wireless Networks

In this work we address the question how important is the knowledge of geometric location and network density to the efficiency of (distributed) wireless communication in ad hoc networks. We study fundamental communication task of broadcast and develop well-scalable, randomized algorithms that do not rely on GPS information, and which efficiency formulas do not depend on how dense the geometric network is. We consider two settings: with and without spontaneous wake-up of nodes. In the former setting, in which all nodes start the protocol at the same time, our algorithm accomplishes broadcast in $O(D\log n + \log^2 n)$ rounds under the SINR model, with high probability (whp), where $D$ is the diameter of the communication graph and $n$ is the number of stations. In the latter setting, in which only the source node containing the original message is active in the beginning, we develop a slightly slower algorithm working in $O(D\log^2 n)$ rounds whp. Both algorithms are based on a novel distributed coloring method, which is of independent interest and potential applicability to other communication tasks under the SINR wireless model

Proofs of Knowledge with Several Challenge Values

In this paper we consider the problem of increasing the number of possible challenge values from 2 to $s$ in various zero-knowledge cut and choose protocols. First we discuss doing this for graph isomorphism protocol. Then we show how increasing this number improves efficiency of protocols for double discrete logarithm and $e$-th root of discrete logarithm which are potentially very useful tools for constructing complex cryptographic protocols. The practical improvement given by our paper is 2-4 times in terms of both time complexity and transcript size

Brief Announcement: New Clocks, Fast Line Formation and Self-Replication Population Protocols

In this paper we consider a known variant of the standard population protocol model in which agents can be connected by edges, referred to as the network constructor model. During an interaction between two agents the relevant connecting edge can be formed, maintained or eliminated by the transition function. The state space of agents is fixed (constant size) and the size n of the population is not known, i.e., not hard-coded in the transition function. Since pairs of agents are chosen uniformly at random the status of each edge is updated every Θ(n2) interactions in expectation which coincides with Θ(n) parallel time. This phenomenon provides a natural lower bound on the time complexity for any non-trivial network construction designed for this variant. This is in contrast with the standard population protocol model in which efficient protocols operate in O(poly log n) parallel time. The main focus in this paper is on efficient manipulation of linear structures including formation, self-replication and distribution (including pipelining) of complex information in the adopted model. We propose and analyse a novel edge based phase clock counting parallel time Θ(n log n) in the network constructor model, showing also that its leader based counterpart provides the same time guaranties in the standard population protocol model. Note that all currently known phase clocks can count parallel time not exceeding O(poly log n). The new clock enables a nearly optimal O(n log n) parallel time spanning line construction (a key component of universal network construction), which improves dramatically on the best currently known O(n2) parallel time protocol, solving the main open problem in the considered model [9]. We propose a new probabilistic bubble-sort algorithm in which random comparisons and transfers are allowed only between the adjacent positions in the sequence. Utilising a novel potential function reasoning we show that rather surprisingly this probabilistic sorting (via conditional pipelining) procedure requires O(n2) comparisons in expectation and whp, and is on par with its deterministic counterpart. We propose the first population protocol allowing self-replication of a strand of an arbitrary length k (carrying a k-bit message of size independent of the state space) in parallel time O(n(k + log n)). The pipelining mechanism and the time complexity analysis of the strand self-replication protocol mimic those used in the probabilistic bubble-sort. The new protocol permits also simultaneous self-replication, where l copies of the strand can be created in time O(n(k + log n) log l). Finally, we discuss application of the strand self-replication protocol to pattern matching. Our protocols are always correct and provide time guaranties with high probability defined as 1 - n-η, for a constant η > 0

Fast Space Optimal Leader Election in Population Protocols

The model of population protocols refers to the growing in popularity theoretical framework suitable for studying pairwise interactions within a large collection of simple indistinguishable entities, frequently called agents. In this paper the emphasis is on the space complexity in fast leader election via population protocols governed by the random scheduler, which uniformly at random selects pairwise interactions within the population of n agents. The main result of this paper is a new fast and space optimal leader election protocol. The new protocol utilises O(log^2 n) parallel time (which is equivalent to O(n log^2 n) sequential pairwise interactions), and each agent operates on O(log log n) states. This double logarithmic space usage matches asymptotically the lower bound 1/2 log log n on the minimal number of states required by agents in any leader election algorithm with the running time o(n/polylog n). Our solution takes an advantage of the concept of phase clocks, a fundamental synchronisation and coordination tool in distributed computing. We propose a new fast and robust population protocol for initialisation of phase clocks to be run simultaneously in multiple modes and intertwined with the leader election process. We also provide the reader with the relevant formal argumentation indicating that our solution is always correct, and fast with high probability.Comment: 21 pages, 2 figures, published in SODA 2018 proceeding

Increasing brightness in multiphoton microscopy with low-repetition-rate, wavelength-tunable femtosecond fiber laser

Many experiments in biological and medical sciences currently use multiphoton microscopy as a core imaging technique. To date, solid-state lasers are most commonly used as excitation beam sources. However, the most demanding applications require precisely adjusted excitation laser parameters to enhance image quality. Still, the lag in developing easy-to-use laser sources with tunable output parameters makes it challenging. Here, we show that manipulating the temporal and spectral properties of the excitation beam can significantly improve the quality of images. We have developed a wavelength-tunable femtosecond fiber laser that operates within the 760 - 800 nm spectral range and produces ultrashort pulses (below 70 fs) with a clean temporal profile and high pulse energy (1 nJ). The repetition rate could be easily adjusted using an integrated pulse picker unit within the 1 - 25 MHz range and without strongly influencing other parameters of the generated pulses. We integrated the laser with a two-photon excited fluorescence (TPEF) scanning laser microscope and investigated the effect of tunable wavelength and reducing the pulse repetition rate on the quality of obtained images. Using our laser, we substantially improved the images brightness and penetration depth of native fluorescence and stained samples compared with a standard fiber laser. Our results will contribute to developing imaging techniques using lower average laser power and broader use of tailored fiber-based sources

Unlinkable Divisible Digital Cash without Trusted Third Party

We present an efficient divisible digital cash scheme which is unlinkable and does not require Trusted Third Party. The size of the coin is proportional to the size of the primes we use, i.e., hundreds of bytes. The computational and communication complexity of the protocol is proportional to a polynomial of the size of the primes and polylogarithm of the maximum number of pieces to which a coin can be subdivided