Agent-based crawlers are commonly used in network maintenance and information gathering. In order not to disturb the main functionality of the system, whether acting at nodes or being in transit, they need to operate online, perform a single operation fast and use small memory. They should also be preferably deterministic, as crawling agents have limited capabilities of generating a large number of truly random bits. We consider a system in which an agent receives an update, typically an insertion or deletion, of some information upon visiting a node. On request, the agent needs to output hot information, i.e., with the net occurrence above certain frequency threshold. A desired time and memory complexity of such agent should be poly-logarithmic in the number of visited nodes and inversely proportional to the frequency threshold. Ours is the first such agent with rigorous analysis and a complementary almost-matching lower bound.

Group Testing (GT) is about learning a (hidden) subset $K$, of size $k$, of some large domain $N$, of size $n \gg k$, using a sequence of queries. A result of a query provides some information about the intersection of the query with the unknown set $K$. The goal is to design efficient (polynomial time) and scalable (polylogarithmic number of queries per element in $K$) algorithms for constructing queries that allow to decode every hidden set $K$ based on the results of the queries. A vast majority of the previous work focused on randomized algorithms minimizing the number of queries; however, in case of large domains N, randomization may result in asignificant deviation from the expected precision of learning the set $K$. Others assumed unlimited computational power (existential results) or adaptiveness of queries (next query could be constructed taking into account the results of the previous queries) – the former approach is less practical due to non-efficiency, and the latter has several drawbacks including non-parallelization. To avoid all the abovementioned drawbacks, for Quantitative Group Testing (QGT) where query result is the size of its intersection with the hidden set, we present the first efficient and scalable non-adaptive deterministic algorithms for constructing queries and decoding a hidden set K from the results of the queries – these solutions do not use any randomization, adaptiveness or unlimited computational power.

We study the problem of distributed task allocation by workers in an ant colony in a setting of limited capabilities and noisy environment feedback. We assume that each task has a demand that should be satisfied but not exceeded, i.e., there is an optimal number of ants that should be working on this task at a given time. The goal is to assign a near-optimal number of workers to each task in a distributed manner without explicit access to the value of the demand nor to the number of ants working on the task.

In this paper, we study local and global broadcast in the dual graph model, which describes communication in a radio network with both reliable and unreliable links. Existing work proved that efficient solutions to these problems are impossible in the dual graph model under standard assumptions. In real networks, however, simple back-off strategies tend to perform well for solving these basic communication tasks. We address this apparent paradox by introducing a new set of constraints to the dual graph model that better generalize the slow/fast fading behavior common in real networks. We prove that in the context of these new constraints, simple back-off strategies now provide efficient solutions to local and global broadcast in the dual graph model. We also precisely characterize how this efficiency degrades as the new constraints are reduced down to non-existent, and prove new lower bounds that establish this degradation as near optimal for a large class of natural algorithms. We conclude with an analysis of a more general model where we propose an enhanced back-off algorithm. These results provide theoretical foundations for the practical observation that simple back-off algorithms tend to work well even amid the complicated link dynamics of real radio networks.

We study a process of \emph{averaging} in a distributed system with \emph{noisy communication}. Each of the agents in the system starts with some value and the goal of each agent is to compute the average of all the initial values. In each round, one pair of agents is drawn uniformly at random from the whole population, communicates with each other and each of these two agents updates their local value based on their own value and the received message. The communication is noisy and whenever an agent sends any value $v$, the receiving agent receives $v+N$, where $N$ is a zero-mean Gaussian random variable. The two quality measures of interest are (i) the total sum of squares $TSS(t)$, which measures the sum of square distances from the average load to the \emph{initial average} and (ii) $\barϕ(t)$, measures the sum of square distances from the average load to the \emph{running average} (average at time $t$). It is known that the simple averaging protocol---in which an agent sends its current value and sets its new value to the average of the received value and its current value---converges eventually to a state where $\barϕ(t)$ is small. It has been observed that $TSS(t)$, due to the noise, eventually diverges and previous research---mostly in control theory---has focused on showing eventual convergence w.r.t. the running average. We obtain the first probabilistic bounds on the convergence time of $\barϕ(t)$ and precise bounds on the drift of $TSS(t)$ that show that albeit $TSS(t)$ eventually diverges, for a wide and interesting range of parameters, $TSS(t)$ stays small for a number of rounds that is polynomial in the number of agents. Our results extend to the synchronous setting and settings where the agents are restricted to discrete values and perform rounding.

Two mobile robots are initially placed at the same point on an infinite line. Each robot may move on the line in either direction not exceeding its maximal speed. The robots need to find a stationary target placed at an unknown location on the line. The search is completed when both robots arrive at the target point. The target is discovered at the moment when either robot arrives at its position. The robot knowing the placement of the target may communicate it to the other robot. We look for the algorithm with the shortest possible search time (i.e. the worst-case time at which both robots meet at the target) measured as a function of the target distance from the origin (i.e. the time required to travel directly from the starting point to the target at unit velocity). We consider two standard models of communication between the robots, namely wireless communication and communication by meeting. In the case of communication by meeting, a robot learns about the target while sharing the same location with a robot possessing this knowledge. We propose here an optimal search strategy for two robots including the respective lower bound argument, for the full spectrum of their maximal speeds. This extends the main result of Chrobak et al. (in: Italiano, Margaria-Steffen, Pokorný, Quisquater, Wattenhofer (eds) Current trends in theory and practice of computer science, SOFSEM, 2015) referring to the exact complexity of the problem for the case when the speed of the slower robot is at least one third of the faster one. In the wireless communication model, a message sent by one robot is instantly received by the other robot, regardless of their current positions on the line. For this model, we design a strategy which is optimal whenever the faster robot is at most $$\sqrt{17}+4\approx 8.123$$ times faster than the slower one. We also prove that otherwise the wireless communication offers no advantage over communication by meeting.

In wireless networks, consisting of battery-powered devices, energy is a costly resource and most of it is spent on transmitting messages. Broadcast is a problem where a message needs to be transmitted from one node to all other nodes of the network. We study algorithms that can work under limited energy measured as the maximum number of transmissions among all the stations. The goal of the paper is to study tradeoffs between time and energy complexity of broadcast problem in unknown multi-hop radio networks with no collision detection.

In this paper, we study local broadcast in the dual graph model, which describes communication in a radio network with both reliable and unreliable links. Existing work proved that efficient solutions to these problems are impossible in the dual graph model under standard assumptions. In real networks, however, simple back-off strategies tend to perform well for solving these basic communication tasks. We address this apparent paradox by introducing a new set of constraints to the dual graph model that better generalize the slow/fast fading behavior common in real networks. We prove that in the context of these new constraints, simple back-off strategies now provide efficient solutions to local broadcast in the dual graph model. These results provide theoretical foundations for the practical observation that simple back-off algorithms tend to work well even amid the complicated link dynamics of real radio networks.

We derive several new results on multiple random walks on "low dimensional" graphs. First, inspired by an example of a weighted random walk on a path of three vertices given by Efremenko and Reingold, we prove the following dichotomy: as the path length n tends to infinity, we have a super-linear speed-up w.r.t. the cover time if and only if the number of walks k is equal to 2. An important ingredient of our proofs is the use of a continuous-time analogue of multiple random walks, which might be of independent interest. Finally, we also present the first tight bounds on the speed-up of the cover time for any d-dimensional grid with d >= 2 being an arbitrary constant, and reveal a sharp transition between linear and logarithmic speed-up.

The rotor-router mechanism was introduced as a deterministic alternative to the random walk in undirected graphs. In this model, an agent is initially placed at one of the nodes of the graph. Each node maintains a cyclic ordering of its outgoing arcs, and during successive visits of the agent, propagates it along arcs chosen according to this ordering in round-robin fashion. The behavior of the rotor-router is fully deterministic but its performance characteristics (cover time, return time) closely resemble the expected values of the corresponding parameters of the random walk. In this work we consider the setting in which multiple, indistinguishable agents are deployed in parallel in the nodes of the graph, and move around the graph in synchronous rounds, interacting with a single rotor-router system. We propose new techniques which allow us to perform a theoretical analysis of the multi-agent rotor-router model, and to compare it to the scenario of parallel independent random walks in a graph. Our main results concern the n-node ring, and suggest a strong similarity between the performance characteristics of this deterministic model and random walks. We show that on the ring the rotor-router with k agents admits a cover time of between $$\varTheta (n^2 / k^2)$$ in the best case and $$\varTheta (n^2 / \log k)$$ in the worst case, depending on the initial locations of the agents, and that both these bounds are tight. The corresponding expected value of the cover time for k random walks, depending on the initial locations of the walkers, is proven to belong to a similar range, namely between $$\varTheta (n^2 / (k^2/\log ^2 k))$$ and $$\varTheta (n^2 / \log k)$$ . Finally, we study the limit behavior of the rotor-router system. We show that, once the rotor-router system has stabilized, all the nodes of the ring are always visited by some agent every $$\varTheta (n / k)$$ steps, regardless of how the system was initialized. This asymptotic bound corresponds to the expected time between successive visits to a node in the case of k random walks. All our results hold up to a polynomially large number of agents ( $$1 \le k < n^{1/11}$$ ).

Abstract. A fence, represented by a unit interval is to be patrolled collectively by n robots. At any moment a robot may move in one of the two possible states: walking or patrolling. Each state is associated with a maximal moving speed which cannot be exceeded. A robot may have a unique pair of speeds, but its patrolling speed is always smaller than its walking speed. Each robot is allowed to patrol while moving only in one of the two directions (not necessarily the same for all robots). We want to schedule the perpetual movements of the robots so as to minimize the idleness, defined as the smallest time interval within which every point is always visited by some robot. First, we give a centralized algorithm constructing schedules with optimal idleness, and subsequently we show a nice application to a transportation problem concerning Scheduling with Regular Delivery. Our main contribution is the study of distributed, dynamical schedules for patrolling robots with only primitive capabilities. Surprisingly we are able to design a dynamic schedule for very weak collections of two robots (silent, oblivious, passively mobile), achieving the optimal idleness. Our algorithm defines a dynamical system of memoryless robots moving back and forth in an interval. In general, analysis of the system dynamics is very complex. Part of our contribution is a very technical analysis of the dynamics of special families of dynamical systems of n robots that we call regular. For such systems we also propose a highly non-trivial O(n2) algorithm to decide whether or not robots converge to a stable configuration thus verifying if the dynamic schedule is optimal. It turns out that a very natural family of

In this paper we present a fast leader election protocol for single-hop wireless networks, provably robust against jamming by an external and powerful adversary. A (T,1--ε)-bounded adversary can jam at most (1--ε)w out of any w ≥ T contiguous time slots, for 0 < ε < 1. The network consists of n stations that do not have knowledge of any global parameter n, T,ε. Each station can transmit or listen to the common communication channel. In each slot, all listeners are notified in which of the three states the communication channel is in the current slot: no transmitters, exactly one transmitter or at least two transmitters. To the listening stations, a jammed slot is indistinguishable from the case of at least two transmitters.

The rotor-router mechanism was introduced as a deterministic alternative to the random walk in undirected graphs. In this model, a set of k identical walkers is deployed in parallel, starting from a chosen subset of nodes, and moving around the graph in synchronous steps. During the process, each node maintains a cyclic ordering of its outgoing arcs, and successively propagates walkers which visit it along its outgoing arcs in round-robin fashion, according to the fixed ordering. We consider the cover time of such a system, i.e., the number of steps after which each node has been visited by at least one walk, regardless of the starting locations of the walks. In the case of k=1, [Yanovski et al., 2003] and [Bampas et al., 2009] showed that a single walk achieves a cover time of exactly Theta(mD) for any n-node graph with m edges and diameter D, and that the walker eventually stabilizes to a traversal of an Eulerian circuit on the set of all directed edges of the graph. For k>1 parallel walks, no similar structural behaviour can be observed. In this work we provide tight bounds on the cover time of k parallel rotor walks in a graph. We show that this cover time is at most (mD/log(k)) and at least Theta(mD/k) for any graph, which corresponds to a speedup of between Theta(log(k)) and Theta(k) with respect to the cover time of a single walk. Both of these extremal values of speedup are achieved for some graph classes. Our results hold for up to a polynomially large number of walks, k=O(poly(n)).

In this paper we investigate leader election protocols for single-hop radio networks from the perspective of energetic complexity. We discuss different models of energy consumption and their impact on time complexity. We also present some results about energy consumption in classic protocols optimal with respect to time complexity - we show that some very basic, intuitive algorithms for simpler model (with known number of stations) do not have to be optimal when energy of stations is restricted. We show that they can be significantly improved by introducing very simple modifications. Our main technical result is however a protocol for solving leader election problem in case of unknown number of stations n, with expected time O(log epsilon n), such that each station transmits O(1) number of times and no station is awake for more than O(log log log n) rounds.

The rotor-router mechanism was introduced as a deterministic alternative to the random walk in undirected graphs. In this model, an agent is initially placed at one of the nodes of the graph. Each node maintains a cyclic ordering of its outgoing arcs, and during successive visits of the agent, propagates it along arcs chosen according to this ordering in round-robin fashion. In this work we consider the setting in which multiple, indistinguishable agents are deployed in parallel in the nodes of the graph, and move around the graph in synchronous rounds, interacting with a single rotor-router system. We propose new techniques which allow us to perform a theoretical analysis of the multi-agent rotor-router model, and to compare it to the scenario of parallel independent random walks in a graph. Our main results concern the n-node ring, and suggest a strong similarity between the performance characteristics of this deterministic model and random walks.

In this paper we introduce and analyse the λ-Alert problem: in a single hop radio network a subset of stations is activated. The aim of the protocol is to decide if the number of activated stations is greater or equal to λ. This problem is similar to the k-Selection problem. It can also be seen as an extension of the standard Alert problem. In our paper we consider the λ-Alert problem in various settings. We describe characteristics of oblivious and adaptive deterministic algorithms for the model with and without collision detection. We also show some results for randomized algorithms. In particular, we present a very efficient Las Vegastype algorithm which is immune to an adversary.