Jakub Lemiesz

Two-phase cardinality estimation protocols for sensor networks with provable precision

Efficient cardinality estimation is a common requirement for many wireless sensor network (WSN) applications. The task must be accomplished at extremely low overhead due to severe sensor resource limitation. This poses an interesting challenge for large-scale WSNs. In this paper we present a two-phase probabilistic algorithm based on order statistics and Bernoulli scheme, which effectively estimates the cardinality of WSNs. We thoroughly examine properties of estimators used in each phase as well as the precision of the whole procedure. The algorithm discussed in this paper is a modification of a recently published idea - the modification enables us to obtain a provable precision.

On cardinality estimation protocols for wireless sensor networks

In this article we address the problem of estimating a size of wireless sensor networks (WSNs). We restrict our attention to sensors with very limited storage capabilities. The problem arises when sensors have to quickly obtain approximate size of the network to use algorithms which require such information. Another application area is the problem of counting the number of different objects (e.g. people in public bus transportation) and use of such information to optimize the routes and frequency of buses. In this paper we present two-phase probabilistic algorithm based on order statistics and balls-bins model which effectively solves the presented problem.

On message complexity of extrema propagation techniques

In this paper we discuss the message complexity of some variants of the Extrema Propagation techniques in wireless networks. We show that the average message complexity, counted as the number of messages sent by each given node, is

On size estimation protocols for Sensor Networks

\mathrm{O}\left(\log n\right)

On alarm protocol in wireless sensor networks

, where n denotes the size of the network. We indicate the connection between our problem and the well known and deeply studied problem of the number of records in a random permutation. We generalize this problem onto an arbitrary simple and locally finite graphs, prove some basic theorems and find message complexity for some classical graphs such us lines, circles, grids and trees.

On structural entropy of uniform random intersection graphs

In this paper we discuss a two-phase algorithm for estimating the size of a wireless network consisting of weak devices, such as Wireless Sensor Networks (WSN). The main idea is based on employing randomly generated identifiers. In the first phase of the algorithm we use the properties of order statistics and calculate an approximate estimator of the number of nodes. In the second phase we use this estimator and a series of Bernoulli independent trials in order to get a more precise estimator. We discuss the precision of the algorithm and we show that using a little more than 100 bytes of memory ensures 20% precision for networks consisting of up to 109 nodes. We also prove some lower bounds for memory requirements. We compare our algorithm with HyperLogLog and Extrema Propagation algorithms. Finally, we show that the communication complexity of our algorithm is of order O(log n) where n is the network size.

Ghost Train for Anonymous Communication

We consider the problem of efficient alarm protocol for ad-hoc radio networks consisting of devices that try to gain access for transmission through a shared radio communication channel. The problem arise in tasks that sensors have to quickly inform the target user about an alert situation such as presence of fire, dangerous radiation, seismic vibrations, and more. In this paper, we present a protocol which uses O(log n) time slots and show that Ω(log n/ log log n) is a lower bound for used time slots.

On distributed cardinality estimation: random arcs recycled

Recently, the need for efficient representations of data conveyed by graphical structures has emerged in many different contexts. While compressing such data one must consider two types of information. The first type is the information carried by the labels embedded in the structure. The second type is the information conveyed by the structure itself. In this extended abstract we address the latter type, namely we study the information carried by the structure of Uniform Random Intersection Graphs (URIGs). Random Intersection Graphs emerge in many scenarios, e.g., they correspond to the topology of many social networks and secure wireless networks, and they are induced in the clusterization process. We analyze algebraic properties of an automorphism group of the underlying structure of URIGs and derive a precise asymptotic formula for their structural entropy for various values of model parameters.

One- and Multi-Pass Long-Hop Routing for Wireless Network

We study the problem of hiding communication: while it is easy to encrypt a message sent from Alice to Bob, it is hard to hide that such a communication takes place. Communiaction hiding is one of the fundamental privacy challenges, especially in case of an adversary having a complete view of the traffic and controlling a large number of nodes.