Marcin Zawada

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.

How to Improve the Reliability of Chord

In this paper we focus on Chord P2P protocol and we study the process of unexpected departures of nodes from this system. Each of such departures may effect in losing any information and in classical versions of this protocol the probability of losing some information is proportional to the quantity of information put into this system. This effect can be partially solved by gathering in the protocol multiple copies (replicas) of information. The replication mechanism was proposed by many authors. We present a detailed analysis of one variant of blind replication and show that this solution only partially solves the problem. Next we propose two less obvious modifications of the Chord protocol. We call the first construction a direct sums of Chords and the second - a folded Chord. We discuss the recovery mechanisms of partially lost information in each of these systems and investigate their reliability. We show that our modification increases essentially the expected lifetime of information put into the system. Our modifications of the Chord protocol are very soft and require only a small interference in the programming code of the original Chord protocol.

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.

An Application of GPU Parallel Computing to Power Flow Calculation in HVDC Networks

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.

Analysis of the bounded-hops converge-cast distributed protocol in ad-hoc networks

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.

Adaptive initialization algorithm for ad hoc radio networks with carrier sensing

Numerical computation on GPU has become easily accessible and offers good computation power for relatively little cost. Recently an application of Newton-Rap son method for analyzing power flow in multi-terminal high-voltage direct current (HVDC) networks was proposed and shown to have good results on five terminal grids. Since this method involves costly matrix operation, especially the inverse, increasing the number of terminals in the grid yields prohibitively large execution times in sequential operation. To address this issue, we adjust the algorithm so that it benefits from parallel computation and test our approach on recent GPU from NVidia. We give experimental results for grids up to few thousand terminals and show that execution time is still acceptable for real applications. We also provide some benchmarks of the GPU computation compared with other platforms.

Power of Discrete Nonuniformity - Optimizing Access to Shared Radio Channel in Ad Hoc Networks

We consider the problem of bounded hops converge cast in ad-hoc networks. Let us assume that stations are located on the d- dimensional Euclidean space and there is one distinguished station called a base station. This problem, called the d-Dim h-HOPS CONVERGECAST, is defined as finding a minimal energy-cost range assignment, which allows each station to communicate with a base station in at most h hops. Clementi et al. [2] proposed a distributed protocol h-PROT for d = 2 and proved that in case of h = 2 the expected approximation ratio of this protocol is O(1) on random instances. However, for h = 3, ..., 8 they provided only an experimental study showing that the protocol has good performances. In this paper, we introduce the protocol (d, h)- PROT which extends the protocol h-PROT on the d-dimensional space. We address the probabilistic analysis and show formally that the protocol (d, h)-PROT achieves an approximation ratio of O(1) in expectation on random instances for any d, h ≥ 2.