Selecting Forwarding Neighbors in Wireless Ad Hoc Networks

Broadcasting is a fundamental operation which is frequent in wireless ad hoc networks. A simple broadcasting mechanism, known as flooding, is to let every node retransmit the message to all its 1-hop neighbors when receiving the first copy of the message. Despite its simplicity, flooding is very inefficient and can result in high redundancy, contention, and collision. One approach to reducing the redundancy is to let each node forward the message only to a small subset of 1-hop neighbors that cover all of the node's 2-hop neighbors. In this paper we propose two practical heuristics for selecting the minimum number of forwarding neighbors: an O(nlogn) time algorithm that selects at most 6 times more forwarding neighbors than the optimum, and an O(nlog² n) time algorithm with an improved approximation ratio of 3, where n is the number of 1- and 2-hop neighbors. The best previously known algorithm, due to Bronnimann and Goodrich [2], guarantees O(1) approximation in O(n ³ logn) time.     

A New Bluetooth Scatternet Formation Protocol

A Bluetooth ad hoc network can be formed by interconnecting piconets into scatternets. The constraints and properties of Bluetooth scatternets present special challenges in forming an ad hoc network efficiently. In this paper, we present and analyze a new randomized distributed protocol for Bluetooth scatternet formation. We prove that our protocol achieves O(logn) time complexity and O(n) message complexity. The scatternets formed by our protocol have the following properties: (1) any device is a member of at most two piconets, and (2) the number of piconets is close to be optimal. These properties can help prevent overloading of any single device and lead to low interference between piconets. We validate the theoretical results by simulations, which also show that the scatternets formed have O(logn) diameter. As an essential part of the scatternet formation protocol, we study the problem of device discovery: establishing multiple connections simultaneously with many Bluetooth devices. We investigate the collision rate and time requirement of the inquiry and page processes. Our simulation results indicate that the total number of packets sent is O(n) and that the maximum number of packets sent by any single device is O(logn).     

Gaussian radial basis functions and inner product spaces

An approximation result is given concerning Gaussian radial basis functions in a general inner product space. Applications are described concerning the classification of the elements of disjoint sets of signals, and also the approximation of continuous real functions defined on all of ⁿ using radial basis function (RBF) networks. More specifically, it is shown that an important large class of classification problems involving signals can be solved using a structure consisting of only a generalized RBF network followed by a quantizer. It is also shown that Gaussian radial basis functions defined on ⁿ can uniformly approximate arbitrarily well over all of ⁿ any continuous real functionalf on ⁿ that meets the condition that |f(x)|0 as x.     

Approximation Algorithms for the Mobile Piercing Set Problem with Applications to Clustering in Ad-Hoc Networks

The main contributions of this paper are two-fold. First, we present a simple, general framework for obtaining efficient constant-factor approximation algorithms for the mobile piercing set (MPS) problem on unit-disks for standard metrics in fixed dimension vector spaces. More specifically, we provide low constant approximations for L ₁ and L norms on a d-dimensional space, for any fixed d>0, and for the L ₂ norm on two- and three-dimensional spaces. Our framework provides a family of fully-distributed and decentralized algorithms, which adapt (asymptotically) optimally to the mobility of disks, at the expense of a low degradation on the best known approximation factors of the respective centralized algorithms: Our algorithms take O(1) time to update the piercing set maintained, per movement of a disk. We also present a family of fully-distributed algorithms for the MPS problem which either match or improve the best known approximation bounds of centralized algorithms for the respective norms and space dimensions.Second, we show how the proposed algorithms can be directly applied to provide theoretical performance analyses for two popular 1-hop clustering algorithms in ad-hoc networks: the lowest-id algorithm and the Least Cluster Change (LCC) algorithm. More specifically, we formally prove that the LCC algorithm adapts in constant time to the mobility of the network nodes, and minimizes (up to low constant factors) the number of 1-hop clusters maintained. While there is a vast literature on simulation results for the LCC and the lowest-id algorithms, these had not been formally analyzed prior to this work.We also present an O(logn)-approximation algorithm for the mobile piercing set problem for nonuniform disks (i.e., disks that may have different radii), with constant update time.     

Energy-Efficient Broadcasting in All-Wireless Networks

In all-wireless networks, minimizing energy consumption is crucial as in most cases the nodes are battery-operated. We focus on the problem of power-optimal broadcast, for which it is well known that the broadcast nature of radio transmissions can be exploited to optimize energy consumption. This problem appears to be difficult to solve [30]. We provide a formal proof of NP-completeness for the general case and give an NP-completeness result for the geometric case; in the former, the network topology is represented by a generic graph with arbitrary weights, whereas in the latter a Euclidean distance is considered. For the general case, we show that it cannot be approximated better than O(logN), where N is the total number of nodes. We then describe an approximation algorithm that achieves the O(logN) approximation ratio. We also describe a new heuristic, Embedded Wireless Multicast Advantage. We show that it compares well with other proposals and we explain how it can be distributed.     

A new distributed approximation algorithm for constructing minimum connected dominating set in wireless ad hoc networks

In recent years, constructing a virtual backbone by nodes in a connected dominating set (CDS) has been proposed to improve the performance of ad hoc wireless networks. In general, a dominating set satisfies that every vertex in the graph is either in the set or adjacent to a vertex in the set. A CDS is a dominating set that also induces a connected sub‐graph. However, finding the minimum connected dominating set (MCDS) is a well‐known NP‐hard problem in graph theory. Approximation algorithms for MCDS have been proposed in the literature. Most of these algorithms suffer from a poor approximation ratio, and from high time complexity and message complexity. In this paper, we present a new distributed approximation algorithm that constructs a MCDS for wireless ad hoc networks based on a maximal independent set (MIS). Our algorithm, which is fully localized, has a constant approximation ratio, and O(n) time and O(n) message complexity. In this algorithm, each node only requires the knowledge of its one‐hop neighbours and there is only one shortest path connecting two dominators that are at most three hops away. We not only give theoretical performance analysis for our algorithm, but also conduct extensive simulation to compare our algorithm with other algorithms in the literature. Simulation results and theoretical analysis show that our algorithm has better efficiency and performance than others. Copyright © 2005 John Wiley & Sons, Ltd.     

Finding a Maximal Weighted Independent Set in Wireless Networks

This paper introduces MWIS, a distributed algorithm for the efficient determination of a maximal weighted independent set in the topology graph G of a wireless network. Motivated by the observation that the problem of partitioning wireless nodes into clusters easily reduces to the problem of finding a maximal weighted independent set of nodes, the proposed algorithm is described by taking into account two main characteristics of wireless networks, namely, the broadcast nature of the wireless medium and the possibility to support nodes mobility. MWIS is executed at each node by means of fast message triggered procedures that require the sole knowledge of the topology local to the node. Moreover, its time complexity is proven to be bounded by a topology dependent parameter of the network (the stability number (G) of the network topology graph G), rather than by the invariant number n of the network nodes. Based on this result, and by using a well known result about (G) in the theory of random graphs the paper concludes with a brief discussion on the average time complexity of MWIS.     

A Distributed Algorithm for Dynamic Channel Allocation

Recent demand for mobile telephone service has been growing rapidly while the electro-magnetic spectrum of frequencies allocated for this purpose remains limited. Any solution to the channel assignment problem is subject to this limitation, as well as the interference constraint between adjacent channels in the spectrum. Channel allocation schemes provide a flexible and efficient access to bandwidth in wireless and mobile communication systems. In this paper, we present an efficient distributed algorithm for dynamic channel allocation based upon mutual exclusion model, where the channels are grouped by the number of cells in a cluster and each group of channels cannot be shared concurrently within the cluster. We discuss the algorithm and prove its correctness. We also show that the algorithm requires at most (worst case) O(N _gN _n logN _n) messages, where N _g is the number of groups and N _n is the number of neighbors. This is compared to Choy's algorithm which requires O(N _g ²N _n), where N _g is the number of groups and N _n is the number of neighboring cells in the system. We report our algorithm's performance with several channel systems using different types of call arrival patterns. Our results indicate that significant low denial rate, low message complexity and low acquisition time can be obtained using our algorithm.     

On the structure of the privacy hierarchy

An N argument function f(x ₁,...,x _N ) is called t-private if a protocol for computing f exists so that no coalition of at most t parties can infer any additional information from the execution, other than the value of the function. The motivation of this work is to understand what levels of privacy are attainable. So far, only two levels of privacy are known for N argument functions which are defined over finite domains: functions that are N-private and functions that are (N – 1)/2-private but not N/2-private.In this work we show that the privacy hierarchy for N-argument functions which are defined over finite domains, has exactly (N + 1)/2 levels. We prove this by constructing, for any N/2 t N – 2, an N-argument function which is t-private but not (t + 1)-private.This research was supported by US-Israel Binational Science Foundation Grant 88-00282.     

A VLSI decoder for a new type of constellations adapted to the Rayleigh Fading Channel

Diversity is the key solution to obtain efficient channel coding in wireless communications, where the signal is subject to fading (Rayleigh Fading Channel). For high spectral efficiency, the best solutions used nowadays are based on QAM constellations of 1-order diversity, associated with a binary code or a trellis coded modulation to increase the overall diversity. It has been shown that a new class of d-dimensional non-QAM constellations, named -constellations, can bring a d-order diversity without the addition of redundancy. Combined with classical coding techniques, -constellations are very efficient. However, the decoding algorithm is far more complicated for -constellations than for QAM-constellations. A sub-optimal algorithm that allows the decoding of -constellations is proposed. An example of an application for a 4 bits/Hz/s spectral efficiency with a 4-D -constellation is given. The VLSI architecture of the decoder is described. The implementation leads to 72 K gates, a binary rate of 32 Mbits/s and a BER of 10^-3 for a SNR of 14 dB.     

A doubling procedure for constructing minimal broadcast networks

Broadcast is the task of disseminating a message from any node to all the other nodes in a network. A minimal broadcast network (mbn) withn nodes is a communication network in which a message originated at any node can be broadcasted in [log₂ n] time units. An optimal broadcast network (obn) is an mbn with minimum number of edges. No method is known for constructing an obn with an arbitrary number of nodes. In this paper, a new method called the doubling procedure is presented to construct mbn's with 2n and 2n–1 nodes when an obn or a good mbn withn nodes is known. The new construction method is based on the concepts of center node and center node set of an mbn. An algorithm is proposed to find a center node set of a given mbn. It is shown that an obn with 2n nodes can be constructed based on a known obn withn nodes for alln 9,n=15, 31 and 63,n=2 ^m –1 andn=2 ^m ,mZ ⁺, by applying the doubling procedure. This method also generates the best mbn's for some values of [n64.     

A New Scheme to Realize Crosstalk-Free Permutation in Vertically Stacked Optical MINs*

Vertical stacking is a novel alternative for constructing nonblocking multistage interconnection networks (MINs). Rearrangeably nonblocking optical MINs are attractive since they have lower complexity than their strictly nonblocking counterparts. In this paper, we study the realization of crosstalk-free permutations in rearrangeably nonblocking, self-routing banyan-type optical MINs built on vertical stacking. An available scheme for realizing crosstalk-free permutation in this type of optical MINs requires to first decompose a permutation into multiple crosstalk-free partial permutations based on the Euler-Split technique, and then to realize them crosstalk-free in different planes (stacked copies) of the MIN simultaneously. The overall time complexity of this scheme to realize a crosstalk-free permutation in an N × N optical MIN is O(N log N) which is dominated by the complexity of crosstalk-free decomposition. In this paper, we propose a new scheme for realizing permutations in this class of vertically stacked optical MINs crosstalk-free. The basic idea of the new scheme is to classify permutations into permutation classes such that all permutations in one class share the same crosstalk-free decomposition pattern. By running the Euler-Split based crosstalk-free decomposition only once for a permutation class and applying the obtained crosstalk-free decomposition pattern to all permutations in the class, crosstalk-free decomposition of permutations can be realized in a more efficient way. We show that the number of permutations in a permutation class is huge (N!)^N when log₂N is even and (2N!)^N/2 when log₂N is odd), and thus the average time complexity of crosstalk-free decomposition of a permutation becomes O(N).     

Cleaning and Doping of Silicon in a BF3Plasma during Fabrication of Ohmic Contacts

The formation of reliable ohmic contacts to silicon is considered. Silicon surface cleaning, contact window doping, and molybdenum application by cathode sputtering in the BF₃atmosphere are carried out in a single vacuum cycle. A model of semiconductor–plasma and dielectric–plasma contacts under stationary discharge conditions is discussed. It is shown that the rates of processes with the participation of charged particles on p-Si and n-Si surfaces substantially differ. The resistivity of Mo-n ⁺Si and Mo-p ⁺Si contacts is the least when the molybdenum films are applied by sputtering in the Ar + (10–15) vol% BF₃atmosphere.     

On the distribution of characteristics in bijective mappings

Differential cryptanalysis is a method of attacking iterated mappings based on differences known as characteristics. The probability of a given characteristic is derived from the XOR tables associated with the iterated mapping. If is a mapping : Z ₂ ^m , then for each , X, Y Z ₂ ^m the XOR table for gives the number of input pairs of difference X=X+X for which gp(X)+(X)=Y.The complexity of a differential attack depends upon two properties of the XOR tables: the density of zero entries in the table, and the size of the largest entry in the table. In this paper we present the first results on the expected values of these properties for a general class of mappings . We prove that if : Z ₂ ^m Z ₂ ^m is a bijective mapping, then the expected size of the largest entry in the XOR table for is bounded by 2m, while the fraction of the XOR table that is zero approaches e ^–1/2=0.60653. We are then able to demonstrate that there are easily constructed classes of iterated mappings for which the probability of a differential-like attack succeeding is very small.The author is presently employed by the Distributed System Technology Center, Brisbane, Australia.     

Geometric problems on two-dimensional array processors

Parallel algorithms for solving geometric problems on two array processor models—the mesh-connected computer (MCC) and a two-dimensional systolic array—are presented. We illustrate a recursive divide- and-conquer paradigm for MCC algorithms by presenting a time-optimal solution for the problem of finding thenearest neighbors of a set of planar points represented by their Cartesian coordinates. The algorithm executes on an×n MCC, and requires an optimalO(n) time. An algorithm for constructing theconvex hull of a set of planar points and anupdate algorithm for thedisk placement problem on ann ^2/3×n ^2/3 two-dimensional systolic array are presented. Both these algorithms requireO(n ^2/3) time steps. The advantage of the systolic solutions lies in their suitability for direct hardware implementation.This research was partially supported by an IBM Faculty Development Award.     

Multidimensional fourier transforms by systolic architectures

In this paper, time-efficient systolic and semi-systolic architectures for the implementation of multidimensional DFTs are proposed that allow modularity and easy expansibility while keeping throughput independent of the dimension of the DFT. We shall call an array semi-systolic if the input data is to be preloaded into every cell of the array or if the output data can be calculated not only in the boundary cells of the array. DFT algorithms are represented by FORTRAN-like code, in order to explicitly display the suggested rotational transformations in the index space. After the transformation, multidimensional DFT algorithm can be mapped onto a systolic structure. The area-time² complexity of the proposed design is within logk factor of the lower bound for ak-point DFT (AT ²=(k ² log² k)), i.e. equals 0(k ² log³ k)=0(N ^2M log³ N) fork=N ^2M point DFT;A is the area complexity andT is the system throughput.     

Construction of Time-Relaxed c-Broadcast Networks

C-broadcasting is an information dissemination task where a message, originated at any node in a network, is transmitted to all other nodes with the restriction that each node having the message can transmit it to almost c neighbors simultaneously. If the transmission time of the message is set to be one time unit, a minimal c-broadcast network (c-MBN) is a communication network in which c-broadcasting from any node can be accomplished in log _c+1 n time units, where n is the number of nodes and log _c+1 n is the fastest possible broadcast time. If networks are sparse, additional time units may be required to perform c-broadcasting. A time-relaxed c-broadcast network, denoted as (t,c)-RBN, is a network where c-broadcasting from any node can be completed in log _c+1 n+t time units. In this paper, a network compounding algorithm is proposed to construct large sparse (t,c)-RBNs by linking multiple copies of a time-relaxed network of small size using the structure of another time-relaxed network. Computational results are presented to show the effectiveness of the proposed algorithm.     

Routing with multiple QoS requirements for supporting multimedia applications

Distributed multimedia applications usually require multiple QoS performance guarantees. However, in general, searching such a route in the network, to support multimedia applications, is known to be NPcomplete. In this paper, we propose a new heuristic QoS routing algorithm, called QoSR_DKS, for supporting multimedia applications in highspeed networks. QoSR_DKS is a modification of rulebased Fallback routing and Dijkstra algorithms. It can search a unicast route that would have enough network resources so that multiple QoS requirements (bandwidth, delay, and delay jitter) of the requested flow could be guaranteed. Its worst case computation time complexity is the same as that of the Dijkstra algorithm, i.e., O(V²), where V is the number of nodes in the network. Extensive simulations were done with various network sizes, upto 500 nodes networks, where each node uses Weighted Fair Queueing (WFQ) service discipline. Results show that QoSR_DKS is very efficient. It could always find the QoS satisfying route, whenever there exists one (success rate is optimal), and its average computation time is near to simple shortest path Dijkstra algorithm.     

A fully pipelined RLS-based array for channel equalization

It is shown that several recursive least squares (RLS) type equalization algorithms such as, e.g., decisiondirected schemes and orthogonalized constant modulus algorithms, possess a common algorithmic structure and are therefore rather straightforwardly implemented on an triangular array (filter structure) for RLS estimation with inverse updating. While the computational complexity for such algorithms isO(N ²), whereN is the problem size, the throughput rate for the array implementation isO(1), i.e., independent of the problem size. Such a throughput rate cannot be achieved with standard (Gentleman-Kung-type) RLS/QR-updating arrays because of feedback loops in the computational schemes.     

A distributed link scheduling algorithm for CDMA packet radio networks

A distributed algorithm for the conflict-free channel allocation in CDMA (code division multiple access) networks is presented. Dynamic adjustment to topological changes is also considered. Though the schedules produced by our algorithm are not optimal with respect to link schedule length, the algorithm is simple and practical. The link schedule length minimization problem is NP-complete. Here the length of a link schedule is the number of time slots it uses. The algorithm guarantees a bound 2 — 1 time slots on the TDMA cycle length, where is the maximum degree of a station (i.e., maximum number of stations that a station can reach by radio links) in the network. The message complexity of a station isO().