Alan A. Bertossi

Assigning codes in wireless networks: bounds and scaling properties

In the Code Division Multiple Access (CDMA) framework, collisions that can occur in wireless networks are eliminated by assigning orthogonal codes to stations, a problem equivalent to that of coloring graphs associated to the physical network. In this paper we present new upper and lower bounds for two versions of the problem (hidden and primary collision avoidance – HP‐CA – or hidden collision avoidance only – H‐CA). In particular, optimal assignments for special topologies and heuristics for general topologies are proposed. The schemes show better average results with respect to existing alternatives. Furthermore, the gaps between the upper bound given by the heuristic solution, the lower bound obtained from the maximum‐clique problem, and the optimal solution obtained by branch and bound are investigated in the different settings. A scaling law is then proposed to explain the relations between the number of codes needed in Euclidean networks with different station densities and connection distances. The substantial difference between the two versions HP‐CA and H‐CA of the problem is investigated by studying the probabilistic distribution of connections as a function of the distance, and the asymptotic size of the maximum cliques.

Efficient heuristics for data broadcasting on multiple channels

The problem of data broadcasting over multiple channels consists in partitioning data among channels, depending on data popularities, and then cyclically transmitting them over each channel so that the average waiting time of the clients is minimized. Such a problem is known to be polynomially time solvable for uniform length data items, while it is computationally intractable for non-uniform length data items. In this paper, two new heuristics are proposed which exploit a novel characterization of optimal solutions for the special case of two channels and data items of uniform lengths. Sub-optimal solutions for the most general case of an arbitrary number of channels and data items of non-uniform lengths are provided. The first heuristic, called Greedy+, combines the novel characterization with the known greedy approach, while the second heuristic, called Dlinear, combines the same characterization with the dynamic programming technique. Such heuristics have been tested on benchmarks whose popularities are characterized by Zipf distributions, as well as on a wider set of benchmarks. The experimental tests reveal that Dlinear finds optimal solutions almost always, requiring good running times. However, Greedy+ is faster and scales well when changes occur on the input parameters, but provides solutions which are close to the optimum.

Mappings for Conflict-Free Access of Paths in Bidimensional Arrays, Circular Lists, and Complete Trees

Since the divergence between the processor speed and the memory access rate is progressively increasing, an efficient partition of the main memory into multibanks is useful to improve the overall system performance. The effectiveness of the multibank partition can be degraded by memory conflicts, that occur when there are many references to the same memory bank while accessing the same memory pattern. Therefore, mapping schemes are needed to distribute data in such a way that data can be retrieved via regular patterns without conflicts. In this paper, the problem of conflict-free access of arbitrary paths in bidimensional arrays, circular lists and complete trees is considered for the first time and reduced to variants of graph-coloring problems. Balanced and fast mappings are proposed which require an optimal number of colors (i.e., memory banks). The solution for bidimensional arrays is based on a particular Latin Square. The functions that map an array node or a circular list node to a memory bank can be calculated in constant time. As for complete trees, the mapping of a tree node to a memory bank takes time that grows logarithmically with the number of nodes of the tree. The problem solved here has further application in minimizing the number of frequencies assigned to the stations of a wireless network so as to avoid interference.

Channel assignment on strongly-simplicial graphs

Given a vector (/spl delta//sub 1/, /spl delta/2,..., /spl delta//sub t/) of non increasing positive integers, and an undirected graph G = (V, E), an L(/spl delta//sub 1/, /spl delta/2,..., /spl delta//sub t/)-coloring of G is a function f from the vertex set V to a set of nonnegative integers such that |f(u) - f (v)| /spl ges/ /spl delta//sub i/, if d(u, v) = i, 1 /spl les/ i /spl les/ t, where d(u,v) is the distance (i.e. the minimum number of edges) between the vertices u and v. This paper presents efficient algorithms for finding optimal L(1,..., 1)-colorings of trees and interval graphs. Moreover, efficient algorithms are also provided for finding approximate L(/spl delta//sub 1/, 1,..., 1)-colorings of trees and interval graphs, as well as approximate L(/spl delta//sub 1/, /spl delta//sub 2/) colorings of unit interval graphs.

Efficient corona training protocols for sensor networks

Phenomenal advances in nano-technology and packaging have made it possible to develop miniaturized low-power devices that integrate sensing, special-purpose computing, and wireless communications capabilities. It is expected that these small devices, referred to as sensors, will be mass-produced and deployed, making their production cost negligible. Due to their small form factor and modest non-renewable energy budget, individual sensors are not expected to be GPS-enabled. Moreover, in most applications, exact geographic location is not necessary, and all that the individual sensors need is a coarse-grain location awareness. The task of acquiring such a coarse-grain location awareness is referred to as training. In this paper, two scalable energy-efficient training protocols are proposed for massively-deployed sensor networks, where sensors are initially anonymous and unaware of their location. The training protocols are lightweight and simple to implement; they are based on an intuitive coordinate system imposed onto the deployment area which partitions the anonymous sensors into clusters where data can be gathered from the environment and synthesized under local control.

Optimal multi-channel data allocation with flat broadcast per channel

Summary form only given. Broadcast is an efficient and scalable way of transmitting data to an unlimited number of clients that are listening to a channel. Cyclically broadcasting data over the channel is a basic scheduling technique, which is known as flat scheduling. When multiple channels are available, partitioning data among channels in an unbalanced way, depending on data popularities, is an allocation technique known as skewed allocation. In this paper, the problem of data broadcasting over multiple channels is considered assuming skewed data allocation to channels and fiat data scheduling per channel, with the objective of minimizing the average waiting time of the clients. Several algorithms, based on dynamic programming, are presented which provide optimal solutions for N data items and K channels. Specifically, for data items with uniform lengths, an O(NKlogN) time algorithm is proposed, which improves over the previously known O(N/sup 2/K) time algorithm. When K /spl les/ 4, faster O(N) time algorithms are exhibited. Moreover, for data items with nonuniform lengths, it is shown that the problem is NP-hard when K = 2, and strong NP-hard for arbitrary K. In the former case, a pseudo-polynomial algorithm is discussed, whose time is O(NZ) where Z is the sum of the data lengths.

Scheduling Hard-Real-Time Tasks with Backup Phasing Delay

This paper presents several fault-tolerant extensions of the Rate-Monotonic First-Fit multiprocessor scheduling algorithm handling both active and passive task copies. In particular, the technique of backup phasing delay is used to reduce the portions of active task copies that must be always executed and to deallocate active task copies as soon as their primary task copies have been successfully executed. It is also shown how to employ this technique while considering passive task duplication so as to over-book each processor with many passive task copies, assigning tasks to processors in such a way that tasks with equal or multiple periods have a high chance to be assigned to the same processor, and partitioning the processors into groups to avoid the mix of primary, active, and passive task copies on the same processor. Extensive simulations reveal a remarkable saving of both the overall number of processors used and the total computation time of the schedulability test (achieved especially by two new algorithms, called ARR3 and S-PR-PASS) with respect to previously proposed algorithms

Efficient Location Training Protocols for Heterogeneous Sensor and Actor Networks

In this work, we consider a large-scale geographic area populated by tiny sensors and some more powerful devices called actors, authorized to organize the sensors in their vicinity into short-lived, actor-centric sensor networks. The tiny sensors run on miniature nonrechargeable batteries, are anonymous, and are unaware of their location. The sensors differ in their ability to dynamically alter their sleep times. Indeed, the periodic sensors have sleep periods of predefined lengths, established at fabrication time; by contrast, the free sensors can dynamically alter their sleep periods, under program control. The main contribution of this work is to propose an energy-efficient location training protocol for heterogeneous actor-centric sensor networks where the sensors acquire coarse-grain location awareness with respect to the actor in their vicinity. Our theoretical analysis, confirmed by experimental evaluation, shows that the proposed protocol outperforms the best previously known location training protocols in terms of the number of sleep/awake transitions, overall sensor awake time, and energy consumption.

Parallel string matching with variable length don't cares

Abstract String matching is the problem of finding all the occurrences of a pattern P in a text T, where P and T are strings over a finite alphabet Σ. A variable length don′t care is a special character, not belonging to Σ, which can match any string in Σ*. The string-matching problem with variable length don′t cares is an extension of the classical string-matching problem in which the pattern P may contain an arbitrary number of don′t cares. An efficient parallel algorithm is given for solving the string-matching problem with variable length don′t cares. The EREW PRAM model of parallel computer with scan operations is used to obtain an O(log n) running time using O(mn/log n) processors, where m and n are, respectively, the lengths of P and T. The proposed parallel algorithm has an Ω(1/log n) processor utilization, since the fastest serial algorithm known so far has an O(mn/log n) running time.

Asynchronous training in wireless sensor networks

A scalable energy-efficient training protocol is proposed for massively-deployed sensor networks, where sensors are initially anonymous and unaware of their location. The protocol is based on an intuitive coordinate system imposed onto the deployment area which partitions the anonymous sensors into clusters. The protocol is asynchronous, in the sense that the sensors wake up for the first time at random, then alternate between sleep and awake periods both of fixed length, and no explicit synchronization is performed between them and the sink. Theoretical properties are stated under which the training of all the sensors is possible. Moreover, a worst-case analysis as well as an experimental evaluation of the performance is presented, showing that the protocol is lightweight and flexible.