Abstract: We address an important communication issue arising in
wireless cellular networks that utilize frequency division
multiplexing (FDM) technology. In such networks, many
users within the same geographical region (cell) can communicate
simultaneously with other users of the network
using distinct frequencies. The spectrum of the available
frequencies is limited; thus, efficient solutions to the call
controlproblemareessential.Theobjectiveofthecallcontrol
problem is, given a spectrum of available frequencies
and users that wish tocommunicate, to maximize the benefit,
i.e., the number of users that communicate without
signalinterference.Weconsidercellularnetworksofreuse
distance k ≥ 2 and we study the online version of the
problem using competitive analysis. In cellular networks
of reuse distance 2, the previously best known algorithm
that beats the lower bound of 3 on the competitiveness
of deterministic algorithms, works on networks with one
frequency, achieves a competitive ratio against oblivious
adversaries, which is between 2.469 and 2.651, and uses
a number of random bits at least proportional to the size
of the network.We significantly improve this result by presentingaseriesofsimplerandomizedalgorithmsthathave
competitiveratiossignificantlysmallerthan3,workonnetworks
with arbitrarily many frequencies, and use only a
constant number of random bits or a comparable weak
random source. The best competitiveness upper bound
we obtain is 16/7 using only four random bits. In cellular
networks of reuse distance k > 2, we present simple
randomized online call control algorithms with competitive
ratios, which significantly beat the lower bounds on
the competitiveness of deterministic ones and use only
O(log k )randombits. Also,weshownewlowerboundson
thecompetitivenessofonlinecallcontrolalgorithmsincellularnetworksofanyreusedistance.
Inparticular,weshow
thatnoonline algorithm can achieve competitive ratio better
than 2, 25/12, and 2.5, in cellular networks with reuse
distancek ∈ {2, 3, 4},k = 5,andk ≥ 6, respectively.
Abstract: This paper deals with systems of multiple mobile robots each of which observes the positions of the other robots and moves to a new position so that eventually the robots form a circle. In the model we study, the robots are anonymous and oblivious, in the sense that they cannot be distinguished by their appearance and do not have a common x-y coordinate system, while they are unable to remember past actions.
We propose a new distributed algorithm for circle formation on the plane. We prove that our algorithm is correct and provide an upper bound for its performance. In addition, we conduct an extensive and detailed comparative simulation experimental study with the DK algorithm described in [7]. The results show that our algorithm is very simple and takes considerably less time to execute than algorithm DK.
Abstract: This paper deals with systems of multiple mobile robots each of which observes the positions of the other robots and moves to a new position so that eventually the robots form a circle. In the model we study, the robots are anonymous and oblivious, in the sense that they cannot be distinguished by their appearance and do not have a common x-y coordinate system, while they are unable to remember past actions.
We propose a new distributed algorithm for circle formation on the plane. We prove that our algorithm is correct and provide an upper bound for its performance. In addition, we conduct an extensive and detailed comparative simulation experimental study with the DK algorithm. The results show that our algorithm is very simple and takes considerably less time to execute than algorithm DK.
Abstract: Two important performance parameters of distributed, rate-based flow control algorithms are their locality and convergence complexity. The former is characterized by the amount of global knowledge that is available to their scheduling mechanisms, while the latter is defined as the number of update operations performed on rates of individual sessions until max-min fairness is reached. Optimistic algorithms allow any session to intermediately receive a rate larger than its max-min fair rate; bottleneck algorithms finalize the rate of a session only if it is restricted by a certain, highly congested link of the network. In this work, we present a comprehensive collection of lower and upper bounds on convergence complexity, under varying degrees of locality, for optimistic, bottleneck, rate-based flow control algorithms. Say that an algorithm is oblivious if its scheduling mechanism uses no information of either the session rates or the network topology. We present a novel, combinatorial construction of a capacitated network, which we use to establish a fundamental lower bound of dn 4 + n 2 on the convergence complexity of any oblivious algorithm, where n is the number of sessions laid out on a network, and d, the session dependency, is a measure of topological dependencies among sessions. Moreover, we devise a novel simulation proof to establish that, perhaps surprisingly, the lower bound of dn 4 + n 2 on convergence complexity still holds for any partially oblivious algorithm, in which the scheduling mechanism is allowed to use information about session rates, but is otherwise unaware of network topology. On the positive side, we prove that the lower bounds for oblivious and partially oblivious algorithms are both tight. We do so by presenting optimal oblivious algorithms, which converge after dn 2 + n 2 update operations are performed in the worst case. To complete the picture, we show that linear convergence complexity can indeed be achieved if information about both session rates and network topology is available to schedulers. We present a counterexample, nonoblivious algorithm, which converges within an optimal number of n update operations. Our results imply a surprising convergence complexity collapse of oblivious and partially oblivious algorithms, and a convergence complexity separation between (partially) oblivious and nonoblivious algorithms for optimistic, bottleneck rate-based flow control.
Abstract: Information retrieval (IR) in peer-to-peer (P2P) networks,
where the corpus is spread across many loosely coupled
peers, has recently gained importance. In contrast to IR
systems on a centralized server or server farm, P2P IR faces
the additional challenge of either being oblivious to global
corpus statistics or having to compute the global measures
from local statistics at the individual peers in an efficient,
distributed manner. One specific measure of interest is the
global document frequency for different terms, which would
be very beneficial as term-specific weights in the scoring and
ranking of merged search results that have been obtained
from different peers.
This paper presents an efficient solution for the problem
of estimating global document frequencies in a large-scale
P2P network with very high dynamics where peers can join
and leave the network on short notice. In particular, the
developed method takes into account the fact that the lo-
cal document collections of autonomous peers may arbitrar-
ily overlap, so that global counting needs to be duplicate-
insensitive. The method is based on hash sketches as a
technique for compact data synopses. Experimental stud-
ies demonstrate the estimator?s accuracy, scalability, and
ability to cope with high dynamics. Moreover, the benefit
for ranking P2P search results is shown by experiments with
real-world Web data and queries.
Abstract: Information retrieval (IR) in peer-to-peer (P2P) networks,
where the corpus is spread across many loosely coupled
peers, has recently gained importance. In contrast to IR
systems on a centralized server or server farm, P2P IR faces
the additional challenge of either being oblivious to global
corpus statistics or having to compute the global measures
from local statistics at the individual peers in an efficient,
distributed manner. One specific measure of interest is the
global document frequency for different terms, which would
be very beneficial as term-specific weights in the scoring and
ranking of merged search results that have been obtained
from different peers.
This paper presents an efficient solution for the problem
of estimating global document frequencies in a large-scale
P2P network with very high dynamics where peers can join
and leave the network on short notice. In particular, the
developed method takes into account the fact that the lo-
cal document collections of autonomous peers may arbitrar-
ily overlap, so that global counting needs to be duplicate-
insensitive. The method is based on hash sketches as a
technique for compact data synopses. Experimental stud-
ies demonstrate the estimator?s accuracy, scalability, and
ability to cope with high dynamics. Moreover, the benefit
for ranking P2P search results is shown by experiments with
real-world Web data and queries.
Abstract: Flow control is the main technique currently used to prevent some of the ordered traffic from entering a communication network, and to avoid congestion. A challenging aspect of flow control is how to treat all sessions "fairly " when it is necessary to turn traffic away from the network. In this work, we show how to extend the theory of max-min fair flow control to the case where priorities are assigned to different varieties of traffic, which are sensitive to traffic levels. We examine priorities expressible in the general form of increasing functions of rates, considering yet in combination the more elaborative case with unescapable upper and lower bounds on rates of traffic sessions. We offer optimal, priority bottleneck algorithms, which iteratively adjust the session rates in order to meet a new condition of max-min fairness under priorities and rate bounds. In our setting, which is realistic for today's technology of guaranteed quality of service, traffic may be turned away not only to avoid congestion, but also to respect particular minimum requirements on bandwidth. Moreover, we establish lower bounds on the competitiveness of network-oblivious schemes compared to optimal schemes with complete knowledge of network structure. Our theory extends significantly the classical theory of max-min fair flow control [2]. Moreover, our results on rejected traffic are fundamentally different from those related to call control and bandwidth allocation, since not only do we wish to optimize the number and rates of accepted sessions, but we also require priority fairness.
Abstract: We propose a novel, generic definition of probabilistic schedulers for population protocols. We then identify the consistent probabilistic schedulers, and prove that any consistent scheduler that assigns a non-zero probability to any transition i->j, where i and j are configurations satisfying that i is not equal to j, is fair with probability 1. This is a new theoretical framework that aims to simplify proving specific probabilistic schedulers fair. In this paper we propose two new schedulers, the State Scheduler and the Transition Function Scheduler. Both possess the significant capability of being protocol-aware, i.e. they can assign transition probabilities based on information concerning the underlying protocol. By using our framework we prove that the proposed schedulers, and also the Random Scheduler that was defined by Angluin et al., are all fair with probability 1. We also define and study equivalence between schedulers w.r.t. performance (time equivalent schedulers) and correctness (computationally equivalent schedulers). Surprisingly, we prove the following.
1. The protocol-oblivious (or agnostic) Random Scheduler is not time equivalent to the State and Transition Function Schedulers, although all three are fair probabilistic schedulers (with probability 1). To prove the statement we study the performance of the One-Way Epidemic Protocol (OR Protocol) under these schedulers. To illustrate the unexpected performance variations of protocols under different fair probabilistic schedulers, we additionally modify the State Scheduler to obtain a fair probabilistic scheduler, called the Modified Scheduler, that may be adjusted to lead the One-Way Epidemic Protocol to arbitrarily bad performance.
2. The Random Scheduler is not computationally equivalent to the Transition Function Scheduler. To prove the statement we study the Majority Protocol w.r.t. correctness under the Transition Function Scheduler. It turns out that the minority may win with constant probability under the same initial margin for which the majority w.h.p. wins under the Random Scheduler (as proven by Angluin et al.).
Abstract: This research further investigates the recently introduced
(in [4]) paradigm of radiation awareness in ambient environments with abundant heterogeneous wireless networking
from a distributed computing perspective. We call radiation
at a point of a wireless network the total amount of electromagnetic quantity the point is exposed to; our de nition incorporates the e ect of topology as well as the time domain
and environment aspects. Even if the impact of radiation to
human health remains largely unexplored and controversial,
we believe it is worth trying to understand and control, in
a way that does not decrease much the quality of service
o ered to users of the wireless network.
In particular, we here focus on the fundamental problem
of ecient data propagation in wireless sensor networks, try-
ing to keep latency low while maintaining at low levels the
radiation cumulated by wireless transmissions. We rst propose greedy and oblivious routing heuristics that are radiation aware. We then combine them with temporal back-o
schemes that use local properties of the network (e.g. number of neighbours, distance from sink) in order to spread" radiation in a spatio-temporal way. Our proposed radiation
aware routing heuristics succeed to keep radiation levels low,
while not increasing latency.
Abstract: We address an important communication issue in wireless cellular networks that utilize Frequency Division Multiplexing (FDM) technology. In such networks, many users within the same geographical region (cell) can communicate simultaneously with other users of the network using distinct frequencies. The spectrum of the available frequencies is limited; thus, efficient solutions to the call control problem are essential. The objective of the call control problem is, given a spectrum of available frequencies and users that wish to communicate, to maximize the number of users that communicate without signal interference. We consider cellular networks of reuse distance kge 2 and we study the on-line version of the problem using competitive analysis.
In cellular networks of reuse distance 2, the previously best known algorithm that beats the lower bound of 3 on the competitiveness of deterministic algorithms works on networks with one frequency, achieves a competitive ratio against oblivious adversaries which is between 2.469 and 2.651, and uses a number of random bits at least proportional to the size of the network. We significantly improve this result by presenting a series of simple randomized algorithms that have competitive ratios smaller than 3, work on networks with arbitrarily many frequencies, and use only a constant number of random bits or a comparable weak random source. The best competitiveness upper bound we obtain is 7/3.
In cellular networks of reuse distance k>2, we present simple randomized on-line call control algorithms with competitive ratios which significantly beat the lower bounds on the competitiveness of deterministic ones and use only random bits. Furthermore, we show a new lower bound on the competitiveness of on-line call control algorithms in cellular networks of reuse distance kge 5.
