Abstract: We study the problem of scheduling permanent jobs on un-
related machines when the objective is to minimize the Lp
norm of the machine loads. The problem is known as load
balancing under the Lp norm. We present an improved up-
per bound for the greedy algorithm through simple analy-
sis; this bound is also shown to be best possible within the
class of deterministic online algorithms for the problem. We
also address the question whether randomization helps on-
line load balancing under Lp norms on unrelated machines;
this is a challenging question which is open for more than a
decade even for the L2 norm. We provide a positive answer
to this question by presenting the ¯rst randomized online
algorithms which outperform deterministic ones under any
(integral) Lp norm for p = 2; :::; 137. Our algorithms es-
sentially compute in an online manner a fractional solution
to the problem and use the fractional values to make ran-
dom choices. The local optimization criterion used at each
step is novel and rather counterintuitive: the values of the
fractional variables for each job correspond to °ows at an ap-
proximate Wardrop equilibrium for an appropriately de¯ned
non-atomic congestion game. As corollaries of our analysis
and by exploiting the relation between the Lp norm and the
makespan of machine loads, we obtain new competitive algo-
rithms for online makespan minimization, making progress
in another longstanding open problem.

Abstract: We study the problem of scheduling permanent jobs on un-
related machines when the objective is to minimize the Lp
norm of the machine loads. The problem is known as load
balancing under the Lp norm. We present an improved up-
per bound for the greedy algorithm through simple analy-
sis; this bound is also shown to be best possible within the
class of deterministic online algorithms for the problem. We
also address the question whether randomization helps on-
line load balancing under Lp norms on unrelated machines;
this is a challenging question which is open for more than a
decade even for the L2 norm. We provide a positive answer
to this question by presenting the ¯rst randomized online
algorithms which outperform deterministic ones under any
(integral) Lp norm for p = 2; :::; 137. Our algorithms es-
sentially compute in an online manner a fractional solution
to the problem and use the fractional values to make ran-
dom choices. The local optimization criterion used at each
step is novel and rather counterintuitive: the values of the
fractional variables for each job correspond to °ows at an ap-
proximate Wardrop equilibrium for an appropriately de¯ned
non-atomic congestion game. As corollaries of our analysis
and by exploiting the relation between the Lp norm and the
makespan of machine loads, we obtain new competitive algo-
rithms for online makespan minimization, making progress
in another longstanding open problem.

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 competitiveanalysis. 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: In this paper we consider communication issues arising in mobile networks that utilize Frequency Division Multiplexing (FDM) technology. In such networks, many users within the same geographical region can communicate simultaneously with other users of the network using distinct frequencies. The spectrum of available frequencies is limited; thus, efficient solutions to the frequency allocation and the call control problem are essential. In the frequency allocation problem, given users that wish to communicate, the objective is to minimize the required spectrum of frequencies so that communication can be established without signal interference. 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 served. We consider cellular, planar, and arbitrary network topologies. In particular, we study the on-line version of both problems using competitiveanalysis. For frequency allocation in cellular networks, we improve the best known competitive ratio upper bound of 3 achieved by the folklore Fixed Allocation algorithm, by presenting an almost tight competitiveanalysis for the greedy algorithm; we prove that its competitive ratio is between 2.429 and 2.5. For the call control problem, we present the first randomized algorithm that beats the deterministic lower bound of 3 achieving a competitive ratio of 2.934 in cellular networks. Our analysis has interesting extensions to arbitrary networks. Also, using Yao's Minimax Principle, we prove two lower bounds of 1.857 and 2.086 on the competitive ratio of randomized call control algorithms for cellular and arbitrary planar networks, respectively.

Abstract: In this paper we consider communication issues arising in cellular (mobile) networks that utilize frequency division multiplexing (FDM) technology. In such networks, many users within the same geographical region can communicate simultaneously with other users of the network using distinct frequencies. The spectrum of available frequencies is limited; thus, efficient solutions to the frequency-allocation and the call-control problems are essential. In the frequency-allocation problem, given users that wish to communicate, the objective is to minimize the required spectrum of frequencies so that communication can be established without signal interference. 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 served. We consider cellular, planar, and arbitrary network topologies.
In particular, we study the on-line version of both problems using competitiveanalysis. For frequency allocation in cellular networks, we improve the best known competitive ratio upper bound of 3 achieved by the folklore Fixed Allocation algorithm, by presenting an almost tight competitiveanalysis for the greedy algorithm; we prove that its competitive ratio is between 2.429 and 2.5 . For the call-control problem, we present the first randomized algorithm that beats the deterministic lower bound of 3 achieving a competitive ratio between 2.469 and 2.651 for cellular networks. Our analysis has interesting extensions to arbitrary networks. Also, using Yao's Minimax Principle, we prove two lower bounds of 1.857 and 2.086 on the competitive ratio of randomized call-control algorithms for cellular and arbitrary planar networks, respectively.

Abstract: We address the call control problem 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 available frequency spectrum is limited; hence, its management should be done efficiently. The objective of the call control problem is, given a spectrum of available frequencies and users that wish to communicate in a cellular network, to maximize the number of users that communicate without signal interference. We study the online version of the problem in cellular networks using competitiveanalysis and present new upper and lower bounds.

Abstract: In this paper we present an efficient general simulation strategy for
computations designed for fully operational BSP machines of n ideal processors,
on n-processor dynamic-fault-prone BSP machines. The fault occurrences are failstop
and fully dynamic, i.e., they are allowed to happen on-line at any point of the
computation, subject to the constraint that the total number of faulty processors
may never exceed a known fraction. The computational paradigm can be exploited
for robust computations over virtual parallel settings with a volatile underlying
infrastructure, such as a NETWORK OF WORKSTATIONS (where workstations may be
taken out of the virtual parallel machine by their owner).
Our simulation strategy is Las Vegas (i.e., it may never fail, due to backtracking
operations to robustly stored instances of the computation, in case of locally
unrecoverable situations). It adopts an adaptive balancing scheme of the workload
among the currently live processors of the BSP machine.
Our strategy is efficient in the sense that, compared with an optimal off-line
adversarial computation under the same sequence of fault occurrences, it achieves an O
¡
.log n ¢ log log n/2¢
multiplicative factor times the optimal work (namely, this
measure is in the sense of the “competitive ratio” of on-line analysis). In addition,
our scheme is modular, integrated, and considers many implementation points.
We comment that, to our knowledge, no previous work on robust parallel computations
has considered fully dynamic faults in the BSP model, or in general distributed
memory systems. Furthermore, this is the first time an efficient Las Vegas
simulation in this area is achieved.

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 competitiveanalysis.
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.