Abstract: We propose a MAC protocol for mobile ad hoc networks that
uses power control for the RTS/CTS and DATA frame
transmissions in order to improve energy and capacity
utilization efficiency. Unlike IEEE 802.11, in our scheme the
RTS frames are not sent using the maximum transmission
power to silence neighbouring nodes, and the CTS frames do
not silence all receiving nodes to the same degree. In contrast,
the transmission power of the RTS frames follows a slow
start principle, while the CTS frames, which are sent at
maximum transmission power, prevent the neighbouring
nodes from transmitting their DATA frames with power more
than a computed threshold, while allowing them to transmit at
power levels less than that threshold. This is done by
including in the RTS and the CTS frames additional
information, such as the power of the transmissions, and the
interference tolerance of the nodes. Moreover the DATA
frames are sent at the minimum required transmission power
increased by a small margin to ensure connectivity with the
intended receiver, so as to cause minimal interference to
neighbouring nodes and allow for future interference to be
added to the receiver of the DATA frames. The power to be
used by the transmitter is computed by the recipient of the
RTS frame and is included in the CTS frame. It is expected
that a network with such a power management scheme would
achieve a better throughput performance and more power
savings than a network without such a scheme.

Abstract: We propose a MAC protocol for mobile ad hoc networks that
uses power control for the RTS/CTS and DATA frame
transmissions in order to improve energy and capacity
utilization efficiency. Unlike IEEE 802.11, in our scheme the
RTS frames are not sent using the maximum transmission
power to silence neighbouring nodes, and the CTS frames do
not silence all receiving nodes to the same degree. In contrast,
the transmission power of the RTS frames follows a slow
start principle, while the CTS frames, which are sent at
maximum transmission power, prevent the neighbouring
nodes from transmitting their DATA frames with power more
than a computed threshold, while allowing them to transmit at
power levels less than that threshold. This is done by
including in the RTS and the CTS frames additional
information, such as the power of the transmissions, and the
interference tolerance of the nodes. Moreover the DATA
frames are sent at the minimum required transmission power
increased by a small margin to ensure connectivity with the
intended receiver, so as to cause minimal interference to
neighbouring nodes and allow for future interference to be
added to the receiver of the DATA frames. The power to be
used by the transmitter is computed by the recipient of the
RTS frame and is included in the CTS frame. It is expected
that a network with such a power management scheme would
achieve a better throughput performance and more power
savings than a network without such a scheme.

Abstract: We consider the problem of planning a mixed line
rates (MLR) wavelength division multiplexing (WDM) transport
optical network. In such networks, different modulation formats
are usually employed to support the transmission at different line
rates. Previously proposed planning algorithms, have used a
transmission reach limit for each modulation format/line rate,
mainly driven by single line rate systems. However, transmission
experiments in MLR networks have shown that physical layer
interference phenomena are more significant between
transmissions that utilize different modulation formats. Thus, the
transmission reach of a connection with a specific modulation
format/line rate depends also on the other connections that copropagate
with it in the network. To plan a MLR WDM network,
we present routing and wavelength assignment (RWA)
algorithms that take into account the adaptation of the
transmission reach of each connection according to the use of the
modulation formats/line rates in the network. The proposed
algorithms are able to plan the network so as to alleviate
interference effects, enabling the establishment of connections of
acceptable quality over paths that would otherwise be prohibited

Abstract: We design and implement an algorithm for solving the static RWA problem based on an LP relaxation formulation. This formulation is capable of providing integer optimal solutions despite the absence of integrality constraints for a large subset of RWA input instances. In static RWA there is no a-priori knowledge of the channels usage and the interference among them cannot be avoided once the solution has been found. To take into consideration adjacent channel interference, we extend our formulation and model the interference by a set of analytical formulas as additional constraints on RWA.

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: 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 competitive analysis. 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 competitive analysis 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 competitive analysis. 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 competitive analysis 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: ManyWSN algorithms and applications are based on knowledge
regarding the position of nodes inside the network area.
However, the solution of using GPS based modules in order
to perform localization in WSNs is a rather expensive solution
and in the case of indoor applications, such as smart
buildings, is also not applicable. Therefore, several techniques
have been studied in order to perform relative localization
in WSNs; that is, to compute the position of
a node inside the network area relatively to the position
of other nodes. Many such techniques are based on indicators
like the Radio Signal Strength Indicator (RSSI)
and the Link Quality Indicator (LQI). These techniques are
based on the assumption that there is strong correlation between
the Euclidian distance of the communicating motes
and these indicators. Therefore, high values of RSSI and
LQI should indicate physical proximity of two communicating
nodes. However, these indicators do not depend solely on
distance. Physical obstacles, ambient electromagnetic noise
and interferences from other wireless transmissions also affect
the quality of wireless communication in a stochastic
way. In this paper we propose, implement, experimentally
fine tune and evaluate a localization algorithm that exploits
the stochastic nature of interferences during wireless communications
in order to perform localization in WSNs. Our
algorithm is particularly designed for in-door localisation of
moving people in smart buildings. The localisation achieved
is fine-grained, i.e. the position of the target mote is successfully
computed with approximately one meter accuracy.
This fine-grained localisation can be used by smart Building
Management Systems in many applications such as room
adaptation to presence. In our scenario, our proposed algorithm is used by a smart room in order to localise the
position of people inside the room and adapt room illumination
accordingly.

Abstract: The technological as well as software advances in
microelectronics and embedded component design have led to the
development of low cost, small-sized devices capable of forming
wireless, ad-hoc networks and sensing a number of qualities of
their environment, while performing computations that depend
on the sensed qualities as well as information received by their
peers. These sensor networks rely on the collective power of
the separate devices as well as their computational and sensing
capabilities to understand "global" environmental states through
locally sampled information and local sensor interactions. Due
to the locality of the sensor networks, that naturally arises due
to the locality of their communications capabilities, a number
of interesting connections exist between these networks and
geometrical concepts and problems. In this paper we study two
simple problems that pertain to the formation of low power
and low interference communication patterns in fixed topology
sensor networks. We study the problem of using multihop
communication links instead of direct ones as well as the problem
of forming a communication ring of sensor networks so as to
reduce power consumption as well as interference from other
nodes. Our focus is on the connection between sensor networks
and geometrical concepts, rather than on practicality, so as to
highlight their interrelationship.

Abstract: We consider the offline version of the routing and
wavelength assignment (RWA) problem in transparent all-optical networks. In such networks and in the absence of regenerators, the signal quality of transmission degrades due to physical layer
impairments. We initially present an algorithm for solving the static RWA problem based on an LP relaxation formulation that tends to yield integer solutions. To account for signal degradation due to physical impairments, we model the effects of the path length, the path hop count, and the interference among ligthpaths by imposing additional (soft) constraints on RWA. The objective of the resulting optimization problem is not only to serve the
connection requests using the available wavelengths, but also to minimize the total accumulated signal degradation on the selected lightpaths. Our simulation studies indicate that the proposed RWA algorithms select the lightpaths for the requested connections so as to avoid impairment generating sources, thus dramatically reducing the overall physical-layer blocking when compared to RWA algorithms that do not account for impairments.

Abstract: We consider the online impairment-aware routing
and wavelength assignment (IA-RWA) problem in transparent
WDM networks. To serve a new connection, the online algorithm,
in addition to finding a route and a free wavelength (a lightpath),
has to guarantee its transmission quality, which is affected by
physical-layer impairments. Due to interference effects, the establishment
of the new lightpath affects and is affected by the other
lightpaths. We present two multicost algorithms that account
for the actual current interference among lightpaths, as well as
for other physical effects, performing a cross-layer optimization
between the network and physical layers. In multicost routing,
a vector of cost parameters is assigned to each link, from which
the cost vectors of the paths are calculated. The first algorithm
utilizes cost vectors consisting of impairment-generating source
parameters, so as to be generic and applicable to different physical
settings. These parameters are combined into a scalar cost
that indirectly evaluates the quality of candidate lightpaths. The
second algorithm uses specific physical-layer models to define
noise variance-related cost parameters, so as to directly calculate
the -factor of candidate lightpaths. The algorithms find a set of
so-called nondominated paths to serve the connection in the sense
that no path is better in the set with respect to all cost parameters.
To select the lightpath, we propose various optimization functions
that correspond to different IA-RWA algorithms. The proposed
algorithms combine the strength of multicost optimization with
low execution times, making them appropriate for serving online
connections

Abstract: In this work we study the combination of multicost
routing and adjustable transmission power in wireless
ad hoc networks, so as to obtain dynamic energy- and
interference-efficient routes to optimize network performance.
In multi-cost routing, a vector of cost parameters is
assigned to each network link, from which the cost vectors
of candidate paths are calculated. Only at the end these
parameters are combined in various optimization functions,
corresponding to different routing algorithms, for selecting
the optimal path. The multi-cost routing problem is a
generalization of the multi-constrained problem, where no
constraints exist, and is also significantly more powerful
than single-cost routing. Since energy is an important
limitation of wireless communications, the cost parameters
considered are the number of hops, the interference caused,
the residual energy and the transmission power of the
nodes on the path; other parameters could also be included,
as desired. We assume that nodes can use power control to
adjust their transmission power to the desired level. The
experiments conducted show that the combination of multicost
routing and adjustable transmission power can lead to
reduced interference and energy consumption, improving
network performance and lifetime.

Abstract: In this work we study the combination of
multicost routing and adjustable transmission power
in wireless ad-hoc networks, so as to obtain dynamic
energy and interference-efficient routes to optimize network performance. In multi-cost routing, a vector of
cost parameters is assigned to each network link, from
which the cost vectors of candidate paths are calcu-
lated. Only at the end are these parameters combined in
various optimization functions, corresponding to different routing algorithms, for selecting the optimal path.
The multi-cost routing problem is a generalization of
the multi-constrained problem, where no constraints exist, and is also significantly more powerful than single-
cost routing. Since energy is an important limitation of
wireless communications, the cost parameters consid
ered are the number of hops, the interference caused,
the residual energy and the transmission power of the
nodes on the path; other parameters could also be in
cluded, as desired.We assume that nodes can use power
control to adjust their transmission power to the desired
level. The experiments conducted show that the com
bination of multi-cost routing and adjustable transmis sion power can lead to reduced interference and energy
consumption, improving network performance and life-
time.

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 competitive analysis and present new upper and lower bounds.

Abstract: The Frequency Assignment Problem (FAP) in radio networks is the problem of assigning frequencies to transmitters exploiting frequency reuse while keeping signal interference to acceptable levels. The FAP is usually modelled by variations of the graph coloring problem. The Radiocoloring (RC) of a graph G(V,E) is an assignment function Φ: V → IN such that ¦Φ(u)-Φ(v)≥ 2, when u; v are neighbors in G, and ¦Φ(u)-Φ(v)≥1 when the minimum distance of u; v in G is two. The discrete number and the range of frequencies used are called order and span, respectively. The optimization versions of the Radiocoloring Problem (RCP) are to minimize the span or the order. In this paper we prove that the min span RCP is NP-complete for planar graphs. Next, we provide an O(nΔ) time algorithm (¦V¦ = n) which obtains a radiocoloring of a planar graph G that approximates the minimum order within a ratio which tends to 2 (where Δ the maximum degree of G). Finally, we provide a fully polynomial randomized approximation scheme (fpras) for the number of valid radiocolorings of a planar graph G with λ colors, in the case λ ≥ 4λ + 50.

Abstract: We consider the offline version of the routing and
wavelength assignment (RWA) problem in transparent all-optical
networks. In such networks and in the absence of regenerators,
the signal quality of transmission degrades due to physical layer
impairments. Because of certain physical effects, routing choices
made for one lightpath affect and are affected by the choices made
for the other lightpaths. This interference among the lightpaths
is particularly difficult to formulate in an offline algorithm since,
in this version of the problem, we start without any established
connections and the utilization of lightpaths are the variables of
the problem.We initially present an algorithm for solving the pure
(without impairments) RWA problem based on a LP-relaxation
formulation that tends to yield integer solutions. Then, we extend
this algorithm and present two impairment-aware (IA) RWA algorithms
that account for the interference among lightpaths in their
formulation. The first algorithm takes the physical layer indirectly
into account by limiting the impairment-generating sources. The
second algorithm uses noise variance-related parameters to directly
account for the most important physical impairments. The
objective of the resulting cross-layer optimization problem is not
only to serve the connections using a small number of wavelengths
(network layer objective), but also to select lightpaths that have
acceptable quality of transmission (physical layer objective).
Simulations experiments using realistic network, physical layer,
and traffic parameters indicate that the proposed algorithms can
solve real problems within acceptable time.

Abstract: We consider the problem of planning a mixed line rates (MLR) WDM transport optical network. In a MLR network, the interference between different modulation format/line rate connections affect the transmission reach of these connections. We present algorithms to plan a MLR network that take into account the variation of the transmission reach according to the use of the modulation formats/line rates in the network.

Abstract: The Frequency Assignment Problem (FAP) in radio networks is the problem of assigning frequencies to transmitters, by exploiting frequency reuse while keeping signal interference to acceptable levels. The FAP is usually modelled by variations of the graph coloring problem. A Radiocoloring (RC) of a graph G(V,E) is an assignment function View the MathML source such that |{\"O}(u)-{\"O}(v)|greater-or-equal, slanted2, when u,v are neighbors in G, and |{\"O}(u)-{\"O}(v)|greater-or-equal, slanted1 when the distance of u,v in G is two. The number of discrete frequencies and the range of frequencies used are called order and span, respectively. The optimization versions of the Radiocoloring Problem (RCP) are to minimize the span or the order. In this paper we prove that the radiocoloring problem for general graphs is hard to approximate (unless NP=ZPP) within a factor of n1/2-{\aa} (for any View the MathML source), where n is the number of vertices of the graph. However, when restricted to some special cases of graphs, the problem becomes easier. We prove that the min span RCP is NP-complete for planar graphs. Next, we provide an O(n{\"A}) time algorithm (|V|=n) which obtains a radiocoloring of a planar graph G that approximates the minimum order within a ratio which tends to 2 (where {\"A} the maximum degree of G). Finally, we provide a fully polynomial randomized approximation scheme (fpras) for the number of valid radiocolorings of a planar graph G with {\"e} colors, in the case where {\"e}greater-or-equal, slanted4{\"A}+50.

Abstract: The Frequency Assignment Problem (FAP) in radio networks is the problem of assigning frequencies to transmitters, by exploiting frequency reuse while keeping signal interference to acceptable levels. The FAP is usually modelled by variations of the graph coloring problem. A Radiocoloring (RC) of a graph G(V,E) is an assignment function View the MathML source such that |{\"O}(u)-{\"O}(v)|greater-or-equal, slanted2, when u,v are neighbors in G, and |{\"O}(u)-{\"O}(v)|greater-or-equal, slanted1 when the distance of u,v in G is two. The number of discrete frequencies and the range of frequencies used are called order and span, respectively. The optimization versions of the Radiocoloring Problem (RCP) are to minimize the span or the order. In this paper we prove that the radiocoloring problem for general graphs is hard to approximate (unless NP=ZPP) within a factor of n1/2-{\aa} (for any View the MathML source), where n is the number of vertices of the graph. However, when restricted to some special cases of graphs, the problem becomes easier. We prove that the min span RCP is NP-complete for planar graphs. Next, we provide an O(n{\"A}) time algorithm (|V|=n) which obtains a radiocoloring of a planar graph G that approximates the minimum order within a ratio which tends to 2 (where {\"A} the maximum degree of G). Finally, we provide a fully polynomial randomized approximation scheme (fpras) for the number of valid radiocolorings of a planar graph G with {\"e} colors, in the case where {\"e}greater-or-equal, slanted4{\"A}+50.

Abstract: The Frequency Assignment Problem (FAP) in radio networks is the problem of assigning frequencies to transmitters exploiting frequency reuse while keeping signal interference to acceptable levels. The FAP is usually modelled by variations of the graph coloring problem. A Radiocoloring (RC) of a graph G(V,E) is an assignment function View the MathML source such that |{\"E}(u)−{\"E}(v)|greater-or-equal, slanted2, when u,v are neighbors in G, and |{\"E}(u)−{\"E}(v)|greater-or-equal, slanted1 when the distance of u,v in G is two. The discrete number of frequencies used is called order and the range of frequencies used, span. The optimization versions of the Radiocoloring Problem (RCP) are to minimize the span (min span RCP) or the order (min order RCP).
In this paper, we deal with an interesting, yet not examined until now, variation of the radiocoloring problem: that of satisfying frequency assignment requests which exhibit some periodic behavior. In this case, the interference graph (modelling interference between transmitters) is some (infinite) periodic graph. Infinite periodic graphs usually model finite networks that accept periodic (in time, e.g. daily) requests for frequency assignment. Alternatively, they can model very large networks produced by the repetition of a small graph.
A periodic graph G is defined by an infinite two-way sequence of repetitions of the same finite graph Gi(Vi,Ei). The edge set of G is derived by connecting the vertices of each iteration Gi to some of the vertices of the next iteration Gi+1, the same for all Gi. We focus on planar periodic graphs, because in many cases real networks are planar and also because of their independent mathematical interest.
We give two basic results:
• We prove that the min span RCP is PSPACE-complete for periodic planar graphs.
• We provide an O(n({\"A}(Gi)+{\'o})) time algorithm (where|Vi|=n, {\"A}(Gi) is the maximum degree of the graph Gi and {\'o} is the number of edges connecting each Gi to Gi+1), which obtains a radiocoloring of a periodic planar graph G that approximates the minimum span within a ratio which tends to View the MathML source as {\"A}(Gi)+{\'o} tends to infinity.
We remark that, any approximation algorithm for the min span RCP of a finite planar graph G, that achieves a span of at most {\'a}{\"A}(G)+constant, for any {\'a} and where {\"A}(G) is the maximum degree of G, can be used as a subroutine in our algorithm to produce an approximation for min span RCP of asymptotic ratio {\'a} for periodic planar graphs.

Abstract: The Frequency Assignment Problem (FAP) in radio networks is the problem of assigning frequencies to transmitters exploiting frequency reuse while keeping signal interference to acceptable levels. The FAP is usually modelled by variations of the graph coloring problem. The Radiocoloring (RC) of a graph G(V,E) is an assignment function {\"O}: V → IN such that ∣{\"O}(u) - {\"O}(v)∣ ≥2, when u, v are neighbors in G, and ∣{\"O}(u) - {\"O}(v)∣ ≥1 when the distance of u, v in G is two. The range of frequencies used is called span. Here, we consider the optimization version of the Radiocoloring Problem (RCP) of finding a radiocoloring assignment of minimum span, called min span RCP. In this paper, we deal with a variation of RCP: that of satisfying frequency assignment requests with some periodic behavior. In this case, the interference graph is an (infinite) periodic graph. Infinite periodic graphs model finite networks that accept periodic (in time, e.g. daily) requests for frequency assignment. Alternatively, they may model very large networks produced by the repetition of a small graph. A periodic graph G is defined by an infinite two-way sequence of repetitions of the same finite graph G i (V i ,E i ). The edge set of G is derived by connecting the vertices of each iteration G i to some of the vertices of the next iteration G i +1, the same for all G i . The model of periodic graphs considered here is similar to that of periodic graphs in Orlin [13], Marathe et al [10]. We focus on planar periodic graphs, because in many cases real networks are planar and also because of their independent mathematical interest. We give two basic results: - We prove that the min span RCP is PSPACE-complete for periodic planar graphs. - We provide an O(n({\"A}(G i ) + {\'o})) time algorithm, (where ∣V i ∣ = n, {\"A}(G i ) is the maximum degree of the graph G i and {\'o} is the number of edges connecting each G i to G i +1), which obtains a radiocoloring of a periodic planar graph G that approximates the minimum span within a ratio which tends to 2 as {\"A}(Gi) + {\'o} tends to infinity.

Abstract: We consider the problem of planning a mixed line rate
(MLR) wavelength division multiplexing (WDM) transport
optical network. In such networks, different modulation formats
are usually employed to support transmission at different line
rates. Previously proposed planning algorithms have used a
transmission reach bound for each modulation format/line rate,
mainly driven by single line rate systems. However, transmission
experiments in MLR networks have shown that physical layer
interference phenomena are more severe among transmissions
that utilize different modulation formats. Thus, the transmission
reach of a connection with a specific modulation format/line rate
depends also on the other connections that co-propagate with it
in the network. To plan a MLR WDM network, we present
routing and wavelength assignment (RWA) algorithms that
adapt the transmission reach of each connection according to the
use of the modulation formats/line rates in the network. The
proposed algorithms are able to plan the network so as to
alleviate cross-rate interference effects, enabling the
establishment of connections of acceptable quality over paths that
would otherwise be prohibited.

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.