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A General Interference-Aware Framework for Joint Routing and Link Scheduling in Wireless Mesh Networks

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IEEE Network • January/February 2008
32
0890-8044/08/$25.00 © 2008 IEEE
n a wireless mesh network (WMN) [1] end users are pro- vided with wireless broadband connectivity by means of apredefined system hierarchy. The end terminals, alsoreferred to as mesh clients (MCs), are connected to spe-cial nodes, called mesh routers (MRs). These nodes do notgenerate traffic, since they are simply meant to relay the pack-ets of their MCs. Additionally, some MRs, called mesh accesspoints (MAPs), can be provided with cabled connection, andcan therefore act as gateways toward the Internet. A MAP isalso wirelessly interconnected to every other MR in a multi-hop fashion. In contrast, an MC can interact only with theMR to which it is connected. MRs form what is usuallyreferred to as the
backbone
of the WMN, which can physicallycover a large region using wireless multihop communication. A possible realization of a WMN is depicted in Fig. 1. Thisstructure offers a good cost/benefit balance, since it almostentirely avoids cable setup. For this reason, it is deemed appli-cable in rural areas as well as dense residential or businessareas, where the deployment of wireline networks may be tooexpensive or difficult because of physical obstacles.The first hop from any MC to its related MR is oftenassumed to employ widespread cost-effective radio technolo-gies (e.g., IEEE 802.11 [2]). The multihop communicationamong MRs is an open issue and involves several challengesrelated to different layers of the protocol stack. On one hand,the creation of low-interference high-rate paths to the MAPsis key to achieve good rates at each MR. On the other hand,the link layer needs to schedule packets over multiple links inorder to achieve good transmission parallelism and possiblyforward more data toward the MAPs at the same time. Find-ing the optimal path toward an MAP and scheduling links soas to maximize the transmission parallelism are traditionallyperformed by the routing algorithm running at the networklayer and by the medium access control (MAC) protocol atthe link layer, respectively. However, in a multihop wirelessnetwork, the routing algorithm needs to deal with link schedul-ing. If predefined routes (e.g., based on a shortest path criteri-on) are used, any scheduling algorithm will be forced toactivate only the links belonging to that route. The combinedresult may be suboptimal in the sense that not all availablenetwork resources are utilized. In [3] the authors addressedthe question of combining optimal link scheduling with subop-timal routing and vice versa, and pointed out that these tasksaffect each other, and their optimality is strongly coupled.This is mainly due to the broadcast nature of the wirelessmedium, which combines the advantage of allowing each MRto communicate with multiple MRs through a single networkinterface with the disadvantage that simultaneous transmis-sions from different MRs may interfere with each other.Therefore, the main conclusion of [3] is that interferenceawareness available at the link layer must be exploited at therouting level.Cross-layer design, which solves a joint routing and schedul-ing (JRS) optimization problem, is thus considered verypromising to fully exploit WMN capacity. Recently, severalpapers have proposed solutions in this area. An exampleframework for JRS has been proposed in [4], where theauthors introduce a heuristic technique to solve the cross-layer problem. In [5] JRS for multihop networks is presented, which also includes power control. The leitmotif of all the
I
I
Leonardo Badia and Alessandro Erta, IMT Lucca Institute for Advanced StudiesLuciano Lenzini, University of PisaMichele Zorzi, University of Padova Abstract
Joint design and optimization of traditionally independent problems such as routingand link scheduling have recently become one of the leading research trends inwireless mesh networks. Although technically challenging, cross-layering is, in fact,expected to bring significant benefits from the network resource exploitation stand-point to achieve high system utilization. In this article we propose a versatile frame-work for joint design of routing and link scheduling, introducing the notion of linkactivation constraints, which are related to the transceiver capability and thebroadcast nature of the wireless medium. To this end, we introduce a taxonomy of wireless interference models to harmonize existing approaches presented in the lit-erature. Finally, we evaluate the impact on network capacity of the various interfer-ence models when optimal joint routing and link scheduling are employed.
A General Interference-Aware Framework for Joint Routing and Link Scheduling in Wireless Mesh Networks
IEEE Network • January/February 2008
33
papers described above is that approaching a JRS problemrequires the specification of an
interference model
, which basi-cally defines whether or not simultaneous transmissions of dif-ferent MRs can be correctly decoded at their receivers. Themost widely used classification of interference models in theliterature dates back to [6], and distinguishes between the so-called
physical
and
protocol
interference models. In the for-mer, the feasibility of simultaneous link activations isdetermined by the signal-to-interference ratio (SIR) of allreceivers being above a given threshold. The latter insteadimposes simpler interference conditions modeled throughgraph neighborhood relationships. The main problem of theexisting approaches is that the proposed algorithms arestrongly coupled with the interference model adopted. Thus,they may turn out to be suboptimal if more realistic modelsare considered.In this article we present a general framework that decou-ples the notions of transceiver capability and wireless inter-ference from the JRS algorithms. To study routing andscheduling under the graph formulation, we use the languageof constrained linear programming problems, as commonlydone in related work [4]. We represent the backbone of aWMN as a directed graph
G
= (
N
,
E
). The
nodes
in set
N
arethe MRs, which are in turn connected by
directed edges
belonging to set
E
, which are ordered pairs of nodes and thusrepresent the communication links of the backbone. The link where a sender node i
∈
N
transmits to a receiver
j
∈
N
isrepresented by (
i
,
j
), included in
E
only if node
j
can receivea transmission from
i
in the absence of any other interfer-ence source. We also denote with
R
i
and
S
i
the set of nodesthat are possible receivers from and senders to node
i
,respectively (i.e., the
one-hop output and input neighbors
of
i
). Formally:
R
i
= {
j
∈
N
: (
i
,
j
)
∈
E
},
S
i
= {
j
∈
N
: (
j
,
i
)
∈
E
}.We also consider a parameter
g
ij
corresponding to the wire-less link gain when transmitting from
i
to
j
. The rule for theinclusion of (
i
,
j
) in
E
can thus be that
g
ij
is above a giventhreshold. Note that in realistic wireless scenarios, the per-formance of the forward and reverse links are not necessari-ly the same. Actually, the existence of the reverse link (
j
,
i
)for every (
i
,
j
)
∈
E
is not even guaranteed. One notableexception in this sense is represented by WMNs using theIEEE 802.11 MAC on the backbone, since in this standardbidirectionality of links is required.We speak of
activation
of link
e
= (
i
,
j
) at time
t
if
i
istransmitting to
j
at time
t
. To thisend, we use a binary indicator vari-able
x
ij
(
t
), equal to 1 if (
i
,
j
) isactive at time
t
and 0 otherwise.The JRS problem corresponds todetermining the pattern of linkactivations described by variables
x
e
(
t
) as time goes by. To someextent, this addresses both schedul-ing and routing as the routes canbe implicitly inferred by trackingsubsequent link activations. Forexample, consider the WMN rep-resented in Fig. 2. In this networka packet can be routed from A toF, say, by activating links A
→
B, B
→
E, and eventually E
→
F atthree separate time instants. Thesesubsequent activations must be apacket transmission time apartfrom each other.Furthermore, we speak of
con- straints
to describe any limitationimposed on the activation of links by MAC and physicallayers. In the rest of this article we discuss the constraintsthat must be satisfied for multiple transmissions to be feasi-ble, and their impact on network performance. The analysisof these constraints is subdivided into two parts. First, wetalk about the constraints involving the physical capabilitiesof the radio transceiver. This class of constraints is verygeneral and independent of those due to wireless interfer-ence, and confusion between the two concepts should beavoided. Second, we describe the constraints specificallyrelated to interference, also giving pointers to interferencemodels present in the literature and referring to the MACprotocols specified in some common wireless interfacestandards that inspire the formulation of these constraints.Finally, we provide numerical insights into the performanceof JRS in WMNs when different interference models areemployed. To this end, we consider an underlying space-and time-division multiple access (STDMA) scheme whereJRS is performed.
Figure 1.
A possible structure for a wireless mesh network.
Mesh clientsWireless meshbackboneMesh clientsMesh clientsMesh routersMesh access pointMesh access point
Figure 2.
A sample wireless mesh network topology.
A BCDE F
IEEE Network • January/February 2008
34
Wireless Transceiver Constraints
The first constraint on link activation to solve JRS relates tothe fact that the node capabilities for transmission and recep-tion are limited. In particular, we focus on WMNs operating with a single omnidirectional antenna on narrowband chan-nels, where it is not possible to receive simultaneously frommultiple sources. Special techniques, such as wideband code-division multiple access (WCDMA) or multiple-input multi-ple-output (MIMO) channels, can improve this condition. Forsimplicity, we do not investigate these issues; however, thesimple model analyzed here can easily be extended to alsotake these cases into account. Therefore, we assume that atmost one signal can be decoded, and any other transmissionthe receiver is able to hear can only be regarded as interfer-ence. The presence of interference at the receiver does notnecessarily mean that the packet cannot be correctly decoded:the interference model comes into play at this point. Howev-er, regardless of the interference model, the maximum num-ber of possible simultaneous successful receptions is
one
. A similar situation happens for the transmitter. In particu-lar, observe that we focus on unicast transmissions. Thus, eventhough the wireless medium is broadcast, and therefore thesame transmission can be heard by many receivers, the mes-sage has only one intended destination. On the other hand,
multiple transmissions
from the same node are not possible.This assumption can be modified to account for cooperationamong nodes [7] or network coding [8], which are not dis-cussed here for space limitations, even though they are verypromising research directions in wireless networks. For thesereasons, we assume that a node can serve as the transmitteron at most one active link.Finally, not only can simultaneous transmissions and recep-tions at the same node be at most one, but also the wirelesscommunication medium is intrinsically
half-duplex
; that is, anode cannot listen on the same channel on which it is trans-mitting at the same time, or the transmitted power signal will jam any packet reception. Therefore, we impose the con-straint of not activating more than one operation (i.e., eithertransmission or reception) for each node. Formally, this con-straint translates into(1)The importance of constraint 1 is often underestimated when modeling multihop wireless networks. In fact, even theneed for such a constraint is rarely mentioned. This may bedue to mistaking it for an interference condition, whereas itrefers to a physical limitation that holds irrespective of theinterference model. To clarify this aspect, consider Fig. 2again to check compatibility among link activations. Theaforementioned transceiver constraint prevents, for example,simultaneous activation of links A
→
B and A
→
D, sincethey share the same transmitter. Also, B
→
E and D
→
Eshould not be activated together, as they share the samereceiver; nor should A
→
B and B
→
E, since B cannotreceive and transmit simultaneously. Constraint 1, instead,does not say anything about simultaneous activation, forexample, of links A
→
D and B
→
E, which involve entirelydifferent pairs of nodes. However, due to the broadcast char-acteristic of wireless propagation, nodes can be reached by atransmission even though they are not the intended receiver,as happens, say, with transmission A
→
D also reaching E.Thus, this kind of transmission is possibly limited by the
wire- less interference constraint
, a further limitation described in thenext section.
Wireless Interference Constraint
The usual classification of wireless interference models distin-guishes between the
protocol
and the
physical interference model
[6]. Sometimes, other extensions of these models areintroduced to represent further transmission aspects such asdirectional antennas, thresholds for the capture effect, and soon. An overview of these aspects can be found in [9].The protocol interference model, in its srcinal version, fol-lows the rationale behind the IEEE 802.11 MAC, which mod-els interference as causing
collision
, or the impossibility of correctly decoding a received packet if some neighboringnodes simultaneously exchange messages, disturbing the ongo-ing transmission. The main advantage of an interferencedescription through the protocol model is its conceptual sim-plicity and the ease of mathematically formalizing the result-ing interference conditions.The rules of the protocol interference model impose thecondition that when certain transmissions are assumed tocause collision, they are simply forbidden to be simultaneouslyactivated. A way to formalize this constraint is to define, asso-ciated with any edge
e
∈
E
, a
conflicting set
I
(
e
)
⊆
E
\ {
e
}. Therequired condition is that if edge
e
is active,
I
(
e
) must containno active edges. Formally,(2)In the literature, several possibilities have been presentedto determine the set
I
(
e
), all generically called the
protocolinterference model
but presenting subtle differences. Our goalhere is to propose a taxonomy for what we identify as a classof interference models, since it actually encompasses severalmathematical formulations. Moreover, we aim to show therelationship, suggested by the name itself, with the MAC pro-tocols possibly used in the WMN. As a first step, we intentionally introduce a very simplemember of the protocol interference model class, using thestraightforward possibility
I
(
e
) =
E
\ {
e
} for all
e
∈
E
; that is, atmost one edge can be activated at any given time throughoutthe whole network. In other words, either exactly one edge isactive, or no edge is active at all. Due to this property, werefer to this version as the
01protocol
model. Even though it isquite oversimplified, this model can be useful as a theoreticalterm of comparison. In fact, the 01protocol model takes themost conservative approach to interference protection, sospace diversity is not exploited to obtain transmission paral-lelism. Actually, this situation necessarily occurs in certainspecial topologies. For example, in [9] this model is men-tioned as used in [2] to derive the performance of the dis-tributed control function (DCF) in an IEEE 802.11 hotspotcontrolled by a single access point. Indeed, it is true that the01protocol model holds here, but the reason is not electro-magnetic interference, but rather that the topology is a starnetwork (every node is connected only to the access point).Therefore, this situation is due to the wireless transceiver con-straint, not to interference. Apart from the 01protocol model, other versions rely onpropagation aspects, described with simplified geometricapproaches. The idea is to define interference regions, areasof the physical space where ongoing transmissions interfere with each other and cannot coexist. We also remark that mostof the existing work takes a very simplified approach wherethe interference region is modeled as a circular area withfixed range equal for all nodes. Within these regions, therationale of the 01protocol model is kept, so the limitation of having at most one active transmission is restricted to a small-
if then
x t x t
e f f e
(),().
()
==
∈
∑
10
I
∀∈∀+≤
∈∈
∑∑
i t x t x t
ji ij j j
ii
N
R S
,:()().1
IEEE Network • January/February 2008
35
er region. In the end this simply translates to a different (i.e.,stricter) definition of the set
I
(
e
).In the following we implicitly assume that all propagationand interference aspects are again described through thegraph
G
= (
N
,
E
); not only can node
i
∈
N
transmit to
j
∈
N
if and only if (
i
,
j
)
∈
E
, but also,
i
can disturb other transmissionsintended for
j
from other nodes. Actually, the requirement of correct reception is generally more restrictive than pure dis-turbance, since it is possible to jam the reception of anothernode without being able to transmit to it. However, for sim-plicity we assume that the transmission range of a node equalsits interference range. The analysis of the cases where thisdoes not happen can be done in an entirely similar manner byconsidering additional
virtual
links not representing any realcommunication, just interference.In the srcinal and more common version, which we callhereafter the
11protocol
model, it is implicitly assumed thatIEEE 802.11 MAC is employed. Note that IEEE 802.11 isdesigned to work for bidirectional links only and heavily relieson this hypothesis: for IEEE 802.11-based networks, (
i
,
j
)
∈
E
if and only if (
j
,
i
) also belongs to
E
. Following IEEE 802.11MAC, the 11protocol model dictates that a transmission on (
i
,
j
)
∈
E
is interference-free and can therefore be activated onlyif there are no transmitters or receivers belonging to anyactive link that can disturb either
i
or
j
. Note that the reasonfor requiring the absence of interferers in both the receiver’sand transmitter’s disturbance area of both interfering trans-mitters and receivers is that the IEEE 802.11 standard forcesthe receiver to acknowledge request to send (RTS) and datapackets with clear to send (CTS) and acknowledgments(ACKs), respectively. In other words, during the ACK exchange, a logical receiver becomes a physical
transmitter
, soit can cause disturbance to others. Similarly, the logical trans-mitter needs to perform
reception
(of ACKs), for which it hasto be collision-free. This also justifies the need for the exis-tence of both forward and reverse links. A possible definition of
I
(
e
) in the 11protocol model is thus
I
((
i
,
j
)) = {(
k
,
l
)
∈
E
, {
k
,
l
}
∩
{
i
,
j
} =
∅
:{
i
,
j
}
∩
(
R
k
∪
R
l
)
≠∅
.(3)Clearly, this condition can be relaxed if the IEEE 802.11MAC protocol is not used (e.g., if IEEE 802.16 is usedinstead). There are differences, not discussed here since theyare out of the scope of this analysis, between the handshakeprocedures of IEEE 802.11 and IEEE 802.16, which changethe relationships of interference among nodes. We can thenformulate a
16protocol interference model
, which proceedsidentically to the 11protocol model, with the notable excep-tion that collision occurs only when the designated receiver isinterfered by another transmitter. Any other combination(transmitter is under coverage of an interfering transmitter, oranother receiver covers either the receiver or the transmitter)does not do any harm. This formally results in
I
((
i
,
j
)) = {(
k
,
l
)
∈
E
, {
k
,
l
}
∩
{
i
,
j
} =
∅
:
j
∈
R
k
}.(4)The 16protocol model simplifies the 11protocol model as itconsiders the receiver
j
being under coverage of an interferingtransmitter
k
as the only situation where collision occurs. The11protocol model instead considers four possible combina-tions as colliding: all cases where
i
or
j
is under coverage of either an interfering transmitter
k
or an interfering receiver
l
.In most papers dealing with WMN backbone management,the 11protocol model is what is meant when the protocolmodel is cited. However, if links are not bidirectional and theMAC does not follow the IEEE 802.11 standard, there is noreason to use the 11protocol model. If the MAC protocoldoes not require acknowledgment, the 16protocol model would be more appropriate.To sum up, the protocol interference model is easy toimplement, and offers several possibilities to both describeMAC aspects, which have been classified in the three differ-ent versions (01protocol, 11protocol, 16protocol) and employthe preferred mathematical model (coverage/disturbancerange, conflict graph, neighborhood relationships). However,these practical advantages come at the price of some theoreti-cal drawbacks. In fact, all versions of the protocol model areimperfect in capturing wireless interference. First of all, thecharacterization of wireless propagation is not entirely realis-tic, especially if multiple power levels are adopted. Moreover,a definite criticism of the protocol model is that interferenceis not a binary relationship [3, 10].For example, strong interference, which leads to packetloss, may be present if more than two specific edges are simul-taneously activated, but not when any two of them are. Con-sider again Fig. 2: it is possible that A
→
D and B
→
E can beactivated together if and only if C
→
F is not active simulta-neously. Thus, the condition of interference cannot be trans-lated into a binary relationship, as there is no specific linkamong A
→
D, B
→
E, and C
→
F that causes interference;the problem is the joint effect of all of them. The conflict set
I
(
e
), which must be evaluated pairwise, is not appropriate inthis case.These problems can be overcome by means of the physicalinterference model, whose rationale is as follows. The packeterror rate (PER) at the receiver is a monotonically increasingfunction of the signal-to-interference-plus-noise ratio (SINR).It is often reasonable to consider a simplified thresholdapproach, where a packet is correctly received with probability1 if the SINR is above a given threshold and always erroneousotherwise. Formally, the following condition must hold:(5) where (
i
,
j
) is the link of interest, the index
k
in the sumdenotes a possible interferer (the intended transmitter
i
isexcluded from the sum),
P
x
is the power emitted by node
x
,and
N
j
is the receiver noise at node
j
. It is not restrictive totake the value
γ
, which defines the SINR threshold, equal forall nodes.Other assumptions, made only for ease of presentation but without loss of generality, as avoiding them would only lead toa more cumbersome (though conceptually identical) formula-tion, are as follows: we neglect the noise terms, and we con-sider an equal power level
P
among all transmitting nodes. Inparticular, the last assumption is equivalent to assuming thatthe power level used by each node is constant over time. Inthis case any element
g
ij
can be replaced by
g
′
ij
=
g
ij
P
i
, thusomitting the power term. Otherwise, an extended framework, where power control is also considered, could be realized byfollowing the rationale presented in [5].In the context of our framework, which describes JRSthrough link activation patterns, the constraint can be formal-ized as follows:(6)Reducing the PER function to a step function with transi-tion value
γ
is indeed an approximation. However, it is stillmuch more accurate than the ones made under the protocolmodels, as it better takes into account physical propagation.
if
x t g g x
ij ij kjk ik
j
(),then
\{}
=≥
∑
∈
1
γ
S
l
(().
\{}
t
k
j
∑
∈
l
R
PgP g N
i ijk i k kj j
Σ
≠
+≥
γ
,
IEEE Network • January/February 2008
36
Moreover, as opposed to the collision assumption, in thephysical model a correct packet reception is allowed even inthe presence of (moderate) interference, and the cumulativecharacter of interference is accounted for. Indeed, the choiceof
γ
depends on the shape of the PER function, which in turnrelates to the modulation and coding scheme, and on the PER value, which is considered as acceptable at the applicationlevel. However, none of these factors depend on MAC issues;thus, the physical model allows operating between MAC andother layers in a more modular manner. The drawback of thismodel is that it translates into more complex mathematicalrelationships than the protocol model. Moreover, if a specificMAC needs to be addressed, additional constraints (e.g.,related to acknowledgments) are required. A taxonomy summarizing the mathematical formulationsand the rationale behind each interference model is reportedin Table 1. We remark again that the choice of the model ulti-mately depends on the purpose of the analysis. The protocolmodels offer better conceptual simplicity and offer an easy way to represent network constraints. However, the physicalmodel has a good point against the protocol model, asdescribed in [10], when the analysis comes down to theachieved performance of JRS in a WMN. This aspect is fur-ther investigated in the next section by means of numericalexamples.
Performance Evaluation
In this section we focus on the JRS problem of defining effi-cient link activation patterns that not only satisfy all the con-straints but also efficiently deliver traffic to the MAPs actingas gateways for the WMN. We consider discrete (slotted)time, where a time slot is equal to the packet transmissiontime (assumed, for simplicity, the same for all nodes). Wefocus on the minimal time scheduling problem: to deliver agiven amount of traffic from all non-gateway MRs to theMAPs in the shortest possible time. With minor modifica-tions, our framework can work to solve other problems as well, for example, where the goal is throughput maximization(obtaining the highest amount of traffic delivered to the gate- ways within an assigned time) or fairness and/or prioritizationamong the traffic from different MRs is taken into account.For simplicity, we assume that the initial backlog of eachMR is known a priori, and no further packet arrivals takeplace after link activation has started. Solutions that take intoaccount variations of the estimated traffic from each MR canalso be envisaged, which is an interesting direction for futureresearch. To evaluate the impact of the chosen interferencemodel on the performance results, we have implemented ourframework to verify the transmissions’ compatibility providingsupport for all the interference models described in this arti-cle. We stress that the derivation of efficient algorithms tosolve the minimal time scheduling problem is out of the scopeof this article. Here, we have computed within a simulator theoptimal link schedule with an exhaustive search over all possi-ble link activation patterns that are feasible according to theconstraints, in particular to the specific interference modelemployed.We consider a grid topology, represented in Fig. 3, consist-ing of 30 m
×
30 m squares. Nodes occupy the grid intersec-tions in a contiguous manner. We consider 2
×
3, 3
×
3, 3
×
4,and 4
×
4 grid placements of the nodes. We assume that thereis only one MAP in the network (placed in a corner of thegrid), and each of the other MRs has 12 packets to transmittoward the gateway. Wireless propagation is modeled by con-sidering a simple path loss expression proportional to
d
–4
, where
d
is the sender-receiver distance. A link (
i
,
j
) is includ-ed in
E
when its gain
g
ij
is higher than –60 dB with respect tothe attenuation at 1 m. This results in a simple scheme whereall nodes can only communicate with their physical one-hopneighbors on the grid. However, we stress that the validity of the conclusions drawn in the following holds for any scenarioand also when more complicated propagation models are usedto determine the
g
ij
parameters.In Figs. 4 and 5, we report the length of the optimal sched-ule computed when either protocol or physical interferencemodels are adopted, respectively. In both figures we also
Figure 3.
Grid topology considered for the numerical evalua-tions.
30 m30 m
Table 1.
Taxonomy of interference models.
Class Methodology Mathematical relationship
ProtocolFor each active link
e
, all linksin the set
I
(
e
) must be inactive01protocol model:
I
((
i
,
j
)) =
E
\ {(
i
,
j
)}11protocol model:
I
((
i
,
j
)) = {(
k
,
l
)
∈
E
, {
k
,
l
}
∩
{
i
,
j
} =
∅
:} {
i
,
j
∩
(
R
k
∪
R
l
)
≠∅
}16protocol model:
I
((
i
,
j
)) = {(
k
,
l
)
∈
E
, {
k
,
l
}
∩
{
i
,
j
} =
∅
:
j
∈
R
k
}.PhysicalFor each active link
e
, the SIRmust be over the threshold
γ
g g x t
ij kjk ik j
j k
≥
∈∈
∑∑
γ
S R
\{}\{}
()

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