1
Spatial Reusability-Aware Routing in Multi-Hop
Wireless Networks
Tong Meng, Student Member, IEEE, Fan Wu, Member, IEEE, Zheng Yang, Member, IEEE,
Guihai Chen, Member, IEEE, Athanasios V. Vasilakos, Senior Member, IEEE
Abstract—In the problem of routing in multi-hop wireless networks, to achieve high end-to-end throughput, it is crucial to find the “best”
path from the source node to the destination node. Although a large number of routing protocols have been proposed to find the path
with minimum total transmission count/time for delivering a single packet, such transmission count/time minimizing protocols cannot be
guaranteed to achieve maximum end-to-end throughput. In this paper, we argue that by carefully considering spatial reusability of the
wireless communication media, we can tremendously improve the end-to-end throughput in multi-hop wireless networks. To support our
argument, we propose spatial reusability-aware single-path routing (SASR) and anypath routing (SAAR) protocols, and compare them
with existing single-path routing and anypath routing protocols, respectively. Our evaluation results show that our protocols significantly
improve the end-to-end throughput compared with existing protocols. Specifically, for single-path routing, the median throughput gain
is up to 60%, and for each source-destination pair, the throughput gain is as high as 5.3x; for anypath routing, the maximum per-flow
throughput gain is 71.6%, while the median gain is up to 13.2%.
Index Terms—Routing, Wireless Network, Protocol Design
F
1 INTRODUCTION
Due to limited capacity of wireless communication me-
dia and lossy wireless links [30], it is extremely impor-
tant to carefully select the route that can maximize the
end-to-end throughput, especially in multi-hop wireless
networks. In recent years, a large number of routing
protocols (e.g., [4], [14], [20], etc.) have been proposed for
multi-hop wireless networks. However, a fundamental
problem with existing wireless routing protocols is that
minimizing the overall number (or time) of transmis-
sions to deliver a single packet from a source node to a
destination node does not necessarily maximize the end-
to-end throughput. A detailed example will be presented
in Section 3.2 to show this observation.
In this paper, we investigate two kinds of routing
protocols, including single-path routing and anypath
routing. The task of a single-path routing protocol is to
select a cost minimizing path, along which the packets
are delivered from the source node to the destination
This work was supported in part by the State Key Development Program
for Basic Research of China (973 project 2014CB340303), in part by China
NSF grant 61422208, 61472252, 61272443, 61171067, and 61133006, in
part by CCF-Intel Young Faculty Researcher Program and CCF-Tencent Open
Fund, in part by the Scientific Research Foundation for the Returned Overseas
Chinese Scholars, and in part by Jiangsu Future Network Research Project No.
BY2013095-1-10. The opinions, findings, conclusions, and recommendations
expressed in this paper are those of the authors and do not necessarily reflect
the views of the funding agencies or the government.
T. Meng, F. Wu, and G. Chen are with the Shanghai Key Laboratory of Scal-
able Computing and Systems, Department of Computer Science and Engineer-
ing, Shanghai Jiao Tong University, China. E-mails: mengtong@sjtu.edu.cn,
{fwu,gchen}@cs.sjtu.edu.cn.
Z. Yang is with the School of Software, Tsinghua University, China. E-mail:
yangzheng@tsinghua.edu.cn.
A. V. Vasilakos is with the Department of Computer Science, Lulea University
of Technology, Sweden. E-mail: athanasios.vasilakos@ltu.se.
F. Wu is the corresponding author.
node. Recently, anypath routing (e.g., [2], [4]) appears
as a novel routing technique exploiting the broadcast
nature of wireless communication media to improve
the end-to-end throughput. It aggregates the power of
multiple relatively weak paths to form a strong path,
by welcoming any intermediate node who overhears
the packet to participate in packet forwarding. Most of
existing routing protocols, no matter single-path routing
protocols or anypath routing protocols, rely on link-
quality aware routing metrics, such as link transmission
count-based metrics (e.g., ETX [6] and EATX [32]) and
link transmission time-based metrics (e.g., ETT [7] and
EATT [13]). They simply select the (any)path that min-
imizes the overall transmission counts or transmission
time for delivering a packet.
However, an important property of the wireless com-
munication media, which distinguishes it from tra-
ditional wired communication media, is the spatial
reusability. Specifically, because wireless signals fade
during propagation, two links are free of interference
if they are far away enough, and thus can transmit at
the same time on the same channel. To the best of our
knowledge, most of the existing routing protocols do not
take spatial reusability of the wireless communication
media into account. Our example in Section 3.2 will
show the improper usage of routing metrics by existing
routing protocols, when spectrum spatial reusability is
not considered. In this primer work, we argue that by
carefully considering spatial reusability of the wireless
communication media, we can tremendously improve
the end-to-end throughput in multi-hop wireless net-
works (i.e., up to 5.3× throughput gain in single-path
routing and up to 71.6% gain in anypath routing shown
by our evaluation results).
2
The detailed contributions of our work are as follows.
• To the best of our knowledge, we are the first to
explicitly consider spatial reusability of the wireless
communication media in routing, and design prac-
tical spatial reusability-aware single-path routing
(SASR) and anypath routing (SAAR) protocols.
• We formulate the problem of spatial reusability-
aware single-path routing as a binary program,
and propose two complementary categories of al-
gorithms for path selection. While one category
(SASR-MIN and SASR-FF) tends to exploit the best
performance of the paths, the other category (SASR-
MAX) evaluates the performance of the paths in the
worst case.
• We further investigate the spectrum spatial reusabil-
ity in anypath routing, and propose SAAR algo-
rithm for participating node selection, cost calcula-
tion, and forwarding list determination.
• We have evaluated SASR algorithms and SAAR al-
gorithm with different data rates in NS-2. The eval-
uation results show that our algorithms significantly
improve the end-to-end throughput compared with
existing ones. Specifically, for single-path routing, a
throughput gain up to 5.3× with a median of more
than 60% is achieved in the case of single-flow, and
an average gain of more than 20% is achieved with
multiple flows; for anypath routing, a median gain
of 13.2% and the maximum gain up to 71.6% can be
realized.
The rest of the paper is organized as below. In Sec-
tion 2, we briefly review related works. In Section 3,
we introduce the preliminaries as well as a motivat-
ing example. In Section 4, we present our algorithms
for reusability-aware single-path routing. In Section 5,
we present the algorithm for reusability-aware anypath
routing. In Section 6, we discuss the implementation
issues of the proposed algorithms. In Section 7, we show
the evaluation results. In Section 8, we conclude the
paper and point out future work directions.
2 RELATED WORK
In this section, we briefly review related works on metric
design and protocol implementation. We also compare
our work with those on joint routing problems, as well
as other works considering reusability.
2.1 Routing Metrics
There are a number of works on wireless routing met-
rics. For single-path routing, several link-quality aware
metrics [1], [6], [7], [9] were proposed. RTT [1] weighed
the cost of single wireless link by the round trip delay
of probe packets on it; ETX [6] assigned the link cost
with its expected number of transmissions to success-
fully deliver a packet. Based on ETX, the authors in [9]
designed ETOP metric considering links’ actual position
on the path. In addition, incorporating the multi-rate
ability, ETT [7] took the expected transmission time of
a link as its cost; and EMTT [31] extended the work to
multicast. What’s more, [27] provided some principles
for routing metric design.
There’re also metrics suitable for anypath routing
[4], [13], [32]. Chachulski provided ETOX in [4] which
considers opportunistic receptions at any forwarder. In
[32], the EATX metric was defined to reflect overall
transmissions in any-path forwarding. Laufer et al. [13]
adopted EATX as the hyperlink cost, and defined the
anypath cost composed of the hyperlink cost and the
remaining cost.
However, existing routing metrics tend to calculate
path cost using some mechanism of lossless combination
of link costs. For example, the ETX value of a path is
the addition of each link’s ETX [6]. Similarly, Laufer
calculated the anypath cost while considering all the
forwarders’ costs [13]. Besides, the guidelines in [27],
such as consistency, ignored the effect of reusability.
Such lossless mechanism thus misses the opportunity of
exploiting spectrum spatial reusability in wireless media.
2.2 Routing Protocols
The earliest single-path routing protocols [3], [10], [17],
[18] applied Dijkstra algorithm for route selection. When
it comes to anypath routing, for example, ExOR [2]
appeared as a coordination mechanism between for-
warders; MORE [4] broke such coordination where all
the forwarders worked according to their workload.
Besides, MORE introduced network coding into anypath
routing. On that basis, [13] proposed the shortest any-
path first (SAF) algorithm to determine the forwarders’
priorities, and proved its optimality; [19] incorporated
rate control and used a notion called credit to realize
flow control; CodeOR [14] enabled concurrent transmis-
sions of a window of segments; SOAR [24] considered
the problem of path divergence and rate limitation to
efficiently support multiple flows; SourceSync [20] syn-
chronized senders to achieve combined signals which
lowers the packet error rate. Besides, [23] developed
an optimization framework to exploit communication
opportunities arising by chance; Hu et al. [8] proposed
POR based on a per-packet feedback mechanism.
Because the above routing protocols were designed
based on existing transmission cost minimizing routing
metrics, they cannot guarantee maximum end-to-end
throughput when spatial reusability cannot be ignored.
In addition, different from works such as [2] and [20],
which should to some degree rely on synchronization
between nodes, the throughput improvements of our
algorithms in this work do not need MAC-layer coor-
dination.
2.3 Other Related Works
Some existing cross-layer approaches jointly consider
routing and link scheduling (e.g., [11], [16], [29]). Zhang
et al. [29] formulated joint routing and scheduling into
3
an optimization problem, and solved the problem with a
column generation method. Pan et al. [16] dealt with the
joint problem in cognitive radio networks considering
the vacancy of licensed bands. Jones et al. [11] imple-
mented k-tuple network coding and proved throughput
optimality of their policy. Although these works can
provide good performance theoretically, they need cen-
tralized control to realize MAC-layer scheduling, and
to eliminate transmission contention. The algorithms
proposed in this work do not require any scheduling,
and the SASR algorithms can be implemented in a
distributed manner.
Last but not least, there are also works aimed at
exploiting spatial reusability. Specifically, the authors in
[12] considered the trade-off between spatial reuse and
data rate, and proposed a decentralized power and rate
control algorithm for higher network capacity. Zhai et
al. [28] investigated the optimum carrier sensing range
for throughput maximization. However, none of these
works deal with the problem of route selection.
3 TECHNICAL PRELIMINARIES
In this section, we introduce the preliminary knowledge
related to our work, and provide a motivating exam-
ple to illustrate the importance of exploiting spectrum
spatial reusability for routing in multi-hop wireless net-
works.
3.1 System Model
We consider a static multi-hop wireless network with a
set of N nodes. For clarity, we assume that the nodes
use the same transmission rate, and do not employ any
power control scheme in this work.
1
Let p
ij
be the link delivery probability from node i to
node j, i.e., if a packet is transmitted from node i to node
j, then with probability p
ij
the packet can be decoded.
That is to say, to deliver a packet from node i to node j,
node i is expected to do
z
i
=
1
p
ij
× p
ji
, (1)
times of transmissions, when MAC-layer acknowledg-
ment is required. We note that in practice, the probability
of p
ij
is related to packet size of data packet or MAC-
layer ACK. This is commonly considered in the single
path routing as Expected Transmission Count metric
(ETX) [6]. Let T
data
and T
ack
denote the transmission
time of a data packet and an acknowledgment, respec-
tively. Then, the expected time to deliver a packet from
node i to node j is
t
ij
= z
i
× T
data
+ z
i
× p
ij
× T
ack
=
T
data
p
ij
× p
ji
+
T
ack
p
ji
. (2)
1. However, our approach can be extended to adapt to multiple
transmission rates, as long as the conflict graph of links can be
calculated. We leave it to our future work.
In the case of anypath routing (e.g., [4], [13]), the
hyperlink from a sender to a set of forwarders and the
end-to-end acknowledgment are usually used instead
of previous deterministic link and MAC-layer ACK,
respectively. Let F
i
⊂ N be the forwarding set of node i.
Then, to deliver a packet from node i to at least one of
the nodes in its forwarding set F
i
, the expected number
of transmissions needed to be done by node i is
z
iF
i
=
1
1 −
Q
j∈F
i
(1 − p
ij
)
. (3)
This cost metric is called the expected number of any-
path transmissions (EATX) [4], [32]. Since the packets are
normally sent in batches and only an end-to-end ACK
is needed for a whole batch in anypath routing, the cost
of ACK is very small compared with the total size of the
packets in the batch and can normally be ignored [4].
Therefore, the expected time to deliver a packet from
node i to at least one of the nodes in its forwarding set
F
i
is
t
iF
i
= z
iF
i
× T
data
=
T
data
1 −
Q
j∈F
i
(1 − p
ij
)
. (4)
Since wireless signal fades in the process of propa-
gation, two wireless (hyper-)links can work simultane-
ously, if they are spatially far away enough from each
other. We define non-interfering set I, in which any pair
of (hyper-)links are out of the interference range of each
other, i.e., the (hyper-)links in the same non-interfering
set can work at the same time.
3.2 Improper Usage of ETX/EATX
Although ETX/EATX has been widely incorporated into
many single-path/anypath routing protocols, it is still
not properly used, especially in multi-hop wireless net-
works. There are two reasons:
1) ETX/EATX is designed to capture the quality of
a single-hop wireless link/hyperlink. It does not
naturally indicate the transmission capability of an
end-to-end (any)path.
2) ETX/EATX-based routing protocols tend to
choose the route that minimizes the sum of the
ETXs/EATXs of the links/hyperlinks involved.
Since the wireless communication media has the
property of spatial reusability, minimizing the
total number of transmissions to deliver a packet
from a source node to a destination node does not
necessarily maximize the end-to-end throughput.
Here, we use a toy example as shown in Fig. 1 to
illustrate the importance of considering spatial reusabil-
ity of the communication media in single-path routing
in wireless networks. In the example, we have four in-
termediate nodes {A, B, C, D} between source node Src
and destination node Dst. The dashed circle centered at
each of the nodes indicates the interference range of the
4
2.4
Src
A
B
C
D
Dst
1.7
3.3
1.7
1.9
2.0
Fig. 1. Importance of Spatial Reusability
node; and the ETX cost is marked beside each of the
wireless links.
There are two paths from node Src to node Dst:
Path I : Src − B − C − D − Dst,
Path II : Src − A − B − C − D − Dst.
The ETX cost of path I and path II is 3.3+1.7+1.9+2.0 =
8.9 and 2.4+ 1.7+ 1.7+ 1.9+ 2.0 = 9.7, respectively. Since
path I has a smaller ETX cost, it is normally selected by
traditional ETX-based routing protocols, and is expected
to have better performance. However, our simulation
results show that path II achieves an average end-to-end
throughput of 753 Kbps, which is 10.2% higher than 683
Kbps achieved by path I, when the transmission rate is
11 Mbps. This result indicates that the ETX minimizing
path is not necessarily the throughput maximizing path
in multi-hop wireless networks. If we look into the toy
example, we can find that link (Src, A) and link (D, Dst)
are out of the interference range of each other, and thus
can work simultaneously. Therefore, it is necessary to
“fuse” spatially non-interfering links’ costs when doing
path selection. By fusing costs, we mean that the costs
of a set of non-interfering links should be considered
as a whole, instead of directly summing them up. In
the above example, if we fuse the costs of link (Src, A)
and link (D, Dst), and pick the larger cost of the two
as the fused cost, the cost of path II becomes 7.7, which
is smaller than that of path I.
2
Thus, when the spatial
reusability of wireless communication media is taken
into account, the higher throughput path can be selected.
A similar example can be found for the case of EATX-
based anypath routing. Due to limitations of space, we
do not present the example in this paper.
Considering the improper usage of ETX/EATX rout-
ing metric in existing works, we propose to take into
account the spatial reusability of wireless communica-
tion media during path selection in wireless networks,
and will present our spatial reusability-aware routing
protocols in the following sections.
2. It is sufficient to fuse the ETX costs to show the effect of spatial
reusability. However, as shown in Section 4, for link cost fusion, we
should consider the expected link delivery time t
Sr c,A
and t
D,Dst
instead of the ETX costs.
4 SPATIAL REUSABILITY-AWARE
SINGLE-PATH ROUTING (SASR)
We first consider the spatial reusability-aware path cost
evaluation for single-path routing. Given each of the
paths found by an existing source routing protocol (e.g.,
DSR [10]), our SASR algorithm calculates the spatial
reusability-aware path cost of it. Then, the path with the
smallest cost can be selected.
As mentioned in Section 3.1, we can use a non-
interfering set I to represent a group of wireless links
that can work simultaneously. The fused cost of the
non-interfering set I can be defined as the largest link
delivery time in the set
c(I) = max{t
ij
|(i, j) ∈ I}. (5)
Given the collection I of the non-interfering sets on a
path P , the spatial reusability-aware path delivery time
is
C =
X
I∈I
c(I). (6)
For ease of expression, we use link/path delivery time
and cost interchangeably in the rest of the paper. Then,
the key issue here is to calculate the collection I of
the non-interfering sets
3
, given the interference condition
of the links on the path P . We note that interference
among links on the path can be represented by a conflict
graph G = {P, E}, in which the vertices and the edges
represent the links and interferences, respectively. Here,
E = {[(i, j), (i
0
, j
0
)]| links (i, j) and (i
0
, j
0
) have interfer-
ence between each other}. Like many works utilizing the
conflict graph [21], we compute G with measurement-
based techniques [15], [22] within O(|P|) time. Then I
must be a collection of maximal independent sets on the
conflict graph.
In this section, we present two categories of algorithms
to calculate the collection I. One aims to find a collection
I that minimizes the path cost, while the other one
targets at finding the worst possible fused path cost and
its corresponding collection I. These two categories of
algorithms are complementary to each other. While path
cost minimizing collection reflects the best possible per-
formance of the path, the path cost maximizing collection
indicates how bad the path can be in the worst case.
4.1 Cost Minimizing Fusion
The problem of finding the collection of non-interfering
sets that minimizes the path cost, can be formulated into
a binary program as follows.
Objective:
Minimize C =
X
I∈M
x(I)c(I)
3. The calculation of collection I requires no MAC-layer scheduling
in the packet delivery process. Actually, the proposed algorithms are
all MAC-independent, which is one of the advantages of this work.
5
Subject to:
X
I:(i,j)∈I
x(I) = 1, (i, j) ∈ P, (7)
x(I) ∈ {0, 1}, I ∈ M, (8)
where, M is a collection of all the non-interfering sets
on path P . Here, constraint (7) guarantees that each
link is involved in exactly one non-interfering set. Con-
straint (8) indicates the possible values of x(I). If non-
interfering set I is selected to the collection, then x(I) =
1; otherwise, x(I) = 0.
We note that the above problem of finding the path
cost minimizing collection of non-interfering sets can be
reduced to the minimum set cover problem [26], which
is NP-hard.
4.1.1 Approximation Algorithm for Min-Cost Fusion
Since scale-free networks with degree exponent 2 < λ <
3 possess a diameter D ∼ ln ln |N| [5], the paths in
the network are normally not long. So, we first present
an approximation algorithm for finding the path deliv-
ery time minimizing collection of non-interfering sets,
namely SASR-MIN algorithm, when the collection M
?
of all the maximal non-interfering sets on path P can be
calculated efficiently. We note that a non-interfering set
corresponds to an independent set in the conflict graph,
or equivalently, a clique in the complementary conflict
graph. Therefore, the collection M
?
can be computed
in time O(3
|P |/3
) [25]. Generally, SASR-MIN iteratively
visits all the maximal non-interfering sets in M
?
to pick
the most cost-effective set among the rest ones, until all
the links on path P have been covered by the selected
sets. Here, by cost-effectiveness, we mean the average
cost, at which a maximal non-interfering set induces, to
cover new links, i.e., c(I)/|I|.
Algorithm 1 shows the pseudo-code of our SASR-MIN
algorithm. We use set Q to store covered links. Then, we
iteratively select maximal non-interfering sets to put into
the collection I (Lines 3-15). In each of the iterations,
we check every remaining maximal non-interfering set
I in M
?
. Since each link should be covered exactly once,
if the set I contains already covered links, we need to
remove the covered links from I (Lines 5-6). Then, if
the set I is not empty, we compare it with the currently
most efficient cost factor α in this iteration. If this is
a more cost efficient set, we update the factor α, and
record the corresponding set (Lines 7-9). At the end of
the iteration, we add the cost of the currently most cost-
effective maximal non-interfering set into the collection
I, and update the total path cost C and the covered set
Q correspondingly (Lines 12-14).
Since at least one link is added into the covered set Q
in each iteration, Algorithm 1 iterates at most |P | times.
In each iteration, at most |M
?
| cost-effectiveness factors
are calculated. Thus, the total run time of Algorithm 1
is O(|P ||M
?
|).
Next, we show the approximation ratio of Algorithm
1.
Algorithm 1: SASR-MIN Algorithm
Input: A path P , a profile of link delivery time
(t
ij
)
(i,j)∈P
, and a collection M
?
of all the
maximal non-interfering sets on path P .
Output: Path delivery time C and corresponding
collection I of non-interfering sets.
1 C ← 0;
2 Q ← Ø ;
3 while Q 6= P do
4 α ← +∞;
5 foreach I ∈ M
?
do
6 I ← I \ Q;
7 if I 6= Ø ∧ c(I)/|I| < α then
8 α ← c(I)/|I|;
9 Temp ← I;
10 end
11 end
12 C ← C + c(Temp);
13 I ← I ∪ {Temp};
14 Q ← Q ∪ Temp;
15 end
16 return C and I;
Theorem 1. SASR-MIN algorithm achieves an approxima-
tion ratio of H(|P |), where H(|P |) is the |P |th harmonic
number:
H(|P |) =
|P |
X
k=1
1
k
≤ ln |P | + 1. (9)
Proof. Let η
l
be the cost-effectiveness of link l ∈ I, where
I ∈ I. Then η
l
= c(I)/|I|. Consequently, the path cost is
C =
X
i∈P
η
l
. (10)
Next, we number all the links in the order of being
covered (for those links covered in the same iteration,
number them arbitrarily), and get {l
1
, l
2
, · · · , l
|P |
}. In the
iteration l
k
is covered, the picked I must have a cost-
effectiveness of at most OP T /(|P |−k + 1), which means
that
η
k
≤
OP T
|P | − k + 1
. (11)
Therefore, the calculated path cost is
C =
X
i∈P
η
l
≤ OP T
|P |
X
k=1
1
k
. (12)
This completes the proof.
4.1.2 First-Fit Algorithm for Min-Cost Fusion
However, listing all the maximal non-interfering set on
path P needs O(3
|P |/3
) time, which is still inefficient
when the path P is long. Therefore, we propose a first-
fit algorithm, namely SASR-FF, which can achieve good
performance in most of the cases.
