ONE-TO-ALL AND ALL-TO-ALL BROADCASTING

ALGORITHMS IN CELLULAR NETWORKS

Hiroshi Masuyama, Yuuta Fukudome

Information and Knowledge Engineering, Tottori University,Koyama-cho Minami 4-101, Tottori, Japan

Tetsuo ichimori

Information Science, Osaka Institute of technology, Kitayama 1-79-1 Hirakata, Japan

Keywords: all-to-all broadcasting, cellular network, fault-tolerance

Abstract: In this paper, a one-to-all broadcasting algorithm on a mobile cellular network is first discussed as a

minimum diameter spanning tree problem in a graph where every arc has a constant weight. An all-to-all

broadcasting algorithm is next discussed on a subject of avoiding heavy traffic conditions. Finally, a fault-

tolerant broadcasting scheme is presented.

1 INTRODUCTION

In this paper, we study first the problems of one-to-

all broadcasting in cellular networks. For

communication primitives, Johnsson and Ho

(S.Johnsson, C.T.Ho, 1989) introduced four

different primitives:(1)one-to-all broadcasting (or

single node broadcasting) in which a single node

distributes common data to all other nodes,(2)one-

to-all personalized communication in which a single

node sends different data to all other nodes,(3)all-to-

all broadcasting, and (4)all-to-all personalized

communication.

Many researchers have proposed various

communication algorithms for various kinds of

networks such as multi-computer ( hypercube, mesh,

torus , or Chordal ring) networks (S.Park, B.Bose,

1997), MINs (multi-stage interconnection networks)

(M.Yaku, H.Masuyama, 2001), wireless

(J.E.Wieselthier et. al, 2000) or cellular networks

(A.E.Baert, D. Seme, 2003). Most of their reports

are concentrated on routing and one-to-all

broadcasting in the presence of or in the absence of

faulty components of the networks, because of the

universality and importance of the primitives. This

paper treats such one-to-all broadcasting schemes,

that is, one node of the network, called “source” has

to transmit a message to all other nodes (which are

called base stations afterward). In addition, this

paper treats all-to-all broadcasting schemes.

The importance of wireless or cellular

communications is rapidly growing from the view

points of their inherent convenient services. The

cellular systems studied here are a little different

from wired networks, that is, the emitters of calls are

mobiles which are not connected by a physical link

to the corresponding base station. All base stations

are fixed in the cellular network, and neighboring

base stations can communicate through a cable

linked between them. Since the base stations operate

as omni-directional antennas, then a broadcast from

a base station can be received by all mobiles that lie

within its communication range which is called

“cell”. A mobile cellular network typically covers a

large geographical services area which is partitioned

into many cells. Central offices of a large telephone

network form an irregular and random point pattern

which is caused by spatial variations of population

density, consumer demand, and a number of other

geographical and technological factors (A.E.Baert,

D. Seme, 2003). This network model corresponds to

a PLMN (public land mobile network) counseled by

CCITT.

Mobile environments pose some interesting

problems in designing (1) energy efficient

broadcasting scheme and (2) fault-tolerant

broadcasting scheme. To clear problem (1) is to

avoid transmitting the same information from

redundant plural base stations to a base station. In

other words, we do not consider such “flooding

scheme” that copies of a received packet are sent to

140

Masuyama H., Fukudome Y. and ichimori T. (2005).

ONE-TO-ALL AND ALL-TO-ALL BROADCASTING ALGORITHMS IN CELLULAR NETWORKS.

In Proceedings of the Second International Conference on e-Business and Telecommunication Networks, pages 142-145

DOI: 10.5220/0001412701420145

 SciTePress

its neighbors except the node sending the packet.

The later problem (2) can be cleared by preparing

more than one transmission route to every base

station (where we consider a link fault to be realistic

faults here, and the appropriateness and node faults

are discussed afterward). In these avoidance and

clearance, there exist two approaches where one is to

construct a peculiar broadcast routing tree for each

source, and the other is to prepare a fixed common

broadcast tree in the cellular network in advance.

The former approach presents a drawback leading to

the complexity problem of broadcasting algorithm.

The latter presents a drawback leading to non-

shortest path and the necessity of modification of

routing tree when the topology of interconnection

may change dynamically. B.A.Elisbeth and S.David

(A.E.Baert, D. Seme, 2003) reported on the former

approach where they presented a broadcasting

algorithm whose order of complexity is the diameter

of network. This algorithm is suitable for the fault-

tolerance in the sense that it is available as far as the

network is connected. We will consider the latter

approach.

2 BASIC IDEAS

Mobile cellular network: The network consists of

N nodes which are randomly distributed base

stations over a specified region and, in order to

transfer messages by the links, the neighboring

nodes are connected as shown in Fig.1 as an

example. Thus, we consider this cellular network is

constructed as a mobile cellular network which can

serve in the waves propagating area as shown in

Fig.2. We note that each service area is not always

connected with all its neighboring service areas.

Description of our approach: Fig.3 shows a

broadcast tree which is obtained by applying our

scheme to the network shown in Fig.1, where N=21.

Any node can broadcast its message from its own

position to all other nodes by taking a bold line

route. This broadcast tree is just a spanning tree.

Anywhere the source is, this broadcasting tree is

energy-efficient, because any connected graph needs

at least N-1=20 arcs, that is minimum. That is,

every spanning tree is an energy-efficient tree. We

note that the diameter of this broadcasting tree is 10

while the diameter of another spanning tree is 6. A

spanning tree of minimum diameter is desirable as a

broadcast tree. For the generalized graph, the

minimum diameter spanning tree problem was

discussed in (R.Hassin, A. Tamir 1995). Since our

cellular networks are special in the sense in which

arc lengths are all identical, we can obtain a simpler

algorithm for an optimum broadcast tree, which is

discussed below.

This broadcasting tree is not optimum in all-to-

all broadcastings, because, since every source node

uses this tree as a unique and common routing tree,

the traffic problem occurs. In order to avoid this

problem, we need to select the broadcast trees which

have the smallest number of arcs in common. We

will discuss, an algorithm of this type afterwards.

On the other hand, Fig.4 shows a fault-tolerant

broadcasting route. The condition of constructing

this original circle is that at least two component

nodes are adjacent to each non-component node. In

this fault-tolerant route, nodes on the original circle

accept messages (from a link) and translate the

messages (to all other links), and nodes not on the

original circle operate only as receivers if they are

not source nodes. Then, the route shown in Fig.4

guarantees that any node can accept a message

started from every other node even if any one of

links is cut off. The graphs like this can be

embedded only in graphs where the degree of every

node is over 1. Though the diameter of this fault-

tolerant route is not the minimum among the graphs

which satisfy the above constructing condition, it is

hard to embed the optimum graph like this into a

graph. Then, in Sec.3 we discuss an algorithm to

obtain the fault-tolerant broadcasting route like the

one shown in Fig.4.

Algorithm: The outline of this algorithm is as

follows; Find the shortest path tree with each

different node as its root. Since the number of nodes

in a connected and non-directed graph is N, we

obtain N shortest path trees. Next, find a shortest

path tree with the minimum diameter among all the

spanning trees. This algorithm is based on the theory

that the spanning tree with the minimum diameter in

a graph is also the shortest path tree. This theory is

proved in Appendix1 which is omitted in this paper

for space limitation. Along this outline, we can

establish the following algorithm:

Algorithm A------------------------------------------------

while i = 1 to N do

begin

find the minimum routes from node i to all

other nodes, and make a shortest path tree T(i)

with root i.

find one (j) of the most faraway nodes from i,

next find one (k) of the most faraway nodes

from j, finally define the diameter D(i) of T(i)

as the distance between j and k.

end

find the minimum value among the diameters D(i)

for all i and output a shortest path tree with the

minimum value D(i).

ONE-TO-ALL AND ALL-TO-ALL BROADCASTING ALGORITHMS IN CELLULAR NETWORKS

141

---------------------------------------------------------------

Since it takes O(m) time to find a shortest path

tree, the time complexity of algorithm A is O(mN),

where m is the number of arks in a graph.

All-to-all broadcasting algorithm: The outline of

this all-to-all broadcasting algorithm is as follows:

Each node i has a spanning tree as its own one-to-all

broadcasting route from source node i. An all-to-all

broadcasting route is a set of N one-to-all

broadcasting routes. Then, in the all-to-all

broadcasting, many one-to-all broadcasting routes

hold the same arc in common. Data transmitting on a

common arc is performed in order of source node

number. Optimum solution of this type broadcasting

is to find a set of spanning trees where the maximum

number of duplications of an arc is the smallest.

This problem is defined as follows:

[Let Ti denote a spanning tree rooted at node i

and let S denote a set of p spanning trees of G, i.e.,

S={T1,...,Tp} where p<N, and let (T1,...,TN) be a

permutation of N spanning trees in the set S,

repetitions allowed. Our optimum solution is a

permutation where the maximum number of

duplications of any arc is the smallest. ]

Since the time complexity to solve the above

problem is over the polynomial order, let us consider

another algorithm to obtain an approximate solution.

The outline of this algorithm is as follows; Let a set

of spanning trees of a graph G be S={T1, T2, T3, …,

Tp} where S covers all arcs in G.. To each Ti (i=1,

2, 3,…, p), assign

different nodes in G. A set of nodes assigned to Ti is

a group of source nodes which use Ti as the

broadcast tree. The following algorithm is

considered:

Algorithm B------------------------------------------------

begin

S1: find a set of spanning trees S={T1, T2,

T3,…, Tp } by which all arcs in a

connected graph G are covered.

S2: for every Ti,

assign Ti to a set of nodes where any two

elements are congruent to each other

modulo p.

end

---------------------------------------------------------------

If a simple method to find a spanning tree Ti is

adopted, the time complexity is O(mN), where Ti

covers (N-1) arcs in G. Then, we must find at most

(m-(N-1)) spanning trees where each one can cover

at least one arc uncovered by other spanning trees.

Since the time complexity to find S is O(mmN), we

conclude the time complexity of Algorithm B is

O(mmN).

In order to verify the validity of Algorithm B, let

us compare Algorithm B and another ordinary

algorithm finding a spanning tree for each root node,

and evaluate the complications of broadcasting trees

in both algorithms. Two algorithms are applied to

the graph shown in Fig.5. Figs.6 shows the number

of duplicated paths on an arc in each all-to-all

broadcasting, and proved the superiority of

Algorithm B to the other.

3 FAULT-TOLERANCE

Let us show the following algorithm to obtain the

circle from which a fault-tolerant broadcasting route

originates.

Algorithm C------------------------------------------------

An elemental node is a node adjacent to a node of

degree 2.

A non-elemental node is a node of degree 2 which is

not elemental.

begin

S1: find all elemental nodes and non- elemental

nodes in the mobile cellular network graph

NW.

S2: construct a connected graph G of NW

which contains all the elemental nodes and

as few non-elemental nodes as possible and

in which every node is on at least one of

circles.

S3: remove non-elemental nodes and the arcs

incident to them from NW if these non-

elemental nodes are not in G.

remove node i and the arcs incident to it

from NW if two adjacent nodes of i are in G

and (i has no other adjacent node except in

G or every one of the remainder adjacent

nodes of i has two nodes as adjacent nodes

in G).

S4: remove an arc connecting two adjacent

nodes i and j in G from NW and G if i and j

remain on a loop in G after the arc is

removed from G.

S5: remove an arc connecting two adjacent

nodes i and j in G from NW and G if there

exists at least one path between i and j in

NW but at least a part of the path is not in

G, and add the shortest path of them in G.

S6: go to S2 if NW =G.

end

---------------------------------------------------------------

N/p

⎢⎥

⎣⎦

N/p

⎡⎤

⎢⎥

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142

0～4 5～9 10～14 15～19 20～24 25～29 30～34 35～39 40～44 45～49 50～54 55～59 60～64

number of trees overlapping on the same edge

number of edges overlapped by

the same number of trees

another algorithm

Algorithm B

4 CONCLUSION

In this paper, we showed that an optimum one-to-all

broadcasting algorithm can be applied to the

minimum diameter spanning tree problem on mobile

cellular networks where every arc has a unity cost.

An all-to-all broadcasting scheme is next discussed.

A fault-tolerant broadcasting scheme was finally

presented. We will discuss multicasting schemes

across networks of this type in future.

REFERENCES

S.Johnsson and C.T.Ho, Sept. 1989. Optimum

Broadcasting and Personalized Communication in

Hypercubes, IEEE Trans. Computers, Vol.38, No.9,

pp.1249-1268.

S.Park and B.Bose, July 1997. All-to-All Broadcasting in

faulty Hypercubes, IEEE Trans. Computers, Vol.46,

No.7, pp.749-755.

M.Yaku and H.Masuyama, Oct. 2001. A Method of Fault-

tolerant All-to-All Personalized Communication in

Banyan Networks, IPSJ Journal, Vol.42, No.10,

pp.2476-2484.

J.E.Wieselthier, G.D.Nguyen, and A.Ephremides, 2000.

On the Construction of Energy-Efficient Broadcast

and Multicast Trees in Wireless Networks,

Proceedings of IEEE INFOCOM 2000, pp.585-594.

A.E.Baert and D. Seme, 2003. One-to-all broadcasting in

Voronoi cellular networks, Proceedings of PDPTA

2003.

R.Hassin and A. Tamir, Jan. 1995. On the minimum

diameter spanning tree problem, Information

Processing Letters, Vol.53, No. 2, pp.109-111.

Figure 3: A broadcast tree.

Figure 4: A fault-tolerant broadcasting route.

Figure 5: Network used as an example.

Figure 6: Comparison between two algorithms.

Figure 2: Service area of cellular network based

on the network shown in Fig

ure

Figure 1: A network of base stations.

Interference

Base Station

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