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Data Indexing for Heterogeneous Multiple Broadcast Channel

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Data Indexing for Heterogeneous Multiple Broadcast Channel

Andrew Y. Ho

and Dik Lun Lee

Department of Computer Science
The Hong Kong University of Science and Technology
Clear Water Bay, Hong Kong
Email: andrewho@cs.ust.hk, dlee@cs.ust.hk

Abstract

vision in the computing industry – from traditional wired

This paper studies a heterogeneous multiple channel

and stationary desktops to a fast growing area of mobile

environment (HMCE), in which the channels are

computing. The trend of using notebook computers,

controlled by different wireless operators. To the best of

palm-size computers, and personal digital assistants (PDA)

our knowledge, there is no previous research on this

is already in full swing. Furthermore, the enhancement in

scenario. In this paper, we first present the architecture for

reliability, transmission, and speed of wireless links

HMCE which makes use of a centralized index server to

facilitates the mobility of communication. Usually, a

broadcast index information about the broadcast data on a

wireless communication environment consists of two sets

dedicated index channel. An analog can be drawn between

of entities: a large number of users equipped with mobile

HMCE and WWW: the wireless operators are web sites

devices (mobile clients – MCs) and a relatively fewer

and the index channel is Google; Google indexes web

number of stationary mobile service stations (MSS) that

pages so that users can find the web pages they want,

have base stations (BS) or access points (AP) attached to

whereas in HMCE the index channel indexes the data

provide wireless communication in geographical areas

channels to help mobile users to find the data on the air.

known as cells. Unlike a MSS, a MC is able to move freely

We propose three indexing methods to reduce the time and

from cell to cell and poses queries for retrieving data

energy used to search for data in HMCE. Simulation

provided by the MSS.

results are obtained to evaluate the performance of the

There are two major modes for MCs to access information proposed methods.

on

the

wireless

channels:

pull-based

on-demand mode, which collects the queries sent by the
MCs through an uplink channel, and then delivers the

1. Introduction

requested data through the downlink channel; push-based broadcasting mode, which broadcasts data on the broadcast

The

rapid

advance

of

wireless

communication

channel continuously according to some previous data

technologies during the last decade has brought a new

access statistics in order to reduce access latency and

consumption of bandwidth, thus effectively allowing a

become outdated very soon. To find out where the

large number of MCs to access information simultaneously.

expected data will be broadcast, the most straightforward

Furthermore, as receiving messages consumes less power

method for MCs is to search all broadcast channels, but

than sending messages, MCs are able to stay longer with

this is very time consuming and uses up a lot of battery

the

power. Another way is to announce the data indices

limited

power

supplies

in

the

broadcasting

environment.

through a dedicated index channel so that MCs can

Because of business, economic and technical reasons,

identify where the data will be broadcast. In HMCE, we

some service providers may want to use multiple

propose to makes use of a centralized index server to

low-bandwidth channels to achieve high combined

broadcast index information about the broadcast data on a

bandwidth instead of getting a single high-bandwidth

dedicated index channel. Mobile clients listen to the index

channel. In this homogeneous multi-channel environment,

channel and then tune into the data channel according to

the server has full control over all channels in terms of

the index information and scan for the data it wants. In

scheduling data on the channels and will most likely use a

other words, the index server/channel is the “Google” of

fixed indexing and scheduling scheme. A mobile client

the data on the air.

typically subscribes to one or a few wireless operators and

Researchers

have

proposed

different

broadcast

as such it is easy to identify the available channels and

scheduling [1, 2, 3] and indexing schemes [4, 5, 6] in order

scan them to pick out the interesting information.

to reduce power consumption for a single broadcast

In this paper, we study a heterogeneous multiple

channel. Yet, scheduling and indexing methods used in a

channel environment (HMCE), which, in contrast,

single channel broadcast may not be directly applied to a

consists of a large number of wireless operators ranging

multi-channel environment. There are also studies on

from phone companies to amateurs operating in public

multiple channel scheduling and indexing [3, 4, 7] that

radio frequency bands (e.g., Starbucks) [9]. The wireless

focus on a homogeneous multiple channel environment. To

operators disseminate information on channels that are not

the best of our knowledge, there is no previous research on

related or unorganized. An analog can be drawn between

the HMCE scenario.

HMCE and WWW. In HMCE, the data channels are the web sites and the broadcast data are the web pages.

In this paper, the architecture of HMCE is proposed.
We introduce indexing methods to reduce the time and

As information is disseminated through different

energy used to search for data on multiple data channels.

service providers on different wireless broadcast channels,

Three indexing models are described. Simulation results

it is difficult for mobile users to identify the available

are obtained to evaluate the performance of the three

channels (cf. web sites), let alone those containing the data

proposed methods.

they want (cf. web pages). They need to have knowledge

The rest of this paper is organized as follows. Section

about what channels are available and which channels

2 introduces the background and related work on wireless

carry their requested data. Since the broadcast pattern may

broadcast. Section 3 describes the proposed methods for

change dynamically over time, any static channel

data indexing. Section 4 evaluates the performance of the

information pre-programmed in the mobile devices may

proposed methods. Section 5 concludes the paper.

2. Background

that concerned the conflict of data pages. The page-based strategy (PB) aims at allocating the data pages by their

In single channel environment, one way of reducing

own access frequencies. The request-based strategy (RB)

power consumption is by selective tuning [6, 5], which

is based on user requests rather than pages. The

enables MCs to switch into active mode (power consuming)

conflict-free version (CFV) of the RB further enhances the

only when the expected data is being broadcast. A server is

schedule by checking if the pages in the same request are

required to broadcast indexing information to make

assigned in the same time slot.

selective tuning works.
The (1, m) indexing scheme [6, 5] is an index allocation method that involves the complete index being

3. Data

Dissemination

in

Heterogeneous

Multiple Channel Environments

broadcast m times in a broadcast cycle. MC traverses the index buckets and determine the offset to the requested data bucket. The tree-based indexing scheme [6, 5] was

Three indexing schemes in the centralized model for data dissemination in a HMCE are proposed.

introduced in which an index is only partially replicated in the broadcast cycle. In this scheme, the data file is associated with

a

B+-tree

index

structure.

3.1. Basic Model

The

signature-based indexing scheme was proposed [8] for

The key point in the centralized model is the central

real-time information filtering. Basically, to access

index server (CIS), which is used to manage and broadcast

information, a query signature is constructed and

index information about the data being broadcast on all of

compared with the broadcast signature. If the signatures

the broadcasting channels. In the architecture, we define

match, all records indexed by the signature will be read

the broadcast agent (BA) as any individual that has data to

until checked for correctness or until the expected record is

be broadcast on the broadcast channel.

found in the information frame.
Scheduling and indexing methods used in single channel broadcast may not be directly applied to a multiple channel environment. New algorithms and modified methods were thus proposed, although the algorithms did not address certain issues related to a HMCE. In [3],
Hameed and Vaidya integrated the online algorithm with alternate labeling by assigning instances of the data item

Figure 1. Centralized HMCE

from a single channel schedule into a multiple channel

Each BA is connected to the CIS and CO through a

schedule. In [4], Hsu et al. suggested a method for

wired network (see Figure 1). The CIS is responsible for

indexing and scheduling a multiple channel broadcast that

broadcasting index information on a dedicated wireless

considered data access frequencies based on distributed

channel for the whole HMCE, while the CO is only

indexing [5]. In [7] Ke et al. proposed a scheduling method

responsible for broadcasting a data message (DM) on its

providing the data are sent at or after the EST.

own wireless channels for BAs who subscribe to it.
Assume that a BA has data to be broadcast. The first

Once the BA receives an EST from the index server, it

thing for it to do is to send a “data-to-send” notification

will wait until the indicated time. At that moment, the BA

(DTS) to the CIS through the wired network (Figure 1).

can send its data to the service provider – the CO (Figure

The content of the DTS follows a standard format as

1). Whether the CO broadcasts the BA’s data immediately

defined by the CIS, which includes the BA’s identification,

or appends it to an internal broadcast queue depends on the

the channel ID that the BA has subscribed to, the message

traffic of the channel.

identification, and a list of key attributes describing the

Whenever the MC wants to retrieve data from the

data. When the CIS receives the DTS, it extracts the

wireless channel, it will tune into the index channel and

information from the DTS and converts it into the index

filter all broadcast IMs by listening to the channel until it

message (IM) format, which contains a header with the

finds an IM containing the attribute that matches its

BA’s ID, the channel ID, the message ID, the IM size, the

request. Then the MC can tune into the data channel

number of attributes, and a pointer to the starting of

indicated by the IM header and wait for the requested data

attributes. Next, the CIS puts the IM into the broadcast

to be broadcast. Since each IM header contains the

queue for index broadcast.

corresponding IDs of the BA and the message, the MC

Once the CIS receives the DTS, it is required to reply to

only needs to check both IDs in the DM in order to

the BA at the earliest time that it can broadcast its data

determine if the DM is the one indicated by the IM.

(Figure

the

Otherwise, the MC can doze off until the end of the

“earliest-send-time” notification (EST). The value of the

incorrect DM. The MC may also end the retrieval process

EST is equal to the broadcast end time of the BA’s IM. The

if no attribute in IMs can be found matching its request

EST is very important for serializing the IM and the

within a certain period of time.

1).

The

replied

message

is

called

indexed data in the centralized model. Suppose it is omitted and a BA broadcasts its data a short while after it

3.2. Signature Model

has sent the DTS to the CIS. If there are a lot of IMs queued up in the CIS, it will take a long time for the CIS to

The environment of a signature model is the same as

broadcast all of them. Therefore, there is a chance that the

the environment used in the basic model. The major

BA broadcasts its data before the CIS has broadcast the

difference concerns how indices are constructed. In the

corresponding IM. In this case, the data being broadcast by

basic model, whenever the CIS receives a DTS sent by BAs,

the BA are not properly indexed, and the corresponding IM

all attributes in the attribute list attached to the DTS will be

broadcast by the CIS will be invalid. For data retrieval, if

used to construct the IM. Also, each IM is only responsible

an MC has read this IM and tuned into the specified data

for one DM. If there are a lot of BAs and all of them are

channel, then it will wait forever or terminate after a

sending a DTS with a long attribute list, then it will take a

timeout period, since the data have already gone on that

long period of time for the CIS to broadcast all the IMs on

channel. With the EST replied by the CIS to the BA, they

the index channel. Since the EST is equal to the end time

can ensure that the data will have an index to indicate,

of the corresponding broadcast IM, the BAs also need to

wait for a long period of time to start sending the data to the COs.

In the signature model, indices are only signatures that guide the MCs to the data channel where the requested

In the signature model, to reduce the size of the IM,

data may be found. As a result, the BAs are required to

signatures are used instead of real attributes. An attribute

send with each data item an AL to their CO for broadcast,

list signature (ALS) is formed by hashing each attribute in

such that the MCs can check whether the query attribute is

an attribute list (AL) into a random bit string, and then

actually in the AL attached to the broadcast data.

superimposing all bit strings together (Figure 2).

A false drop can result from a signature comparison.
This happens when an MC finds a matching CS with the query signature, but in fact, the corresponding channel does not contain the requested data item. If this is the case, the MC needs to leave the data channel and tune back into the index channel to filter other CSs. To determine the occurrence of a false drop, a timeout for searching the data

Figure 2. Generation of attribute list signature

channel is required. Since the MC tunes into the indicated

During the filtering process, a query signature is

data channel after finding a matched CS and waits for the

constructed in the same way as the ALS. Then the query

data message, if the length of the searching period is not

signature will be compared with the ALS using the logical

specified and if the CS is in fact a false drop, then the MC

AND operation to find if the query is potentially in the AL.

will wait forever on the data channel without finding any

The CIS maintains two lists for managing signatures: a

useful data.

channel signature (CS) list for storing all CSs with one entry assigned to only one data channel in the system, and

3.3. Signature Model with Operator’s Feedback

an order-array for storing the broadcast order and time for each entry in the CS list. Upon reception of the DTS from a

An improper length for the searching period can

BA, the CIS extracts the channel ID and the ALS from it.

lengthen the retrieval time. No matter how carefully

Then the ALS is superimposed onto the channel signature

chosen is the length of the searching period, there is still

(CS) of the referring channel. The main purpose of the

the possibility of an incident of determining an ‘incorrect

order-array is to keep track of the broadcast time for each

false drop’. An incorrect false drop happens when the MC

non-empty CS (since it is not necessary to broadcast an

finds a matching CS on the index channel but cannot find

empty CS for indexing purposes). Thus, the CIS can

the correct DM within the searching period on the

respond to the BA with the EST according to which

corresponding data channel. In fact, the DM is broadcast

channel it uses. During signature broadcast, the CIS goes

on the indicated data channel, but after the MC’s expiration

through each non-empty entry in the order-array and only

time. Incorrect false drops occur more frequently when the

those CSs in the array will be broadcast. Moreover, after

searching period is too short, or the traffic load of the data

broadcasting, all CSs and the corresponding order-array

channel is heavy, since in both cases, the correct DM

entries will be cleared for future superimpositions.

cannot be broadcast within the MC’s searching period.

To eliminate the effect of incorrect false drops, at least

period. The reason for this is straightforward: as the MC is

one CS needs to be broadcast within the length of a

still searching for the correct attribute on the data channel

searching period before the corresponding DM has been

during the searching period, if the re-sent signature is

broadcast. Hence, when the MC reads the CS and switches

broadcast within this period, it will be gone before the MC

to the data channel, the DM will arrive during the

switches back to the index channel. The purpose of the

searching period. In order to accomplish this method,

re-sent ALS is only to prevent an incorrect false drop.

cooperation from all the COs is needed.

Since the corresponding data is already in the CO’s internal broadcast queue, the second reply of the EST is not required by the BA. The message flow in the feedback model is shown in Figure 3. For the MC, the same procedure for data retrieval is used, but when an incorrect false drop occurs and the MC switches back to the index channel after timeout, the MC can use the re-sent signature on the index channel and switch back to the data channel to retrieve the DM.

Figure 3. Signature Model with Operator’s feedback
In both the basic and signature models, once the BA

4. Performance Evaluation

receives an EST, it waits until the specified time to send the data. But the BA has no idea about the time that the

This section evaluates the performance of the three

data message will be broadcast on the data channel by its

proposed heterogeneous multiple channels broadcast

CO. As a result, the BA has no way of ensuring that at least

models by using simulation. The primary performance

one CS containing the ALS of the data will be broadcast

metric used for evaluating the models for MC is average

within the searching period prior to the broadcast of the

access time.

data. Feedback from the CO plays an important role in

For all experiments, CSIM18 [10] was used for

notifying the BA about the time for the data broadcast. In

implementing the simulation and the same parameters

contrast to the signature model, where the CO receives the

were used in the simulation environment. Besides, we

data from the BA, besides appending the data to the

assume that the capacities of the wired networks are much

broadcast queue, it also gives feedback to the BA who

larger than the wireless broadcast channel (1 byte/unit of

requested the data broadcast about the time that the DM

time), therefore the notification messages, such as DTS and

will be broadcast on the channel. After getting the

EST, and any data going through it does not affect the

feedback from the CO, if the difference between the CS

performance of the system. As a result, time spends on

end time and the data broadcast time is more than one

wired networks is not counted. For attribute used in the

searching period, then the BA can send the same ALS again

simulation, a vocabulary is made, and each time, BA can

to the CIS one searching period prior to the broadcast time

choose 1 to 25 words from the vocabulary as the data

of the data, while avoiding any overlap with the searching

attributes. Similarly, MC chooses one word from the list

for its query attribute. The length for each index message

experiments, while the signature model has slightly higher

in the basic model is added up by the size of the attributes

values due to the longest time for retrieving data. As the

plus a 3 bytes header - BA ID, message ID and size of the

number of channels increases, MC access time in all

message, which ranges from 9 bytes to 153 bytes in total.

models tends to reach the same values and stay unchanged

For the signature models, 128-bit (16 bytes) signature is

regardless of further increases in the number of channels.

used for each channel. The size of data which BA sends to

The reasons are as follows. First of all, the time that CO

CO is ranging from 10 to 10000 bytes. For basic model, 2

receives a data message and the time that CO broadcast the

bytes IDs for verification is added, while in the signature

data message are getting closer. As EST is also the end

models, size of attributes is added.

time of the index broadcast, MC access time can be roughly formulated as the summation of the time spent on

4.1. Impact of the number of channels on MC’s data access

filtering on index channel, the data queuing time, and the time for broadcasting data message. Since the average data sizes in both models are the same, the filtering time

MC access time measures the time elapsed from the

becomes the main factor influencing the access time.

moment the MC poses a request and starts listening on the

7000
6000

received. The performance on MC access time is

5000

15

19

17

15

13

11

0

9

20

1000

7

Basic Model
Signature Model
Feedback Model

25

Basic Model
Signature Models

2000

5

Unit of Time (x 105)

30

3000

3

result is shown in Figure 4.

4000

1

investigated with respect to the number of channels. The

Unit of Time

wireless channels to the moment the requested data is

Number of Channels

10

Figure 5. MC on index channels

5

Figure 5 shows the time that MC has spent on the index
19

17

15

13

9

11

7

5

3

1

0
Number of Channels

Figure 4. MC access time
In the figure, MC access time decreases as the number of channels increases. This is because workload on each

channel. The graph clearly shows that MC spends longer time in the basic model than in the signature models, due to the difference in index size. As a result, MC access time in the basic model obtains higher values in the experiments. channel is reduced by using a larger number of channels, thus enabling each data broadcast to start earlier. The

4.2. Impact of the searching period

figure also shows that MC access time in the feedback model achieves the lowest values at the beginning of the

Figure 6 shows the MC access time with respect to

different length of searching period in signature model and

data message on the data channel. Therefore, MC in the

feedback model. Figure 7 shows the number of false drops

feedback model incurs less access time than in the

with respect to the same searching period.

signature model. As the length of the searching period increases, the number of false drops decreases since MC is

25

Unit of Time (x104)

able to eliminate incorrect false drops. This also explains
20

why the access time for both models tends to overlap with each other by increasing the searching period.

15
10

4.3. Impact of M-size

Signature Model
Feedback Model
Basic Model

5

The number of false drops can influence the MC access

0
0

10

20

30

40

50

60

70

80

90

100

time, but false drop itself is also influenced by the m-size.

Search Period (x103 Unit of Time)

The m-size for a signature stands for the number of 1’s
Figure 6. Access time

generated by the signature generator (usually hash function). If the m-size is too small, then too many 0’s will be in the signature, resulting in under utilized signatures. If

Signature Model
Feedback Model

50

the m-size is too high, then there will be too many 1’s in

40

the signatures, resulting in weakened filtering capabilities.
30

This is because signatures with many 1’s are much easier

20

to match a query signature by chance. Figure 8 shows the

10

number of false drops against m-size.
100

Search Period (x103 Unit of Time)

Figure 7. False drops
As shown in the figures, a short searching period causes a lot of false drops, since MC does not have enough time to reach the correct data message before the end of the searching period. Therefore, they interpret all the missed data as false drops. In the feedback model, since
ALS of the data will be resent to CIS for broadcast again on

20
18
16
14
12
10
8
6
4
2
0

Signature Model
Feedback Model

12
0

90

11
0

80

90
10
0

70

80

60

70

50

60

40

50

30

30

20

10

10

Number of false drop

0

40

0

20

Number of False Drops

60

M-size

Figure 8. False drops Vs M-size

the index channel, MC is able to retrieve the CS the second

The figure shows that by using signatures with m-size

time. Moreover, as the resent of ALS is within one

equal to 20 bits, the lowest false drop rate can be obtained.

searching period prior to the real data broadcast, once MC

Ideally, m-size with half signature size (64 bits in this case)

gets the resent CS, it is most likely that it will receive the

will be the best, since the largest number of bit pattern for

a bit stream is constructed with same numbers of 1’s and

models achieves low and similar access time. In addition,

0’s (nCn/2), thus reducing the chance of collision.

as channel loading increases, the number of data

However, in the proposed models, each CS is in fact a

broadcasts also increases. Thus, CO’s broadcast queue will

superimposition of multiple ALSs from different BAs, and

be filled with awaiting data messages, which also increase

each ALS is in turn generated from a different number of

MC access time by delaying broadcast of the requested

attributes and thus contains different number of 1’s. This

data. The fact that the feedback model has the lowest

explains why the minimum m-size is different from the

access time is the result of the feedback mechanism with

theoretical result, which assumes uniformity in the ALSs.

signature resent.

In a real operational environment, it is difficult to predict

In addition, when loading increases, the differences in

the optimal m-size, because a change in system loading

MC access time between the basic and signature models

can change the optimal m-size.

also increase, which is basically caused by the lengthy AL attached to each IM. In the basic model, the number of

4.4. Impact of system loading on MC access time

BA’s requests is directly related to the number of IMs. If there are 300 BA’s requests, there will be 300 ALs

System loading is defined as the fraction that the

broadcasted on the index channel. Suppose MC’s query

broadcast channels are occupied for broadcasting data

attribute is in the last BA’s request, it is required to scan

messages. In the experiment, the loading is increased by

through all 300 IMs before switching to the data channel,

adding agents to the system in order to increase the usage

which is time consuming compared to the signature

of each data channel. The maximum value ‘1’ means that

models. Although ALs exist in the signature models, the

all channels are occupied at any instance during the

number of ALs that MC has to process is reduced since

simulation.

each channel holds only a fraction of all ALs. MC is only

Unit of Time (x105)

3.5
3

required to filter the ALs that exist on the data channel.
Basic Model
Signature Model
Feedback Model

Therefore, the difference in access time increases as loading increases.

2.5
2

5. Conclusion and Future Work

1.5

In this paper, we propose an HMCE architecture

1
0.125 0.25 0.375 0.5 0.625 0.75 0.875

1

System Loading

consisting of independent wireless channel operators, broadcast agents and a centralized index server. Compared

Figure 9. MC access time Vs System loading

to the existing data dissemination schemes for a

Figure 9 shows MC access time with respect to

multi-channel environment, HMCE provides a channel

different system loading. With light channel loading, fewer

through which MCs are able to know where to fetch their

data will be sent. Hence, the number of false drops is

desired data. Furthermore, three indexing methods

reduced. As a result, MC in the signature and feedback

applicable to the HMCE architecture were proposed,

(MOBICOM97). Budapest. September 1997.

namely the basic model, the signature model, and the signature model

with

channel

operator’s

feedback

[4]

C.H. Hsu, G. Lee, and A.L.P. Chen, “Index and data allocation on multiple broadcast channels considering data access frequencies,” in Proceedings of the 3rd
International Conference on Mobile Data Management
(MDM2002), pp. 87-93. January 2002.

[5]

T. Imielinski, S. Viswanathan, and B.R. Badrinath,
“Energy efficiency indexing on air,” in Proceedings of the
ACM Conference on Management of Data (SIGMOD94), pp. 25-36. May 1994.

[6]

T. Imielinski, S. Viswanathan, and B.R. Badrinath, “Data on air: Organization and access,” IEEE Transactions on
Knowledge and Data Engineering, 9(3). May/June 1997.

[7]

C.H. Ke, C. Lee, and C.C. Chen, “Broadcast scheduling for multiple channels in wireless information systems,” in
Proceedings of National Computer Symposium (NCS99), pp. 525-532. Taipei, Taiwan. December 1999.

[8]

W.C. Lee and D.L. Lee, “Signature caching techniques for information broadcast and filtering in mobile environments,” ACM/Baltzer Journal of Wireless
Networking (WINET), 5(1), 57-67. 1999.

[9]

A.Y. Ho, “Data indexing in heterogeneous multiple broadcast channels,” M.Phil. Dissertation, Department of
Computer Science, Hong Kong Unviersity of Science
Technology, Hong Kong, HKSAR, 2003.

[10]

CSIM18, Mesquite Software Inc.

(feedback model). The basic model mainly uses data attributes from broadcast agents to form index messages.
The signature model superimposes attribute list signatures for the purpose of indexing. Finally, the signature model with channel operator’s feedback is an enhancement of the signature model for reducing the effect of incorrect false drops. We showed the both the signature model and feedback model are significantly better than the basic model. Our work on HMCE represents the first attempt, to the best of our knowledge, to address a heterogeneous, autonomous broadcast environment. Much more research needs to be done to investigate different architectures (e.g.,
COs and CIS can directly communicate in scheduling the index and data broadcast [9]) and other index schemes.

Acknowledgment
This work was supported in part by grants from the
Research Grant Council of Hong Kong (Grant No.
HKUST 6179/03E).

References
[1]

S. Acharya, R. Alonso, M. Franklin, and S. Zdonik,
“Broadcast disks: Data management for asymmetric communication environments,” in Proceedings of the
ACM Conference on Management of Data (SIGMOD95), pp. 199-210. San Jose, California. May 1995.

[2]

V. Gondhalekar, R. Jain, and J. Werth, “Scheduling on airdisks: Efficient access to personalized information services via periodic wireless data broadcast,” in IEEE
International Conference on Communications (ICC 97), vol. 3, pp. 1276-1280. Montreal. 1997.

[3]

S. Hameed and N.H. Vaidya, “Log-time algorithm for scheduling single and multiple channel data broadcast,” in
Proceedings of the 3rd Annual ACM/IEEE International
Conference on Mobile Computing and Networking…...

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