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A. Search algorithm in MDPN model
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Table A.1: Compact form of connection matrix for example of Figure (A.1).
ROW 1 2 3 3 4 4 4 5 5 5 6 6 6 7 7 8 9 9 10 11 11
COL 10 10 12 11 13 11 14 10 12 18 15 17 14 16 14 13 14 17 19 14 19
Entry 1 11 1 11 1 8 10 6 8 9 1 7 11 1 8 6 6 11 1 3 11
ROW 11 12 12 12 13 13 13 13 14 14 14 14 15 15 15 16 17 17 17 17 18
COL 13 24 20 14 14 16 20 26 17 21 22 16 18 23 17 17 18 22 24 25 26
Entry 13 4 11 13 2 3 8 9 3 8 11 13 3 11 13 2 2 6 8 11 11
Table A.2: Frequency and cumulative matrix of the forward connections.
Site no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Frequency 1 1 2 3 3 3 2 1 2 1 3 3 4 4
Cumulative 1 2 4 7 10 13 15 16 18 19 22 25 29 33
Site no. 15 16 17 18 19 20 21 22 23 24 25 26 27
Frequency 3 1 4 1 0 0 0 0 0 0 0 0 0
Cumulative 36 37 41 42 42 42 42 42 42 42 42 42 42
As we can see, the site numbers in the first row(ROW) of Table are sorted
in increasing order. The number of times a site number appears in ROW of
Table A.1 corresponds to the number of forward connections of that site. This
information in taken up in a frequency table (see second row of Table A.2)
together with its cumulative number of bonds (see third row of Table A.2).
Table A.2 along with second row of Table A.1 can be used to determine to
which sites a given site, N, is connected based on the following formula:
Forward sites
for site N = COL(cumulative(N) − frequency(N) + 1 : cumulative(N))
For example, for site number 12 (N = 12) we will have:
Forward sites
for site 12 = COL(cumulative(12) − frequency(12) + 1 : cumulative(12))
= COL(25 − 3 + 1 : 25) = COL(23 : 25) = [24, 20, 14]
Hence, the sites to which site number 12 is connected forward are located in
position 23 − 25 in the COL of Table A.1 which are sites number 24, 20, and
14.
To find the backward connections, we need to replace ROW and COL of Table
A.1 with each other (since in the connection matrix backward connections are
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