A 1-relaxed minimum broadcast graph on 15 vertices
In 1998, Shastri studied the sparsest possible broadcast graphs in which broadcasting can be accomplished in slightly more than the optimal time of ⌜ log 2 n⌝ . In particular, they constructed the sparsest possible time-relaxed broadcast graphs for small n (≤ 14) and very sparse time-relaxed broadca...
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Published in | Applied mathematics letters Vol. 17; no. 3; pp. 249 - 252 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Oxford
Elsevier Ltd
01.03.2004
Elsevier |
Subjects | |
Online Access | Get full text |
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Summary: | In 1998, Shastri studied the sparsest possible broadcast graphs in which broadcasting can be accomplished in slightly more than the optimal time of
⌜
log
2 n⌝
. In particular, they constructed the sparsest possible time-relaxed broadcast graphs for small
n (≤ 14) and very sparse time-relaxed broadcast graphs for larger
n (≤ 65). Let
B
t
(
n) be the number of edges in the sparsest possible graph on n vertices in which broadcasting can be accomplished in
t additional steps than the optimal (i.e., in
⌜
log
2 n⌝ + t
steps), they conjectured that
B
1(15) = 18. In this paper, we give a 1-relaxed minimum broadcast graph on 15 vertices which shows that
B
1(15) = 17, thus reject the conjecture. |
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ISSN: | 0893-9659 1873-5452 |
DOI: | 10.1016/S0893-9659(04)90059-6 |