On broadcasting in unicyclic graphs

HUB-GA: A heuristic for universal lists broadcasting using genetic algorithm

“…Grid G n×m n+m−2, proved in [26] n+m−2, proved in [15] n + m − 2, proved in [10] n + m − 1, proved in [10] Tori [46] Complete graph Kn ⌈log n⌉, folklore ≤ ⌈log n⌉ + 2⌈ √ log n⌉, proved in [15] ≤ ⌈log n⌉ + 2⌈ √ log n⌉, proved in [10] ≤ ⌈log n⌉ + 2⌈ √ log n⌉, proved in [10] Hypercube which B cl (K n ) is known, there is no optimal bound for this network under universal list models. Besides, as mentioned in [29], the broadcast problem becomes more difficult when there are several intersecting cycles. In the previous experiment, we studied this problem for complete graphs K n .…”

“…Other researches include grid and tori [26], cube connected cycle [27], and shuffle exchange [28]. Later on, more algorithms for non-trivial topologies such as unicyclic graphs [29], fully connected trees [30], and tree of cycles [31] were developed, to name a few.…”

Convergecast with Unbounded Number of Channels

“…In [18] it is shown that the problem remains NP-hard even for 3-regular planar graphs. Polynomial-time algorithms for the exact solution are known only for few special graphs: trees [8], complete graphs [19], and unicyclic graphs [20]. An algorithm based on a combinatorial approach with O(log n) approximated ratio were presented in [21].…”

Broadcasting in Fully Connected Trees

“…The heuristics in [1] and [12] are the best existing heuristics for broadcasting in practice with O(|V | 2 · |E|) and O(|E|) respectively. The broadcast problem has been solved with a linear algorithm only for trees [20], unicyclic graphs [10], [11] and tree of cycles [9]. Also there is an O(n 4k+5 ) broadcast algorithm for partial k-trees [2].…”