{'fraction_non_alphanumeric': 0.022789425706472195, 'fraction_numerical': 0.0, 'mean_word_length': 4.967391304347826, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Computing optimal or near-optimal trees for minimum-energy in wireless networks

We study minimum-energy broadcast routing in all-wireless networks. Up to now, a number of heuristics have been proposed for this NP-hard problem. Among them, the broadcast incremental power (BIP) algorithm, presented by Wieselthier et al., is most known. The contribution of our work consists of a refinement of the BIP algorithm and a novel integer programming formulation. The refined version of BIP is a natural extension of the original algorithm. The integer programming formulation allows us to compute optimal broadcast trees for networks of small size. For large-sized networks, the formulation admits the computation of a sharp lower bound to the optimal tree. We are thus able to efficiently assess the numerical performance of any heuristic algorithm for the problem. In our computational study, we compare the performance of our refined BlP algorithm to that of its original version, and examine the numerical performance of the two algorithms in terms of optimality using our integer programming model.