{'fraction_non_alphanumeric': 0.016375545851528384, 'fraction_numerical': 0.008733624454148471, 'mean_word_length': 5.457746478873239, '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}}
A distributed dual ascent algorithm for Steiner problems in multicast routing

Multicast routing problems are often modeled as Steiner Problems in undirected or directed graphs, the latter case being particularly suitable to cases where most of the traffic has a single source. Sequential Steiner heuristics are not convenient in that context, because one cannot assume that a central node has complete information about the topology and the state of a large wide area network. This article introduces a distributed version of a Dual Ascent primal‐dual heuristic, known for its remarkably good practical results, lower and upper bounds, in both undirected and directed Steiner problems. Complexity analysis and experimental results are also presented, showing the efficiency of the proposed algorithm when compared with the best distributed algorithms in the literature. © 2008 Wiley Periodicals, Inc. NETWORKS, 2009