Fast and Space-Efficient Fixed-Length Path Optimization
Keywords: path optimization, fixed length constraint, space efficiency
TL;DR: We find an optimal path under a length constraint with low runtime and reduced space complexity.
Abstract: Several optimization problems seek a path of predetermined length among network nodes that minimizes a cost function. Conventionally, such problems are tackled by dynamic programming (DP) applying a Bellman-type equation. A prominent example is Viterbi decoding, which returns the path in a Hidden Markov Model that best explains a series of observations, with applications from bioinformatics to communication systems and speech recognition. However, DP-based solutions (i) exhaustively explore a search space linear in both network size and path length in time quadratic in network size, without exploiting data characteristics, and (ii) require memory commensurate with that search space to reconstruct the optimal path. In this paper, we propose Isabella (Dijkstra-Bellman), a novel framework that finds optimal paths of predetermined length in time- and space-efficient fashion by a combination of best-first-search, depth-first-search, and divide-and-conquer strategies. The best-first-search component avoids the exhaustive exploration of the search space using a priority queue; the depth-first-search component keeps the size of that queue in check; and the divide-and-conquer component constructs the optimal path recursively and parsimoniously after determining its cost. We apply Isabella to Viterbi decoding, introducing algorithms that visit the most promising pathways first and control memory consumption. To emphasize the generality of Isabella, we also instantiate it with an algorithm for histogram construction. To our knowledge, no previous work addresses such problems in this manner. Our experimental evaluation shows our solutions to be highly time- and space-efficient compared to standard dynamic programming.
Primary Area: optimization
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Submission Number: 11179
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