On the optimality of Bellman-Ford-Moore shortest path algorithm

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• 作者：Stasys Jukna ; ¹ ; ^{jukna@thi.informatik.uni-frankfurt.de" class="auth_mail" title="E-mail the corresponding author} ; Georg Schnitger ^{schnitger@thi.informatik.uni-frankfurt.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Shortest paths ; Matrix multiplication ; Dynamic programming ; Tropical semiring ; Lower bounds
• 刊名：Theoretical Computer Science
• 出版年：2016
• 出版时间：16 May 2016
• 年：2016
• 卷：628
• 期：Complete
• 页码：101-109
• 全文大小：342 K

文摘

We prove a general lower bound on the size of switching-and-rectifier networks over any semiring of zero characteristic, including the 6002073&_mathId=si1.gif&_user=111111111&_pii=S0304397516002073&_rdoc=1&_issn=03043975&md5=cc29e834216b5cbf95b45e12d0ffbef3" title="Click to view the MathML source">(min⁡,+)$(\min ,+)$ semiring. Using it, we show that the classical dynamic programming algorithm of Bellman, Ford and Moore for the shortest s-t path problem is optimal, if only Min and Sum operations are allowed.