2026-07-28T08:11:47Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:6667 2024-03-06T10:38:38Z ddc:004 open_access

A Direct-Sum Theorem for Read-Once Branching Programs Rao, Anup Sinha, Makrand Direct-sum Information complexity Streaming Algorithms We study a direct-sum question for read-once branching programs. If M(f) denotes the minimum average memory required to compute a function f(x_1,x_2, ..., x_n) how much memory is required to compute f on k independent inputs that arrive in parallel? We show that when the inputs are sampled independently from some domain X and M(f) = Omega(n), then computing the value of f on k streams requires average memory at least Omega(k * M(f)/n). Our results are obtained by defining new ways to measure the information complexity of read-once branching programs. We define two such measures: the transitional and cumulative information content. We prove that any read-once branching program with transitional information content I can be simulated using average memory O(n(I+1)). On the other hand, if every read-once branching program with cumulative information content I can be simulated with average memory O(I+1), then computing f on k inputs requires average memory at least Omega(k * (M(f)-1)). Schloss Dagstuhl – Leibniz-Zentrum für Informatik Anup Rao and Makrand Sinha 2016 Is Part Of LIPIcs, Volume 60, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.APPROX-RANDOM.2016.44 urn:nbn:de:0030-drops-66676 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2016.44 eng https://creativecommons.org/licenses/by/3.0/legalcode