Pushing the Online Matrix-Vector Conjecture Off-Line and Identifying Its Easy Cases

• Published in: Frontiers in Algorithmics Vol. 11458; pp. 156 - 169
• Main Authors: Gąsieniec, Leszek, Jansson, Jesper, Levcopoulos, Christos, Lingas, Andrzej, Persson, Mia
• Format: Book Chapter Conference Proceeding
• Language: English
• Published: Switzerland Springer International Publishing AG 2019; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Boolean matrix; Computer and Information Science; Computer and Information Sciences; Computer Science; Computer Sciences; Data- och informationsvetenskap (Datateknik); Datavetenskap (datalogi); Dynamic graph problems; Natural Sciences; Naturvetenskap; Online computation; Product of matrix and vector; Time complexity
• ISBN: 3030181251; 9783030181253; 9783030181260; 303018126X
• ISSN: 0302-9743; 1611-3349; 1611-3349
• DOI: 10.1007/978-3-030-18126-0_14

Henzinger et al. posed the so called Online Boolean Matrix-vector Multiplication (OMv) conjecture and showed that it implies tight hardness results for several basic partially dynamic or dynamic problems [STOC’15]. We show that the OMv conjecture is implied by a simple off-line conjecture. If a not uniform (i.e., it might be different for different matrices) polynomial-time preprocessing of the matrix in the OMv conjecture is allowed then we can show such a variant of the OMv conjecture to be equivalent to our off-line conjecture. On the other hand, we show that the OMV conjecture does not hold in the restricted cases when the rows of the matrix or the input vectors are clustered.