Improved algorithms for alternating matrix space isometry: From theory to practice
- Publication Type:
- Conference Proceeding
- Citation:
- Leibniz International Proceedings in Informatics, LIPIcs, 2020, 173
- Issue Date:
- 2020-08-01
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Motivated by testing isomorphism of p-groups, we study the alternating matrix space isometry problem (AltMatSpIso), which asks to decide whether two m-dimensional subspaces of n × n alternating (skew-symmetric if the field is not of characteristic 2) matrices are the same up to a change of basis. Over a finite field F with some prime p 6= 2, solving AltMatSpIso in time p is equivalent to testing isomorphism of p-groups of class 2 and exponent p in time polynomial in the group order. The latter problem has long been considered a bottleneck case for the group isomorphism problem. Recently, Li and Qiao presented an average-case algorithm for AltMatSpIso in time p when n and m are linearly related (FOCS’17). In this paper, we present an average-case algorithm for AltMatSpIso in time p . Besides removing the restriction on the relation between n and m, our algorithm is considerably simpler, and the average-case analysis is stronger. We then implement our algorithm, with suitable modifications, in Magma. Our experiments indicate that it improves significantly over default (brute-force) algorithms for this problem. p O (n+m) O (n) O (n+m)
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