Subtree isomorphism revisited

Amir Abboud, Arturs Backurs, Thomas Dueholm Hansen, Virginia Vassilevska Williams, Or Zamir

نتاج البحث: نشر في مجلةمقالةمراجعة النظراء

ملخص

The Subtree Isomorphism problem asks whether a given tree is contained in another given tree. The problem is of fundamental importance and has been studied since the 1960s. For some variants, e.g., orderedtrees, near-linear time algorithms are known, but for the general case truly subquadratic algorithms remain elusive. Our first result is a reduction from the Orthogonal Vectors problem to Subtree Isomorphism, showing that a truly subquadratic algorithm for the latter refutes the Strong Exponential Time Hypothesis (SETH). In light of this conditional lower bound, we focus on natural special cases for which no truly subquadratic algorithms are known. We classify these cases against the quadratic barrier, showing in particular that: • Even for binary, rooted trees, a truly subquadratic algorithm refutes SETH. • Even for rooted trees of depthO(log logn), wheren is the total number of vertices, a truly subquadratic algorithm refutes SETH. • For every constant d, there is a constant εd > 0 and a randomized, truly subquadratic algorithm for degree-d rooted trees of depth at most (1 + εd) logd n. In particular, there is an O(min{2.85h,n2}) algorithm for binary trees of depth h. Our reductions utilize new “tree gadgets” that are likely useful for future SETH-based lower bounds for problems on trees. Our upper bounds apply a folklore result from randomized decision tree complexity.

اللغة الأصليةالإنجليزيّة
رقم المقال27
دوريةACM Transactions on Algorithms
مستوى الصوت14
رقم الإصدار3
المعرِّفات الرقمية للأشياء
حالة النشرنُشِر - يوليو 2018

All Science Journal Classification (ASJC) codes

  • !!Mathematics (miscellaneous)

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