An Efficient Parallel Strong Orientation

Cover An Efficient Parallel Strong Orientation
An Efficient Parallel Strong Orientation
U Vishkin
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Complexitj^ . N processors are used. The classification into the cases takes 0(1) time. The minimum and maximum computations in (b), (c) and (d) can be done in O(log n) time using the obvious algorithm (that is, compare, Iteratively, disjoint pairs of "winners").
Step-4. -2 . Assign to each edge e which was selected at Step A. L a new 'serial number' SERIAL(e) as follows. SERIAL(e) is a pair which consists of the level of Ad-LCA(v) and its original serial number (a number between 1 and m). That
... is SERIAL(e) := (LEVEL(Ad-LCA(V)) . "original serial number of e"). Complexity . N processors, 0(1) time. Let e be any edge in E-T such that SERIAL(e) was not defined in Step 4. 2. For explanation purposes only set SERIAL(e) := (LEVEL(LCA(e)) . "origianl serial number of e" + m). The discussion below explains why we can dispense with this assignment (and actually ignore all edges of E-T whose SERIAL(e) was not defined in Step 4. 2 in the computation of master edges that follows) without affecting the correctness of the algorithm.

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