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@@ -6,11 +6,7 @@
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#include "shapes.hpp"
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#include "heap.hpp"
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-/*
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-The Optimized Insert Protocol
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-Takes in the additive share of the value to be inserted
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-And adds the the value into the heap while keeping the heap property intact
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-
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+/*
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The heap datastructure is stored in an array with the starting index as 1 (and not 0)
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For nodes stored in index i of the array, the parent is stored at i/2 and
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The left and right children are stored at 2i and 2i + 1
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@@ -29,20 +25,24 @@ All the unused array indicies have MAX_INT stored in them
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*/
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/*
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+The Optimized Insert Protocol
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+Takes in the additive share of the value to be inserted
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+and adds the the value into the heap while keeping the heap property intact
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+
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_Protocol 4_ from PRAC: Round-Efficient 3-Party MPC for Dynamic Data Structures
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Consider the following insertion path with: x0 < x1 < x2 < NewElement < x3 < x4
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- x0 x0 x0
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- / \ / \ / \
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- x1 x1 x1
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- \ \ \
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- x2 x2 x2
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- \ \ \
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- x3 ( ) NewElement
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- \ \ \
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- x4 x3 x3
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- \ \ \
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- ( ) x4 x4
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+ x0 x0 x0
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+ / \ / \ / \
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+ x1 x1 x1
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+ / / /
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+ x2 x2 x2
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+ \ \ \
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+ x3 ( ) NewElement
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+ \ \ \
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+ x4 x3 x3
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+ / / /
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+ ( ) x4 x4
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(Path with new element) (binary search to determine (After insertion)
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the point where New Element
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