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@@ -247,10 +247,19 @@ void verify_parent_children_heaps(MPCTIO tio, yield_t &yield, RegAS parent, RegA
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-//
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-//
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-//
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-//
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+// Let "x" be the root, and let "y" and "z" be the left and right children
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+// For an array, we have A[i] = x, A[2i] = y, A[2i + 1] = z.
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+// We want x \le y, and x \le z.
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+// The steps are as follows:
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+// Step 1: compare(y,z); (1st call to to MPC Compare)
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+// Step 2: smaller = min(y,z); This is done with an mpcselect (1st call to mpcselect)
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+// Step 3: if(smaller == y) then smallerindex = 2i else smalleindex = 2i + 1; This is done with an mpcselect (2nd call to mpcselect)
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+// Step 4: compare(x,smaller); (2nd call to to MPC Compare)
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+// Step 5: smallest = min(x, smaller); (3 call to mpcselect)
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+// Step 6: otherchild = max(x, smaller) (4th call to mpcselect)
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+// Step 7: A[i] \gets smallest (1st Duoam Write)
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+// Step 8: A[smallerindex] \gets otherchild (2nd Duoam Write)
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+// Overall restore_heap_property takes 2 MPC Comparisons, 4 MPC Selects, and 2 Duoram Writes
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RegXS HEAP::restore_heap_property(MPCTIO tio, yield_t &yield, RegXS index)
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{
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RegAS smallest;
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avadapal