57 lines
1.3 KiB
Plaintext
57 lines
1.3 KiB
Plaintext
---- MbC ---
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MbC(P: l, r): (finds UH of P from x-coordinates l to r)
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Find median x-coordinate x_m
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Partition points on x_m into Pl and Pr
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Find bridge uv over x_m
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Remove points below bridge
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Recurse MbC(Pl: l, u.x) and MbC(Pr: v.x, r)
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Find bridge is finding the line (y=ax+b) such that:
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1) passes above all the points
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2) has the lowest intersection point with the median line
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---- 1D ----
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Unknown x1
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Minimize c1*x1
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such that
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a1*x1 \leq b1
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a2*x1 \leq b2
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...
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an*x1 \leq bn
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for each of the constraints:
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ai*x1 \leq bi
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=>
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if ai > 0: x1 <= bi/ai
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if ai < 0: x1 >= bi/ai
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if ai = 0:
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if bi < 0: impossible
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if bi \geq 0: always satisfied
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this means that each constraint half of the real line
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therefore run for-loop on bi/ai and check the ifs
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when we have feasible region/interval:
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if c1 > 0: choose minimum of interval
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if c1 < 0: choose maximum of interval
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if c1 = 0: degenerate
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---- 2D ----
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a and b are unknowns
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minimize ax_m + b
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such that y_i \leq ax_i + b, for every input point (x_i, y_i)
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where x_m is given (median)
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Algorithm:
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Initialise v
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Randomly shuffle constraints
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for i=1 to n:
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if constraint i does not violate v, do nothing
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else solve 1d LP on boundary of constraint i
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