International Scholarly Research Notices

Research Article

Polynomial Time Instances for the IKHO Problem

Figure 1

Representing Observation 1. The gray area indicates where 𝑥 is equal to 𝑦 , that is, the knapsacks [ 1 , 𝑎 ] . The arrow represents the left most possible radiation as starting from the left most possible different bit. Since this radiation cannot reach the knapsacks [ 1 , 𝑎 − 𝑢 ] , then, for ℓ ∈ [ 1 , 𝑎 − 𝑢 ] , 𝑤 ( 𝑥 , ℓ ) and 𝑤 ( 𝑦 , ℓ ) cannot differ as they depend only on the common bits [ 1 , 𝑎 ] .
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