핵심 개념
Earth Mover's Distance under Translation (EMDuT) complexity analysis and lower bound proof.
초록
The content discusses the complexity of Earth Mover's Distance under Translation (EMDuT) in computer science. It presents algorithms, conditional lower bounds, and a reduction from the Orthogonal Vectors problem. The construction of red and blue point sets for the reduction is detailed. Key insights include the Orthogonal Vectors Hypothesis (OVH) and the implications of the reduction on EMDuT complexity.
- Introduction to Earth Mover's Distance (EMD) and EMD under Translation (EMDuT).
- Algorithms for EMD and EMDuT in different dimensions.
- Conditional lower bounds based on hypotheses.
- Reduction from the Orthogonal Vectors problem to EMDuT.
- Construction of red and blue point sets for the reduction.
통계
EMDuT(B, R)를 계산하는 데 O(n log n) 시간이 소요됨.
EMDuT(B, R)를 계산하는 데 O(mn(log n + log2 m)) 시간이 소요됨.
Orthogonal Vectors Hypothesis (OVH)에 따르면 O(n2−δ) 시간에 Orthogonal Vectors 문제를 해결할 수 없음.
인용구
"EMDuT in R1, we present an e O(n2)-time algorithm."
"Assuming OVH, for any constant δ > 0 there is no algorithm that computes EMDuT(B, R) in time O(n2−δ)."