Papers
Topics
Authors
Recent
Assistant
AI Research Assistant
Well-researched responses based on relevant abstracts and paper content.
Custom Instructions Pro
Preferences or requirements that you'd like Emergent Mind to consider when generating responses.
Gemini 2.5 Flash
Gemini 2.5 Flash 153 tok/s
Gemini 2.5 Pro 48 tok/s Pro
GPT-5 Medium 28 tok/s Pro
GPT-5 High 18 tok/s Pro
GPT-4o 100 tok/s Pro
Kimi K2 220 tok/s Pro
GPT OSS 120B 447 tok/s Pro
Claude Sonnet 4.5 36 tok/s Pro
2000 character limit reached

Improved Approximation Algorithms for Earth-Mover Distance in Data Streams (1404.6287v1)

Published 24 Apr 2014 in cs.DS

Abstract: For two multisets $S$ and $T$ of points in $[\Delta]2$, such that $|S| = |T|= n$, the earth-mover distance (EMD) between $S$ and $T$ is the minimum cost of a perfect bipartite matching with edges between points in $S$ and $T$, i.e., $EMD(S,T) = \min_{\pi:S\rightarrow T}\sum_{a\in S}||a-\pi(a)||_1$, where $\pi$ ranges over all one-to-one mappings. The sketching complexity of approximating earth-mover distance in the two-dimensional grid is mentioned as one of the open problems in the literature. We give two algorithms for computing EMD between two multi-sets when the number of distinct points in one set is a small value $k=\log{O(1)}(\Delta n)$. Our first algorithm gives a $(1+\epsilon)$-approximation using $O(k\epsilon{-2}\log{4}n)$ space and works only in the insertion-only model. The second algorithm gives a $O(\min(k3,\log\Delta))$-approximation using $O(\log{3}\Delta\cdot\log\log\Delta\cdot\log n)$-space in the turnstile model.

Citations (5)

Summary

We haven't generated a summary for this paper yet.

Lightbulb Streamline Icon: https://streamlinehq.com

Continue Learning

We haven't generated follow-up questions for this paper yet.

List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.