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The Exchange Problem

Authors Mohit Garg , Suneel Sarswat

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LIPIcs.AFT.2025.25.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Applied computing → Electronic commerce
Keywords
  • Exchanges
  • Double Auctions
  • Matching Algorithms
  • Element Distinctness
  • Time Complexity

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Abstract

Auctions are widely used in exchanges to match buy and sell requests. Once the buyers and sellers place their requests, the exchange determines how these requests are to be matched. The two most popular objectives used while determining the matching are maximizing volume with dynamic pricing and maximizing volume at a uniform price. In this work, we study the algorithmic complexity of the problems arising from these matching tasks.
For dynamic-price matching, we establish a lower bound of Ω(n log n) on the running time, thereby proving that the currently best-known O(n log n) algorithm is time-optimal. In contrast, for uniform-price matching, we present a linear-time algorithm, improving upon previous methods that require O(n log n) time to match n requests.

Cite As Get BibTex

Mohit Garg and Suneel Sarswat. The Exchange Problem. In 7th Conference on Advances in Financial Technologies (AFT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 354, pp. 25:1-25:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.AFT.2025.25

Author Details

Mohit Garg
  • Indian Institute of Science, Bengaluru, India
Suneel Sarswat
  • National Institute of Securities Markets, Mumbai, India

Funding

  • Garg, Mohit: Supported in part by a fellowship from the Walmart Center for Tech Excellence at IISc (CSR Grant WMGT-23-0001).

Acknowledgements

The authors express their gratitude to Jaikumar Radhakrishnan for bringing the element distinctness problem to their attention and for engaging in insightful discussions that enriched their understanding of it. They are also thankful to him for helping improve the presentation of this work.

References

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