The Exchange Problem (2403.03046v1)
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 at a uniform price and maximizing volume with dynamic pricing. In this work, we study the algorithmic complexity of the problems arising from these matching tasks. We present a linear time algorithm for uniform price matching which is an improvement over the previous algorithms that take $O(n\log n)$ time to match $n$ requests. For dynamic price matching, we establish a lower bound of $\Omega(n \log n)$ on the running time, thereby proving that the currently known best algorithm is time-optimal.
- Time bounds for selection. J. Comput. Syst. Sci., 7(4):448–461, 1973.
- Ravi B. Boppana. The decision-tree complexity of element distinctness. Inf. Process. Lett., 52(6):329–331, 1994.
- Truthful and competitive double auctions. In Rolf H. Möhring and Rajeev Raman, editors, Algorithms - ESA 2002, 10th Annual European Symposium, Rome, Italy, September 17-21, 2002, Proceedings, volume 2461 of Lecture Notes in Computer Science, pages 361–373. Springer, 2002.
- The design and regulation of exchanges: A formal approach. In Anuj Dawar and Venkatesan Guruswami, editors, 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2022, December 18-20, 2022, IIT Madras, Chennai, India, volume 250 of LIPIcs, pages 39:1–39:21. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022.
- M Garg and S Sarswat. Efficient and Verified Continuous Double Auctions. In R. Piskac and A. Voronkov, editors, Short Papers of the 24th International Conference on Logic for Programming Artificial Intelligence and Reasoning, 2023.
- Kurt Mehlhorn. Data Structures and Algorithms 1: Sorting and Searching, volume 1 of EATCS Monographs on Theoretical Computer Science. Springer, 1984.
- L. Mirsky. A dual of dilworth’s decomposition theorem. The American Mathematical Monthly, 78(8):876–877, 1971.
- Maximizing matching in double-sided auctions. In Maria L. Gini, Onn Shehory, Takayuki Ito, and Catholijn M. Jonker, editors, International conference on Autonomous Agents and Multi-Agent Systems, AAMAS ’13, Saint Paul, MN, USA, May 6-10, 2013, pages 1283–1284. IFAAMAS, 2013.
- Verified double sided auctions for financial markets. In Liron Cohen and Cezary Kaliszyk, editors, 12th International Conference on Interactive Theorem Proving, ITP 2021, June 29 to July 1, 2021, Rome, Italy (Virtual Conference), volume 193 of LIPIcs, pages 28:1–28:18. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021.
- Jaikumar Radhakrishnan. Entropy and counting. Computational mathematics, modelling and algorithms, 146, 2003.
- Flexible double auctions for electronic commerce: theory and implementation. Decis. Support Syst., 24(1):17–27, 1998.
- Maximal matching for double auction. In Jiuyong Li, editor, AI 2010: Advances in Artificial Intelligence - 23rd Australasian Joint Conference, Adelaide, Australia, December 7-10, 2010. Proceedings, volume 6464 of Lecture Notes in Computer Science, pages 516–525. Springer, 2010.