A Recursive Approach to Solving Parity Games in Quasipolynomial Time
Zielonka's classic recursive algorithm for solving parity games is perhaps the simplest among the many existing parity game algorithms. However, its complexity is exponential, while currently the state-of-the-art algorithms have quasipolynomial complexity. Here, we present a modification of Zie...
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| Veröffentlicht in: | Logical methods in computer science Jg. 18, Issue 1; H. 1; S. 8:1 - 8:18 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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Logical Methods in Computer Science Association
01.01.2022
Logical Methods in Computer Science e.V |
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| ISSN: | 1860-5974, 1860-5974 |
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| Abstract | Zielonka's classic recursive algorithm for solving parity games is perhaps
the simplest among the many existing parity game algorithms. However, its
complexity is exponential, while currently the state-of-the-art algorithms have
quasipolynomial complexity. Here, we present a modification of Zielonka's
classic algorithm that brings its complexity down to
$n^{O\left(\log\left(1+\frac{d}{\log n}\right)\right)}$, for parity games of
size $n$ with $d$ priorities, in line with previous quasipolynomial-time
solutions. |
|---|---|
| AbstractList | Zielonka's classic recursive algorithm for solving parity games is perhaps the simplest among the many existing parity game algorithms. However, its complexity is exponential, while currently the state-of-the-art algorithms have quasipolynomial complexity. Here, we present a modification of Zielonka's classic algorithm that brings its complexity down to $n^{O\left(\log\left(1+\frac{d}{\log n}\right)\right)}$, for parity games of size $n$ with $d$ priorities, in line with previous quasipolynomial-time solutions. Zielonka's classic recursive algorithm for solving parity games is perhaps the simplest among the many existing parity game algorithms. However, its complexity is exponential, while currently the state-of-the-art algorithms have quasipolynomial complexity. Here, we present a modification of Zielonka's classic algorithm that brings its complexity down to $n^{O\left(\log\left(1+\frac{d}{\log n}\right)\right)}$, for parity games of size $n$ with $d$ priorities, in line with previous quasipolynomial-time solutions. Zielonka's classic recursive algorithm for solving parity games is perhaps the simplest among the many existing parity game algorithms. However, its complexity is exponential, while currently the state-of-the-art algorithms have quasipolynomial complexity. Here, we present a modification of Zielonka's classic algorithm that brings its complexity down to $n^{\mathcal{O}\left(\log\left(1+\frac{d}{\log n}\right)\right)}$, for parity games of size $n$ with $d$ priorities, in line with previous quasipolynomial-time solutions. |
| Author | Lehtinen, Karoliina Schewe, Sven Parys, Paweł Wojtczak, Dominik |
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| Snippet | Zielonka's classic recursive algorithm for solving parity games is perhaps
the simplest among the many existing parity game algorithms. However, its
complexity... Zielonka's classic recursive algorithm for solving parity games is perhaps the simplest among the many existing parity game algorithms. However, its complexity... |
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| SubjectTerms | Computer Science computer science - computer science and game theory computer science - formal languages and automata theory |
| Title | A Recursive Approach to Solving Parity Games in Quasipolynomial Time |
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