# Improvement in Small Progress Measures

@inproceedings{Gazda2015ImprovementIS, title={Improvement in Small Progress Measures}, author={Maciej Gazda and Tim A. C. Willemse}, booktitle={GandALF}, year={2015} }

Small Progress Measures is one of the classical parity game solving algorithms. For games with n vertices, m edges and d different priorities, the original algorithm computes the winning regions and a winning strategy for one of the players in O(dm.(n/floor(d/2))^floor(d/2)) time. Computing a winning strategy for the other player requires a re-run of the algorithm on that player's winning region, thus increasing the runtime complexity to O(dm.(n/ceil(d/2))^ceil(d/2)) for computing the winning…

## 3 Citations

### From Quasi-Dominions to Progress Measures

- EconomicsArXiv
- 2020

This paper revisits the approaches to the solution of parity games based on progress measures and shows how the notion of quasi dominions can be integrated with those approaches and introduces a novel notion of measure and new approach to prove correctness of the resulting solution technique.

### Oink: an Implementation and Evaluation of Modern Parity Game Solvers

- Computer ScienceTACAS
- 2018

A new and easy to extend tool Oink is implemented, which is a high-performance implementation of modern parity game algorithms and solvers, both on real world benchmarks and randomly generated games.

### Attracting Tangles to Solve Parity Games

- Computer ScienceCAV
- 2018

It is argued that tangles play a fundamental role in the prominent parity game solving algorithms and it is shown that tangle learning is competitive in practice and the fastest solver for large random games.

## References

SHOWING 1-10 OF 20 REFERENCES

### Strategy Derivation for Small Progress Measures

- Computer ScienceArXiv
- 2014

This work provides a novel operational interpretation of progress measures, and modify the algorithm so that it derives the winning strategies for both players in one pass, and reduces the upper bound on strategy derivation for SPM.

### Small Progress Measures for Solving Parity Games

- Computer ScienceSTACS
- 2000

A new algorithm for deciding the winner in parity games, and hence also for the modal µ-calculus model checking, based on a notion of game progress measures, characterized as pre-fixed points of certain monotone operators on a complete lattice.

### A Discrete Strategy Improvement Algorithm for Solving Parity Games

- Computer ScienceCAV
- 2000

A discrete strategy improvement algorithm is given for constructing winning strategies in parity games, thereby providing also a new solution of the model-checking problem for the modal μ-calculus.…

### Algorithms for Parity Games

- Computer ScienceAutomata, Logics, and Infinite Games
- 2001

The aim of this chapter is to review some of the algorithmic approaches to the problem of computing winning strategies in parity games with finite arenas and other two-player games, and to underline the importance of looking for an efficient algorithm solving this particular problem.

### An Optimal Strategy Improvement Algorithm for Solving Parity and Payoff Games

- EconomicsCSL
- 2008

A novel strategy improvement algorithm for parity and payoff games is presented, which is guaranteed to select, in each improvement step, an optimal combination of local strategy modifications.

### Zielonka's Recursive Algorithm: dull, weak and solitaire games and tighter bounds

- Computer ScienceGandALF
- 2013

It is shown that an optimisation of Zielonka's algorithm permits solving games from all three classes in polynomial time, and that there is a family of (non-special) games M that permits the algorithm to establish a lower bound of 2^(n/3), improving on the previous lower bound for the algorithm.

### Solving Parity Games in Practice

- Computer ScienceATVA
- 2009

A generic solver is presented that intertwines optimisations with any of the existing parity game algorithms which is only called on parts of a game that cannot be solved faster by simpler methods, showing that using this approach vastly speeds up the solving process.

### Faster algorithms for mean-payoff games

- Computer ScienceFormal Methods Syst. Des.
- 2009

A new pseudopolynomial algorithm is presented for solving two-player games played on a weighted graph with mean-payoff objective and with energy constraints, improving the best known worst-case complexity for pseudopoly Nominal mean- payoff algorithms.

### Non-oblivious Strategy Improvement

- Computer ScienceLPAR
- 2010

A structural property of these games is described, and it is shown that these structures can affect the behaviour of strategy improvement and can be used to accelerate strategy improvement algorithms.