# Faster algorithms for quantitative verification in constant treewidth graphs

Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. 2015. Faster algorithms for quantitative verification in constant treewidth graphs. CAV: Computer Aided Verification, LNCS, vol. 9206, 140–157. http://arxiv.org/abs/1504.07384

Conference Paper | Published | English

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Department
Series Title
LNCS
Abstract
We consider the core algorithmic problems related to verification of systems with respect to three classical quantitative properties, namely, the mean-payoff property, the ratio property, and the minimum initial credit for energy property. The algorithmic problem given a graph and a quantitative property asks to compute the optimal value (the infimum value over all traces) from every node of the graph. We consider graphs with constant treewidth, and it is well-known that the control-flow graphs of most programs have constant treewidth. Let n denote the number of nodes of a graph, m the number of edges (for constant treewidth graphs m=O(n)) and W the largest absolute value of the weights. Our main theoretical results are as follows. First, for constant treewidth graphs we present an algorithm that approximates the mean-payoff value within a multiplicative factor of ϵ in time O(n⋅log(n/ϵ)) and linear space, as compared to the classical algorithms that require quadratic time. Second, for the ratio property we present an algorithm that for constant treewidth graphs works in time O(n⋅log(|a⋅b|))=O(n⋅log(n⋅W)), when the output is ab, as compared to the previously best known algorithm with running time O(n2⋅log(n⋅W)). Third, for the minimum initial credit problem we show that (i) for general graphs the problem can be solved in O(n2⋅m) time and the associated decision problem can be solved in O(n⋅m) time, improving the previous known O(n3⋅m⋅log(n⋅W)) and O(n2⋅m) bounds, respectively; and (ii) for constant treewidth graphs we present an algorithm that requires O(n⋅logn) time, improving the previous known O(n4⋅log(n⋅W)) bound. We have implemented some of our algorithms and show that they present a significant speedup on standard benchmarks.
Publishing Year
Date Published
2015-07-16
Acknowledgement
The research was partly supported by Austrian Science Fund (FWF) Grant No P23499- N23, FWF NFN Grant No S11407-N23 (RiSE/SHiNE), ERC Start grant (279307: Graph Games), and Microsoft faculty fellows award.
Volume
9206
Page
140 - 157
Conference
CAV: Computer Aided Verification
Conference Location
San Francisco, CA, USA
Conference Date
2015-07-18 – 2015-07-24
IST-REx-ID

### Cite this

Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. Faster algorithms for quantitative verification in constant treewidth graphs. In: Vol 9206. Springer; 2015:140-157. doi:10.1007/978-3-319-21690-4_9
Chatterjee, K., Ibsen-Jensen, R., & Pavlogiannis, A. (2015). Faster algorithms for quantitative verification in constant treewidth graphs (Vol. 9206, pp. 140–157). Presented at the CAV: Computer Aided Verification, San Francisco, CA, USA: Springer. https://doi.org/10.1007/978-3-319-21690-4_9
Chatterjee, Krishnendu, Rasmus Ibsen-Jensen, and Andreas Pavlogiannis. “Faster Algorithms for Quantitative Verification in Constant Treewidth Graphs,” 9206:140–57. Springer, 2015. https://doi.org/10.1007/978-3-319-21690-4_9.
K. Chatterjee, R. Ibsen-Jensen, and A. Pavlogiannis, “Faster algorithms for quantitative verification in constant treewidth graphs,” presented at the CAV: Computer Aided Verification, San Francisco, CA, USA, 2015, vol. 9206, pp. 140–157.
Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. 2015. Faster algorithms for quantitative verification in constant treewidth graphs. CAV: Computer Aided Verification, LNCS, vol. 9206, 140–157.
Chatterjee, Krishnendu, et al. Faster Algorithms for Quantitative Verification in Constant Treewidth Graphs. Vol. 9206, Springer, 2015, pp. 140–57, doi:10.1007/978-3-319-21690-4_9.
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