Certifying Algorithms for Recognizing Interval Graphs and Permutation Graphs

Kratsch, Dieter; McConnell, Ross M.; Mehlhorn, Kurt; Spinrad, Jeremy P.

doi:10.1137/s0097539703437855

Cited by 81 publications

(79 citation statements)

References 25 publications

(56 reference statements)

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“…[KMMS03]), in the sense that, given an optimal pair of strategies, the vector of potentials provided by the algorithm can be used to verify optimality in linear time (otherwise verifying optimality requires solving two linear programs).…”

Section: Potential Transformations and Canonical Forms; Sketch Of Ourmentioning

confidence: 99%

A Pumping Algorithm for Ergodic Stochastic Mean Payoff Games with Perfect Information

Boros

Elbassioni

Gurvich

et al. 2010

Integer Programming and Combinatorial Optimization

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Abstract. We consider two-person zero-sum stochastic mean payoff games with perfect information, or BWR-games, given by a digraph G = (V = VB ∪ VW ∪ VR, E), with local rewards r : E → R, and three types of vertices: black VB, white VW , and random VR. The game is played by two players, White and Black: When the play is at a white (black) vertex v, White (Black) selects an outgoing arc (v, u). When the play is at a random vertex v, a vertex u is picked with the given probability p (v, u). In all cases, Black pays White the value r(v, u). The play continues forever, and White aims to maximize (Black aims to minimize) the limiting mean (that is, average) payoff. It was recently shown in [BEGM09a] that BWR-games are polynomially equivalent with the classical Gillette games, which include many well-known subclasses, such as cyclic games, simple stochastic games (SSG), stochastic parity games, and Markov decision processes. In this paper, we give a new algorithm for solving BWR-games in the ergodic case, that is when the optimal values do not depend on the initial position. Our algorithm solves a BWR-game by reducing it, using a potential transformation, to a canonical form in which the value and optimal strategies of both players are obvious for every initial position, since a locally optimal move in it is optimal in the whole game. We show that this algorithm is pseudo-polynomial when the number of random nodes is constant. We also provide an almost matching lower bound on its running time, and show that this bound holds for a wider class of algorithms. Our preliminary experiments with the algorithm indicate that it behaves much better than its estimated worst-case running time. This and the fact that every iteration is simple and can be implemented in a distributed way makes it a good candidate for practical applications.

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Section: Potential Transformations and Canonical Forms; Sketch Of Ourmentioning

confidence: 99%

A Pumping Algorithm for Ergodic Stochastic Mean Payoff Games with Perfect Information

Boros

Elbassioni

Gurvich

et al. 2010

Integer Programming and Combinatorial Optimization

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“…, a 0 of a polynomial, given its roots. In the following, we give a result, related to certifying algorithms [22], stating that if the vector coefficients a = [a n , a n−1 , . .…”

Section: Queries and Verificationmentioning

confidence: 99%

Optimal Verification of Operations on Dynamic Sets

Papamanthou

Tamassia

Triandopoulos

2011

Lecture Notes in Computer Science

113

123

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We study the verification of set operations in the model of authenticated data structures, namely the problem of cryptographically checking the correctness of outsourced set operations performed by an untrusted server over a dynamic collection of sets that are owned (and updated) by a trusted source. We present a new authenticated data structure scheme that allows any entity to publicly verify the correctness of primitive sets operations such as intersection, union, subset and set difference. Based on a novel extension of the security properties of bilinear-map accumulators as well as on a primitive called accumulation tree, our authenticated data structure is the first to achieve optimal verification and proof complexity (i.e., only proportional to the size of the query parameters and the answer), as well as optimal update complexity (i.e., constant), and without bearing any extra asymptotic space overhead. Queries (i.e., constructing the proof) are also efficient, adding a logarithmic overhead to the complexity needed to compute the actual answer. In contrast, existing schemes entail high communication and verification costs or high storage costs as they recompute the query over authentic data or precompute answers to all possible queries. Applications of interest include efficient verification of keyword search and database queries. We base the security of our constructions on the bilinear q-strong Diffie-Hellman assumption.

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“…This provides a lot of opportunities for bugs to creep in, and certifying algorithms would have the added benefit that they would allow us to be sure of the correctness of the output without having to trust the correctness of the libraries. See [29,23] for more on this point of view.…”

Section: Further Workmentioning

confidence: 99%

Symbolic and Analytic Techniques for Resource Analysis of Java Bytecode

Aspinall

Atkey

MacKenzie

et al. 2010

Trustworthly Global Computing

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Abstract. Recent work in resource analysis has translated the idea of amortised resource analysis to imperative languages using a program logic that allows mixing of assertions about heap shapes, in the tradition of separation logic, and assertions about consumable resources. Separately, polyhedral methods have been used to calculate bounds on numbers of iterations in loop-based programs. We are attempting to combine these ideas to deal with Java programs involving both data structures and loops, focusing on the bytecode level rather than on source code.

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Certifying Algorithms for Recognizing Interval Graphs and Permutation Graphs

Cited by 81 publications

References 25 publications

A Pumping Algorithm for Ergodic Stochastic Mean Payoff Games with Perfect Information

A Pumping Algorithm for Ergodic Stochastic Mean Payoff Games with Perfect Information

Optimal Verification of Operations on Dynamic Sets

Symbolic and Analytic Techniques for Resource Analysis of Java Bytecode

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