2 Search Results for "George, William"

Document
DOI: 10.4230/LIPIcs.MFCS.2020.27
Exact and Approximate Algorithms for Computing a Second Hamiltonian Cycle

Authors: Argyrios Deligkas, George B. Mertzios, Paul G. Spirakis, and Viktor Zamaraev

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

Abstract
In this paper we consider the following total functional problem: Given a cubic Hamiltonian graph G and a Hamiltonian cycle C₀ of G, how can we compute a second Hamiltonian cycle C₁ ≠ C₀ of G? Cedric Smith and William Tutte proved in 1946, using a non-constructive parity argument, that such a second Hamiltonian cycle always exists. Our main result is a deterministic algorithm which computes the second Hamiltonian cycle in O(n⋅2^0.299862744n) = O(1.23103ⁿ) time and in linear space, thus improving the state of the art running time of O*(2^0.3n) = O(1.2312ⁿ) for solving this problem (among deterministic algorithms running in polynomial space). Whenever the input graph G does not contain any induced cycle C₆ on 6 vertices, the running time becomes O(n⋅ 2^0.2971925n) = O(1.22876ⁿ). Our algorithm is based on a fundamental structural property of Thomason’s lollipop algorithm, which we prove here for the first time. In the direction of approximating the length of a second cycle in a (not necessarily cubic) Hamiltonian graph G with a given Hamiltonian cycle C₀ (where we may not have guarantees on the existence of a second Hamiltonian cycle), we provide a linear-time algorithm computing a second cycle with length at least n - 4α (√n+2α)+8, where α = (Δ-2)/(δ-2) and δ,Δ are the minimum and the maximum degree of the graph, respectively. This approximation result also improves the state of the art.
Cite as

Argyrios Deligkas, George B. Mertzios, Paul G. Spirakis, and Viktor Zamaraev. Exact and Approximate Algorithms for Computing a Second Hamiltonian Cycle. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 27:1-27:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{deligkas_et_al:LIPIcs.MFCS.2020.27,
  author =	{Deligkas, Argyrios and Mertzios, George B. and Spirakis, Paul G. and Zamaraev, Viktor},
  title =	{{Exact and Approximate Algorithms for Computing a Second Hamiltonian Cycle}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{27:1--27:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.27},
  URN =		{urn:nbn:de:0030-drops-126953},
  doi =		{10.4230/LIPIcs.MFCS.2020.27},
  annote =	{Keywords: Hamiltonian cycle, cubic graph, exact algorithm, approximation algorithm}
}
Document
DOI: 10.4230/OASIcs.Tokenomics.2019.6
A Smart Contract Oracle for Approximating Real-World, Real Number Values

Authors: William George and Clément Lesaege

Published in: OASIcs, Volume 71, International Conference on Blockchain Economics, Security and Protocols (Tokenomics 2019)

Abstract
A key challenge of smart contract systems is the fact that many useful contracts require access to information that does not natively live on the blockchain. While miners can verify the value of a hash or the validity of a digital signature, they cannot determine who won an election, whether there is a flood in Paris, or even what is the price of ether in US dollars, even though this information might be necessary to execute prediction market, insurance, or financial contracts respectively. A number of promising projects and research developments have provided a better understanding of how one might construct a decentralized, binary oracle - namely an oracle that can respond by one of two possibilities, typically "yes" or "no", even while not requiring the interaction of a trusted third party. In this work, we extend these ideas to construct a general-purpose, decentralized oracle that can estimate the value of a real-world quantity that is in a dense totally ordered set, such as R. In particular, this proposal can be used to estimate real number valued quantities, such as required for a price oracle. We will establish a number of desirable properties about this proposal. Particularly, we will see that the precision of the output is tunable to users' needs.
Cite as

William George and Clément Lesaege. A Smart Contract Oracle for Approximating Real-World, Real Number Values. In International Conference on Blockchain Economics, Security and Protocols (Tokenomics 2019). Open Access Series in Informatics (OASIcs), Volume 71, pp. 6:1-6:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{george_et_al:OASIcs.Tokenomics.2019.6,
  author =	{George, William and Lesaege, Cl\'{e}ment},
  title =	{{A Smart Contract Oracle for Approximating Real-World, Real Number Values}},
  booktitle =	{International Conference on Blockchain Economics, Security and Protocols (Tokenomics 2019)},
  pages =	{6:1--6:15},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-108-5},
  ISSN =	{2190-6807},
  year =	{2020},
  volume =	{71},
  editor =	{Danos, Vincent and Herlihy, Maurice and Potop-Butucaru, Maria and Prat, Julien and Tucci-Piergiovanni, Sara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.Tokenomics.2019.6},
  URN =		{urn:nbn:de:0030-drops-119705},
  doi =		{10.4230/OASIcs.Tokenomics.2019.6},
  annote =	{Keywords: price oracle, Ethereum, blockchain}
}
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