10 Search Results for "Might, Matthew"


Document
Tailstorm: A Secure and Fair Blockchain for Cash Transactions

Authors: Patrik Keller, Ben Glickenhaus, George Bissias, and Gregory Griffith

Published in: LIPIcs, Volume 282, 5th Conference on Advances in Financial Technologies (AFT 2023)


Abstract
Proof-of-work (PoW) cryptocurrencies rely on a balance of security and fairness in order to maintain a sustainable ecosystem of miners and users. Users demand fast and consistent transaction confirmation, and in exchange drive the adoption and valuation of the cryptocurrency. Miners provide the confirmations, however, they primarily seek rewards. In unfair systems, miners can amplify their rewards by consolidating mining power. Centralization however, undermines the security guarantees of the system and might discourage users. In this paper we present Tailstorm, a cryptocurrency that strikes this balance. Tailstorm merges multiple recent protocol improvements addressing security, confirmation latency, and throughput with a novel incentive mechanism improving fairness. We implement a parallel proof-of-work consensus mechanism with k PoWs per block to obtain state-of-the-art consistency guarantees [Patrik Keller and Rainer Böhme, 2022]. Inspired by Bobtail [George Bissias and Brian Neil Levine, 2020] and Storm [awemany, 2019], we structure the individual PoWs in a tree which, by including a list of transactions with each PoW, reduces confirmation latency and improves throughput. Our proposed incentive mechanism discounts rewards based on the depth of this tree. Thereby, it effectively punishes information withholding, the core attack strategy used to reap an unfair share of rewards. We back our claims with a comprehensive analysis. We present a generic system model which allows us to specify Bitcoin, B_k [Patrik Keller and Rainer Böhme, 2022], and Tailstorm from a joint set of assumptions. We provide an analytical bound for the fairness of Tailstorm and Bitcoin in honest networks and we confirm the results through simulation. We evaluate the effectiveness of dishonest behaviour through reinforcement learning. Our attack search reproduces known optimal strategies against Bitcoin, uncovers new ones against B_k, and confirms that Tailstorm’s reward discounting makes it more resilient to incentive layer attacks. Our results are reproducible with the material provided online [Keller and Glickenhaus, 2023]. Lastly, we have implemented a prototype of the Tailstorm cryptocurrency as a fork of Bitcoin Cash. The client software is ready for testnet deployment and we also publish its source online [Griffith and Bissias, 2023].

Cite as

Patrik Keller, Ben Glickenhaus, George Bissias, and Gregory Griffith. Tailstorm: A Secure and Fair Blockchain for Cash Transactions. In 5th Conference on Advances in Financial Technologies (AFT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 282, pp. 6:1-6:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{keller_et_al:LIPIcs.AFT.2023.6,
  author =	{Keller, Patrik and Glickenhaus, Ben and Bissias, George and Griffith, Gregory},
  title =	{{Tailstorm: A Secure and Fair Blockchain for Cash Transactions}},
  booktitle =	{5th Conference on Advances in Financial Technologies (AFT 2023)},
  pages =	{6:1--6:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-303-4},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{282},
  editor =	{Bonneau, Joseph and Weinberg, S. Matthew},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2023.6},
  URN =		{urn:nbn:de:0030-drops-191954},
  doi =		{10.4230/LIPIcs.AFT.2023.6},
  annote =	{Keywords: Proof-of-Work, Blockchain, Cryptocurrency, Mining Rewards, Fairness}
}
Document
Credible, Strategyproof, Optimal, and Bounded Expected-Round Single-Item Auctions for All Distributions

Authors: Meryem Essaidi, Matheus V. X. Ferreira, and S. Matthew Weinberg

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)


Abstract
We consider a revenue-maximizing seller with a single item for sale to multiple buyers with independent and identically distributed valuations. Akbarpour and Li (2020) show that the only optimal, credible, strategyproof auction is the ascending price auction with reserves which has unbounded communication complexity. Recent work of Ferreira and Weinberg (2020) circumvents their impossibility result assuming the existence of cryptographically secure commitment schemes, and designs a two-round credible, strategyproof, optimal auction. However, their auction is only credible when buyers' valuations are MHR or α-strongly regular: they show their auction might not be credible even when there is a single buyer drawn from a non-MHR distribution. In this work, under the same cryptographic assumptions, we identify a new single-item auction that is credible, strategyproof, revenue optimal, and terminates in constant rounds in expectation for all distributions with finite monopoly price.

Cite as

Meryem Essaidi, Matheus V. X. Ferreira, and S. Matthew Weinberg. Credible, Strategyproof, Optimal, and Bounded Expected-Round Single-Item Auctions for All Distributions. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 66:1-66:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{essaidi_et_al:LIPIcs.ITCS.2022.66,
  author =	{Essaidi, Meryem and Ferreira, Matheus V. X. and Weinberg, S. Matthew},
  title =	{{Credible, Strategyproof, Optimal, and Bounded Expected-Round Single-Item Auctions for All Distributions}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{66:1--66:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.66},
  URN =		{urn:nbn:de:0030-drops-156621},
  doi =		{10.4230/LIPIcs.ITCS.2022.66},
  annote =	{Keywords: Credible Auctions, Cryptographically Secure, Single-Item}
}
Document
From Macros to DSLs: The Evolution of Racket

Authors: Ryan Culpepper, Matthias Felleisen, Matthew Flatt, and Shriram Krishnamurthi

Published in: LIPIcs, Volume 136, 3rd Summit on Advances in Programming Languages (SNAPL 2019)


Abstract
The Racket language promotes a language-oriented style of programming. Developers create many domain-specific languages, write programs in them, and compose these programs via Racket code. This style of programming can work only if creating and composing little languages is simple and effective. While Racket’s Lisp heritage might suggest that macros suffice, its design team discovered significant shortcomings and had to improve them in many ways. This paper presents the evolution of Racket’s macro system, including a false start, and assesses its current state.

Cite as

Ryan Culpepper, Matthias Felleisen, Matthew Flatt, and Shriram Krishnamurthi. From Macros to DSLs: The Evolution of Racket. In 3rd Summit on Advances in Programming Languages (SNAPL 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 136, pp. 5:1-5:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{culpepper_et_al:LIPIcs.SNAPL.2019.5,
  author =	{Culpepper, Ryan and Felleisen, Matthias and Flatt, Matthew and Krishnamurthi, Shriram},
  title =	{{From Macros to DSLs: The Evolution of Racket}},
  booktitle =	{3rd Summit on Advances in Programming Languages (SNAPL 2019)},
  pages =	{5:1--5:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-113-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{136},
  editor =	{Lerner, Benjamin S. and Bod{\'\i}k, Rastislav and Krishnamurthi, Shriram},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SNAPL.2019.5},
  URN =		{urn:nbn:de:0030-drops-105482},
  doi =		{10.4230/LIPIcs.SNAPL.2019.5},
  annote =	{Keywords: design principles, macros systems, domain-specific languages}
}
Document
On the Price of Independence for Vertex Cover, Feedback Vertex Set and Odd Cycle Transversal

Authors: Konrad K. Dabrowski, Matthew Johnson, Giacomo Paesani, Daniël Paulusma, and Viktor Zamaraev

Published in: LIPIcs, Volume 117, 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)


Abstract
Let vc(G), fvs(G) and oct(G) denote, respectively, the size of a minimum vertex cover, minimum feedback vertex set and minimum odd cycle transversal in a graph G. One can ask, when looking for these sets in a graph, how much bigger might they be if we require that they are independent; that is, what is the price of independence? If G has a vertex cover, feedback vertex set or odd cycle transversal that is an independent set, then we let, respectively, ivc(G), ifvs(G) or ioct(G) denote the minimum size of such a set. We investigate for which graphs H the values of ivc(G), ifvs(G) and ioct(G) are bounded in terms of vc(G), fvs(G) and oct(G), respectively, when the graph G belongs to the class of H-free graphs. We find complete classifications for vertex cover and feedback vertex set and an almost complete classification for odd cycle transversal (subject to three non-equivalent open cases).

Cite as

Konrad K. Dabrowski, Matthew Johnson, Giacomo Paesani, Daniël Paulusma, and Viktor Zamaraev. On the Price of Independence for Vertex Cover, Feedback Vertex Set and Odd Cycle Transversal. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 63:1-63:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{dabrowski_et_al:LIPIcs.MFCS.2018.63,
  author =	{Dabrowski, Konrad K. and Johnson, Matthew and Paesani, Giacomo and Paulusma, Dani\"{e}l and Zamaraev, Viktor},
  title =	{{On the Price of Independence for Vertex Cover, Feedback Vertex Set and Odd Cycle Transversal}},
  booktitle =	{43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
  pages =	{63:1--63:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Potapov, Igor and Spirakis, Paul and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.63},
  URN =		{urn:nbn:de:0030-drops-96452},
  doi =		{10.4230/LIPIcs.MFCS.2018.63},
  annote =	{Keywords: vertex cover, feedback vertex set, odd cycle transversal, price of independence}
}
Document
A Simple Complete Search for Logic Programming

Authors: Jason Hemann, Daniel P. Friedman, William E. Byrd, and Matthew Might

Published in: OASIcs, Volume 58, Technical Communications of the 33rd International Conference on Logic Programming (ICLP 2017)


Abstract
Here, we present a family of complete interleaving depth-first search strategies for embedded, domain-specific logic languages. We derive our search family from a stream-based implementation of incomplete depth-first search. The DSL's programs' texts induce particular strategies guaranteed to be complete.

Cite as

Jason Hemann, Daniel P. Friedman, William E. Byrd, and Matthew Might. A Simple Complete Search for Logic Programming. In Technical Communications of the 33rd International Conference on Logic Programming (ICLP 2017). Open Access Series in Informatics (OASIcs), Volume 58, pp. 14:1-14:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{hemann_et_al:OASIcs.ICLP.2017.14,
  author =	{Hemann, Jason and Friedman, Daniel P. and Byrd, William E. and Might, Matthew},
  title =	{{A Simple Complete Search for Logic Programming}},
  booktitle =	{Technical Communications of the 33rd International Conference on Logic Programming (ICLP 2017)},
  pages =	{14:1--14:8},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-058-3},
  ISSN =	{2190-6807},
  year =	{2018},
  volume =	{58},
  editor =	{Rocha, Ricardo and Son, Tran Cao and Mears, Christopher and Saeedloei, Neda},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ICLP.2017.14},
  URN =		{urn:nbn:de:0030-drops-84676},
  doi =		{10.4230/OASIcs.ICLP.2017.14},
  annote =	{Keywords: logic programming, streams, search, Racket, backtracking, relational programming}
}
Document
Condorcet-Consistent and Approximately Strategyproof Tournament Rules

Authors: Jon Schneider, Ariel Schvartzman, and S. Matthew Weinberg

Published in: LIPIcs, Volume 67, 8th Innovations in Theoretical Computer Science Conference (ITCS 2017)


Abstract
We consider the manipulability of tournament rules for round-robin tournaments of n competitors. Specifically, n competitors are competing for a prize, and a tournament rule r maps the result of all n(n-1)/2 pairwise matches (called a tournament, T) to a distribution over winners. Rule r is Condorcet-consistent if whenever i wins all n-1 of her matches, r selects i with probability 1. We consider strategic manipulation of tournaments where player j might throw their match to player i in order to increase the likelihood that one of them wins the tournament. Regardless of the reason why j chooses to do this, the potential for manipulation exists as long as Pr[r(T) = i] increases by more than Pr[r(T) = j] decreases. Unfortunately, it is known that every Condorcet-consistent rule is manipulable. In this work, we address the question of how manipulable Condorcet-consistent rules must necessarily be - by trying to minimize the difference between the increase in Pr[r(T) = i] and decrease in Pr[r(T) = j] for any potential manipulating pair. We show that every Condorcet-consistent rule is in fact 1/3-manipulable, and that selecting a winner according to a random single elimination bracket is not alpha-manipulable for any alpha > 1/3. We also show that many previously studied tournament formats are all 1/2-manipulable, and the popular class of Copeland rules (any rule that selects a player with the most wins) are all in fact 1-manipulable, the worst possible. Finally, we consider extensions to match-fixing among sets of more than two players.

Cite as

Jon Schneider, Ariel Schvartzman, and S. Matthew Weinberg. Condorcet-Consistent and Approximately Strategyproof Tournament Rules. In 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 67, pp. 35:1-35:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{schneider_et_al:LIPIcs.ITCS.2017.35,
  author =	{Schneider, Jon and Schvartzman, Ariel and Weinberg, S. Matthew},
  title =	{{Condorcet-Consistent and Approximately Strategyproof Tournament Rules}},
  booktitle =	{8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
  pages =	{35:1--35:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-029-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{67},
  editor =	{Papadimitriou, Christos H.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.35},
  URN =		{urn:nbn:de:0030-drops-81605},
  doi =		{10.4230/LIPIcs.ITCS.2017.35},
  annote =	{Keywords: Tournament design, Non-manipulability, Condorcet-consistent, Strategyproofness}
}
Document
A Superlinear Lower Bound on the Number of 5-Holes

Authors: Oswin Aichholzer, Martin Balko, Thomas Hackl, Jan Kyncl, Irene Parada, Manfred Scheucher, Pavel Valtr, and Birgit Vogtenhuber

Published in: LIPIcs, Volume 77, 33rd International Symposium on Computational Geometry (SoCG 2017)


Abstract
Let P be a finite set of points in the plane in general position, that is, no three points of P are on a common line. We say that a set H of five points from P is a 5-hole in P if H is the vertex set of a convex 5-gon containing no other points of P. For a positive integer n, let h_5(n) be the minimum number of 5-holes among all sets of n points in the plane in general position. Despite many efforts in the last 30 years, the best known asymptotic lower and upper bounds for h_5(n) have been of order Omega(n) and O(n^2), respectively. We show that h_5(n) = Omega(n(log n)^(4/5)), obtaining the first superlinear lower bound on h_5(n). The following structural result, which might be of independent interest, is a crucial step in the proof of this lower bound. If a finite set P of points in the plane in general position is partitioned by a line l into two subsets, each of size at least 5 and not in convex position, then l intersects the convex hull of some 5-hole in P. The proof of this result is computer-assisted.

Cite as

Oswin Aichholzer, Martin Balko, Thomas Hackl, Jan Kyncl, Irene Parada, Manfred Scheucher, Pavel Valtr, and Birgit Vogtenhuber. A Superlinear Lower Bound on the Number of 5-Holes. In 33rd International Symposium on Computational Geometry (SoCG 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 77, pp. 8:1-8:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{aichholzer_et_al:LIPIcs.SoCG.2017.8,
  author =	{Aichholzer, Oswin and Balko, Martin and Hackl, Thomas and Kyncl, Jan and Parada, Irene and Scheucher, Manfred and Valtr, Pavel and Vogtenhuber, Birgit},
  title =	{{A Superlinear Lower Bound on the Number of 5-Holes}},
  booktitle =	{33rd International Symposium on Computational Geometry (SoCG 2017)},
  pages =	{8:1--8:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-038-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{77},
  editor =	{Aronov, Boris and Katz, Matthew J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2017.8},
  URN =		{urn:nbn:de:0030-drops-72008},
  doi =		{10.4230/LIPIcs.SoCG.2017.8},
  annote =	{Keywords: Erd\"{o}s-Szekeres type problem, k-hole, empty k-gon, empty pentagon, planar point set}
}
Document
On Optimal 2- and 3-Planar Graphs

Authors: Michael A. Bekos, Michael Kaufmann, and Chrysanthi N. Raftopoulou

Published in: LIPIcs, Volume 77, 33rd International Symposium on Computational Geometry (SoCG 2017)


Abstract
A graph is k-planar if it can be drawn in the plane such that no edge is crossed more than k times. While for k=1, optimal 1-planar graphs, i.e., those with n vertices and exactly 4n-8 edges, have been completely characterized, this has not been the case for k > 1. For k=2,3 and 4, upper bounds on the edge density have been developed for the case of simple graphs by Pach and Tóth, Pach et al. and Ackerman, which have been used to improve the well-known "Crossing Lemma". Recently, we proved that these bounds also apply to non-simple 2- and 3-planar graphs without homotopic parallel edges and self-loops. In this paper, we completely characterize optimal 2- and 3-planar graphs, i.e., those that achieve the aforementioned upper bounds. We prove that they have a remarkably simple regular structure, although they might be non-simple. The new characterization allows us to develop notable insights concerning new inclusion relationships with other graph classes.

Cite as

Michael A. Bekos, Michael Kaufmann, and Chrysanthi N. Raftopoulou. On Optimal 2- and 3-Planar Graphs. In 33rd International Symposium on Computational Geometry (SoCG 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 77, pp. 16:1-16:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{bekos_et_al:LIPIcs.SoCG.2017.16,
  author =	{Bekos, Michael A. and Kaufmann, Michael and Raftopoulou, Chrysanthi N.},
  title =	{{On Optimal 2- and 3-Planar Graphs}},
  booktitle =	{33rd International Symposium on Computational Geometry (SoCG 2017)},
  pages =	{16:1--16:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-038-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{77},
  editor =	{Aronov, Boris and Katz, Matthew J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2017.16},
  URN =		{urn:nbn:de:0030-drops-72307},
  doi =		{10.4230/LIPIcs.SoCG.2017.16},
  annote =	{Keywords: topological graphs, optimal k-planar graphs, characterization}
}
Document
Casually Evolving Creative Technology Systems

Authors: Matthew R. Lewis

Published in: Dagstuhl Seminar Proceedings, Volume 9291, Computational Creativity: An Interdisciplinary Approach (2009)


Abstract
This position paper will describe the early stages of a development effort in which an interactive evolutionary design approach is being applied to the domain of technology-based system development, in a new media art and design context. These systems connect different technologies and techniques in order to process and transform data of one type into another. For example, location data might be used to select a relevant network information feed, the text of which drives geometry generation, which in turn could be sent to a 3D printer that would produce a sculpture. While the flexibility of this problem domain is idiosyncratic to our interdisciplinary new media environment, the target physical context for using a creativity support tool, and the context’s effect on creative output is rather the primary research focus. The goal is to explore the possibilities of what might be termed "casual design", analogous to the “casual gaming” genre in which games are played by anyone, where ever they might find a few spare minutes, rather than requiring significant time and hardware commitments.

Cite as

Matthew R. Lewis. Casually Evolving Creative Technology Systems. In Computational Creativity: An Interdisciplinary Approach. Dagstuhl Seminar Proceedings, Volume 9291, pp. 1-10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)


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@InProceedings{lewis:DagSemProc.09291.8,
  author =	{Lewis, Matthew R.},
  title =	{{Casually Evolving Creative Technology Systems}},
  booktitle =	{Computational Creativity: An Interdisciplinary Approach},
  pages =	{1--10},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{9291},
  editor =	{Margaret Boden and Mark D'Inverno and Jon McCormack},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.09291.8},
  URN =		{urn:nbn:de:0030-drops-21951},
  doi =		{10.4230/DagSemProc.09291.8},
  annote =	{Keywords: Computational creativity}
}
Document
Approximating Solution Structure

Authors: Iris van Rooij, Matthew Hamilton, Moritz Müller, and Todd Wareham

Published in: Dagstuhl Seminar Proceedings, Volume 7281, Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs (2007)


Abstract
hen it is hard to compute an optimal solution $y in optsol(x)$ to an instance $x$ of a problem, one may be willing to settle for an efficient algorithm $A$ that computes an approximate solution $A(x)$. The most popular type of approximation algorithm in Computer Science (and indeed many other applications) computes solutions whose value is within some multiplicative factor of the optimal solution value, {em e.g.}, $max(frac{val(A(x))}{optval(x)}, frac{optval(x)}{val(A(x))}) leq h(|x|)$ for some function $h()$. However, an algorithm might also produce a solution whose structure is ``close'' to the structure of an optimal solution relative to a specified solution-distance function $d$, {em i.e.}, $d(A(x), y) leq h(|x|)$ for some $y in optsol(x)$. Such structure-approximation algorithms have applications within Cognitive Science and other areas. Though there is an extensive literature dating back over 30 years on value-approximation, there is to our knowledge no work on general techniques for assessing the structure-(in)approximability of a given problem. In this talk, we describe a framework for investigating the polynomial-time and fixed-parameter structure-(in)approximability of combinatorial optimization problems relative to metric solution-distance functions, {em e.g.}, Hamming distance. We motivate this framework by (1) describing a particular application within Cognitive Science and (2) showing that value-approximability does not necessarily imply structure-approximability (and vice versa). This framework includes definitions of several types of structure approximation algorithms analogous to those studied in value-approximation, as well as structure-approximation problem classes and a structure-approximability-preserving reducibility. We describe a set of techniques for proving the degree of structure-(in)approximability of a given problem, and summarize all known results derived using these techniques. We also list 11 open questions summarizing particularly promising directions for future research within this framework. vspace*{0.15in} oindent (co-presented with Todd Wareham) vspace*{0.15in} jointwork{Hamilton, Matthew; M"{u}ller, Moritz; van Rooij, Iris; Wareham, Todd}

Cite as

Iris van Rooij, Matthew Hamilton, Moritz Müller, and Todd Wareham. Approximating Solution Structure. In Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs. Dagstuhl Seminar Proceedings, Volume 7281, pp. 1-24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)


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@InProceedings{vanrooij_et_al:DagSemProc.07281.3,
  author =	{van Rooij, Iris and Hamilton, Matthew and M\"{u}ller, Moritz and Wareham, Todd},
  title =	{{Approximating Solution Structure}},
  booktitle =	{Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs},
  pages =	{1--24},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7281},
  editor =	{Erik Demaine and Gregory Z. Gutin and Daniel Marx and Ulrike Stege},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.07281.3},
  URN =		{urn:nbn:de:0030-drops-12345},
  doi =		{10.4230/DagSemProc.07281.3},
  annote =	{Keywords: Approximation Algorithms, Solution Structure}
}
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