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Showing papers presented at "Conference on Computability in Europe in 2010"


Book ChapterDOI
30 Jun 2010
TL;DR: A relativity theorem is proved stating that algebraic equations are invariant under rigid body transformations, and a geometric process algebra based on affine geometry is introduced.
Abstract: We introduce a geometric process algebra based on affine geometry, with the aim of describing the concurrent evolution of geometric structures in 3D space. We prove a relativity theorem stating that algebraic equations are invariant under rigid body transformations.

63 citations


Journal ArticleDOI
30 Dec 2010
TL;DR: In this article, ImpAct's functionality, design, and prototype applications are described in detail with relevance to the concept of direct touch, giving special attention to novel interaction scenarios and design challenges.
Abstract: This article explores direct touch and manipulation techniques for surface computing environments using a specialized haptic force feedback stylus, called ImpAct, which can dynamically change its effective length and equipped with sensors to calculate its orientation in world coordinates When a user pushes it against a touch screen, the physical stylus shrinks and a rendered projection of the stylus is drawn inside the screen, giving the illusion that it is submerged in the display device Once the users can see the stylus immersed in the digital world below the screen, he or she can manipulate and interact with the virtual objects with active haptic sensations In this article, ImpAct's functionality, design, and prototype applications are described in detail with relevance to the concept of direct touch, giving special attention to novel interaction scenarios and design challenges Furthermore, a technical evaluation was done to study ImpAct's accuracy and controlability and the results presented This article concludes by discussing ImpAct's current limitations and future perspectives as a direct touch and manipulation tool

42 citations


Journal ArticleDOI
31 Dec 2010
TL;DR: The design and implementation of a multimedia system that interactively illustrates the process of preparing one of the masterpieces of the culinary heritage of the Italian city of Bologna, the Tortellino, with the help of no other external hardware device, but a simple camera is described.
Abstract: The innovative aspects introduced by the new hands-free gaming systems, like the Nintendo Wii, Sony Move and Microsoft Kinect, indicate that technology is progressively, and at a limited cost, reaching more natural ways of interacting with human beings, and vice versa. This process can clearly pave the way to beneficial opportunities in a wealth of fields, including those of technical and artistic interactive exhibitions. In fact, while for long all types of tech-inspired exhibitions have been mainly based on artifacts and tools that seldom required any interactions with the public, today this can radically change. The new frontiers of technology for performing arts provide the means for creating active interactions between the public and any object, allowing visitors to enjoy an experience that exceeds what can be solely passively seen or heard. In such domain, we describe the design and implementation of a multimedia system that interactively illustrates the process of preparing one of the masterpieces of the culinary heritage of the Italian city of Bologna, the Tortellino. Step-bystep, with our system, anyone can enjoy a virtual experience learning how to prepare a Tortellino while mimicking the movements a real cook would perform to prepare its recipe when starting from its raw ingredients: eggs and flour. From a scientific viewpoint, the challenging part of this project resides in recognizing cooks’ movements while verifying their correctness. In this paper, we describe how we achieved such result devising the most appropriate techniques able to allow our system to recognize a predefined set of actions (as those performed by a real cook) with the help of no other external hardware device, but a simple camera. Witnessing the importance of the results we got, our multimedia system has been chosen to be part of the expositions that will represent the City of Bologna at the Shanghai Universal Expo, in October 2010.

42 citations


Journal ArticleDOI
31 Dec 2010
TL;DR: This work presents a meta-modelling framework for estimating the response of the immune system to various types of stimuli and shows clear patterns in its response to certain types of stimulation.
Abstract: Author address: University of Padua - Pure and Applied Mathematics, Via Trieste, 63 Padova, D 35131, Italy Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies show this notice on the first page or initial screen of a display along with the full citation. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works requires prior specific permission and/or a fee. Permissions may be requested from Publications Dept., ACM, Inc., 2 Penn Plaza, Suite 701, New York, NY 10121-0701 USA, fax +1 (212) 869-0481, or permissions@acm.org. ©2010 ACM 1544-3574/2010/12-ART23 $10.00 DOI: 10.1145/1921141.1921143 http://doi.acm.org/10.1145/1921141.1921143 ACM Computers in Entertainment, Vol. 8, No. 4, Article 23, Publication date: December 2010

40 citations


Journal ArticleDOI
30 Dec 2010
TL;DR: The PuzzleTale system engages the reader participating in the development of the story through playing tangible puzzle pieces with digital characters as a decision-making tool, thus providing individualized storytelling experiences.
Abstract: We describe the design and development of PuzzleTale, an interactive storytelling system that makes use of tangible puzzle pieces on the surface of an interactive table. In the PuzzleTale system, assembling the tangible puzzle piece can affect the digital characters and create a flexible story context. Different assembled patterns represent the diverse ways that users explore and compose the story.The PuzzleTale system creates a dynamic causal relationship between the process of interactive storytelling and the outcome of a story. There are two variables that continuously affect the story context including the amount and the sequence of digital characters that the reader plays. The system engages the reader participating in the development of the story through playing tangible puzzle pieces with digital characters as a decision-making tool, thus providing individualized storytelling experiences.

29 citations


Journal ArticleDOI
Naoya Koizumi1, Kentaro Yasu1, Angela Liu1, Maki Sugimoto1, Masahiko Inami1 
30 Dec 2010
TL;DR: A new wireless prototyping platform which combines paper, shape memory alloy (SMA), retro-reflective material, and copper foil, which makes it possible to create moving toys out of ordinary print paper with minimal modification to the physical composition of the paper itself, facilitating simple trial-and-error modifications.
Abstract: In recent years, there has been a surge in the number of available rapid prototyping tools, making it easier than ever to create functioning prototypes with minimal technical background and at a low cost However, most of these tools do not have the flexibility to allow for immediate physical modifications once a prototype has been built or programmed, and are often limited in movement by the size or range of the wired system Accordingly, simple paper remains one of the most pervasive creative platforms in the world due to its low cost, light weight, freedom of physical spatial manipulation, disposability, and low interaction overheadIn this article we introduce “Animated Paper,” a new wireless prototyping platform which combines paper, shape memory alloy (SMA), retro-reflective material, and copper foil This platform makes it possible to create moving toys out of ordinary print paper with minimal modification to the physical composition of the paper itself, facilitating simple trial-and-error modifications We also introduce a laser control system which allows for precise, wireless motion control of the SMA-enhanced paper by tracking retro-reflective markers on the paper using a laser and photo sensor Lastly, we present the results of a preliminary user study to demonstrate the usability of our prototype system and also provide possibilities for how to further develop our wirelessly controlled, moving paper platform

29 citations


Book ChapterDOI
30 Jun 2010
TL;DR: It is seen that in contrast to single-objective problems (where the solution notions coincide), the situation is more subtle for multiple objectives, so it is important to exactly specify the NP-hardness notion when discussing the complexity of multi-objectives problems.
Abstract: We study the approximability and the hardness of combinatorial multi-objective NP optimization problems (multi-objective problems, for short). Our contributions are: - We define and compare several solution notions that capture reasonable algorithmic tasks for computing optimal solutions. - These solution notions induce corresponding NP-hardness notions for which we prove implication and separation results. - We define approximative solution notions and investigate in which cases polynomial-time solvability translates from one to another notion. Moreover, for problems where all objectives have to be minimized, approximability results translate from single-objective to multi-objective optimization such that the relative error degrades only by a constant factor. Such translations are not possible for problems where all objectives have to be maximized (unless P = NP). As a consequence we see that in contrast to single-objective problems (where the solution notions coincide), the situation is more subtle for multiple objectives. So it is important to exactly specify the NP-hardness notion when discussing the complexity of multi-objective problems.

28 citations


Journal ArticleDOI
30 Dec 2010
TL;DR: The effect of playout buffering control in haptic media, sound, and video transmission via QoE (Quality of Experience) assessment is investigated via QoS assessment, and it is demonstrated that, with high accuracy, it is possible to estimateQoE parameters from QoS parameters.
Abstract: In this article we investigate the effect of playout buffering control in haptic media, sound, and video transmission via QoE (Quality of Experience) assessment. We assess the operability of the haptic interface device, sound output quality, video output quality, inter-stream synchronization quality, and comprehensive quality. We also evaluate the application-level QoS (Quality of Service), and demonstrate that, with high accuracy, it is possible to estimate QoE parameters from QoS parameters.

21 citations


Book ChapterDOI
30 Jun 2010
TL;DR: It is shown that the computational interpretation of full comprehension via two well-known functional interpretations (dialectica and modified realizability) corresponds to two closely related infinite products of selection functions.
Abstract: We show that the computational interpretation of full comprehension via two well-known functional interpretations (dialectica and modified realizability) corresponds to two closely related infinite products of selection functions.

21 citations


Book ChapterDOI
30 Jun 2010
TL;DR: A very simple proof of a 7n/3 - c lower bound on the circuit complexity of a large class of functions representable by high degree polynomials over GF(2) is given.
Abstract: In this note, we use lower bounds on Boolean multiplicative complexity to prove lower bounds on Boolean circuit complexity. We give a very simple proof of a 7n/3 - c lower bound on the circuit complexity of a large class of functions representable by high degree polynomials over GF(2). The key idea of the proof is a circuit complexity measure assigning different weights to XOR and AND gates.

20 citations


Book ChapterDOI
30 Jun 2010
TL;DR: The use of spatial graph models for the analysis of networks that do not have a direct spatial reality, such as web graphs, on-line social networks, or citation graphs are discussed.
Abstract: This paper discusses the use of spatial graph models for the analysis of networks that do not have a direct spatial reality, such as web graphs, on-line social networks, or citation graphs. In a spatial graph model, nodes are embedded in a metric space, and link formation depends on the relative position of nodes in the space. It is argued that spatial models form a good basis for link mining: assuming a spatial model, the link information can be used to infer the spatial position of the nodes, and this information can then be used for clustering and recognition of node similarity. This paper gives a survey of spatial graph models, and discusses their suitability for link mining.

Book ChapterDOI
30 Jun 2010
TL;DR: A realisability interpretation for inductive and coinductive definitions is studied and its application to program extraction from proofs is discussed, showing how to extract a program computing the average of two real numbers w.r.t. to the binary signed digit representation.
Abstract: We study a realisability interpretation for inductive and coinductive definitions and discuss its application to program extraction from proofs. A speciality of this interpretation is that realisers are given by terms that correspond directly to programs in a lazy functional programming language such as Haskell. Programs extracted from proofs using coinduction can be understood as perpetual processes producing infinite streams of data. Typical applications of such processes are computations in exact real arithmetic. As an example we show how to extract a program computing the average of two real numbers w.r.t. to the binary signed digit representation.

Journal ArticleDOI
Li Zhang1
01 Dec 2010
TL;DR: Developing on equipping the intelligent agent with the abilities of interpreting dynamic inter-relationships between improvisational human-controlled characters and performing contextual affect-sensing, based on the discussion topics, the improvisational "mood" that one has created, relationship interpretation between characters, and the most recent affect profiles of other characters are reported.
Abstract: Real-time contextual affect-detection from open-ended text-based dialogue is challenging but essential for the building of effective intelligent user interfaces. In our previous work, an affect-detection component was developed, which was embedded in an intelligent agent interacting with human-controlled characters under the improvisation of loose scenarios. The affect-detection module is capable of detecting 25 basic and complex emotions based on the analysis of pure individual turn-taking input without any contextual inference. In this article, we report developments on equipping the intelligent agent with the abilities of interpreting dynamic inter-relationships between improvisational human-controlled characters and performing contextual affect-sensing, based on the discussion topics, the improvisational “mood” that one has created, relationship interpretation between characters, and the most recent affect profiles of other characters. Evaluation results on the updated affect-detection component are also reported. Overall, the performances of the contextual affect-sensing and dynamic relationship interpretation are promising. The work contributes to the journal themes on affective computing, human-robots/agent interaction, and narrative-based interactive theatre.

Journal ArticleDOI
01 Dec 2010
TL;DR: A method for selecting a projector from multiple wearable projectors, wherein the method considers the position of the wearable projector, user contexts such as whether he/she is walking or standing, and the type of presentation content.
Abstract: Many projects and practices can now support user tasks by presenting images on the floor or wall using a mobile projector. However, unstable images make communication and task support difficult. The viewability of a projected image depends on several factors; the position of the wearable projector, user contexts such as whether he/she is walking or standing, and the type of presentation content. We describe a method for selecting a projector from multiple wearable projectors, wherein the method considers these factors. We investigated the characteristics of viewability by changing various factors in various contexts and with different content. We also investigated the appropriate position for a wearable mobile projector in various situations and with different content in subjective evaluations. The results indicated that our system dynamically changes the characteristics of a projector for presenting content. We implemented a prototype system that selects the appropriate projector dynamically in response to the situation.

Book ChapterDOI
30 Jun 2010
TL;DR: It is proved that each superlow ML-random set already satisfies a stronger randomness notion called balanced randomness, which implies that for each computable approximation and each constant c, there are infinitely many n such that \(Z_s\upharpoonright n\) changes more than c 2 n times.
Abstract: Consider a Martin-Lof random \({\Delta^0_2}\) set Z. We give lower bounds for the number of changes of \(Z_s \upharpoonright n\) for computable approximations of Z. We show that each nonempty \({\Pi^0_1}\) class has a low member Z with a computable approximation that changes only o(2 n ) times. We prove that each superlow ML-random set already satisfies a stronger randomness notion called balanced randomness, which implies that for each computable approximation and each constant c, there are infinitely many n such that \(Z_s\upharpoonright n\) changes more than c 2 n times.

Journal ArticleDOI
31 Dec 2010
TL;DR: The automatic generation of tailored interactive experiences, through artificial intelligence player modeling and content generation has the potential to address the challenge of scalable personalization.
Abstract: Personalization entails the recommendation or tailoring of goods and services. We see personalization in many domains from education to healthcare to marketing. In the arena of entertainment, there are many systems that recommend movies, books, TV shows, and music; however, there is little tailoring of entertainment content. One reason for this is the economies of scale of personalizing entertainment. Computer-based interactive entertainment – computer games – can be ideal platforms for automated tailoring of interactive content in order to deliver on-demand and just-in-time experiences. The automatic generation of tailored interactive experiences, through artificial intelligence player modeling and content generation has the potential to address the challenge of scalable personalization. The ability to dynamically produce unique, tailored experiences that make use of players’ individual differences such as tastes, preferences, play styles, range of capabilities can potentially change the way we relate to entertainment media and implications for serious applications such as education and training through tailored serious games.

Book ChapterDOI
30 Jun 2010
TL;DR: This work shows that a theorem of Kucera that states that given a Martin-Lof random infinite binary sequence ω and an effectively open set A of measure less than 1, some tail of ω is not in A can be seen as an effective version of Birkhoff's ergodic theorem.
Abstract: A theorem of Kucera states that given a Martin-Lof random infinite binary sequence ω and an effectively open set A of measure less than 1, some tail of ω is not in A. We show that this result can be seen as an effective version of Birkhoff's ergodic theorem (in a special case). We prove several results in the same spirit and generalize them via an effective ergodic theorem for bijective ergodic maps.

Journal ArticleDOI
01 Dec 2010
TL;DR: A multimodal media center interface designed for blind and partially sighted people that features a zooming focus-plus-context graphical user interface coupled with speech output and haptic feedback and is developed and evaluated in close cooperation with representatives from the target user groups.
Abstract: We present a multimodal media center interface designed for blind and partially sighted people. It features a zooming focus-plus-context graphical user interface coupled with speech output and haptic feedback. A multimodal combination of gestures, key input, and speech input is utilized to interact with the interface. The interface has been developed and evaluated in close cooperation with representatives from the target user groups. We discuss the results from longitudinal evaluations that took place in participants’ homes, and compare the results to other pilot and laboratory studies carried out previously with physically disabled and nondisabled users.

Proceedings Article
30 Jun 2010
TL;DR: It is proved that the iterated hairpin lengthening of a language recognizable in O(f(n) time is recognizable inO(n2f( n) time, while the one-step hairpin elongation of such a language is recognizableIn O(nf(N) time.
Abstract: The hairpin completion is a natural operation of formal languages which has been inspired by molecular phenomena in biology and by DNA-computing. We consider here a new variant of the hairpin completion, called hairpin lengthening, which seems more appropriate for practical implementation. The variant considered here concerns the lengthening of the word that forms a hairpin structure, such that this structure is preserved, without necessarily completing the hairpin. Although our motivation is based on biological phenomena, the present paper is more about some algorithmic properties of this operation. We prove that the iterated hairpin lengthening of a language recognizable in O(f(n)) time is recognizable in O(n2f(n)) time, while the one-step hairpin lengthening of such a language is recognizable in O(nf(n)) time. Finally, we propose an algorithm for computing the hairpin lengthening distance between two words in quadratic time.

Book ChapterDOI
30 Jun 2010
TL;DR: A translation of classical minimal logic into minimal logic is referred to as the Peirce translation, and which is applied to interpret both a strengthening of the double-negation shift and the axioms of countable and dependent choice, via infinite products of selection functions.
Abstract: We develop applications of selection functions to proof theory and computational extraction of witnesses from proofs in classical analysis. The main novelty is a translation of classical minimal logic into minimal logic, which we refer to as the Peirce translation, and which we apply to interpret both a strengthening of the double-negation shift and the axioms of countable and dependent choice, via infinite products of selection functions.

Book ChapterDOI
30 Jun 2010
TL;DR: One possible interpretation of the 'least informative model' of a relational and finite theory is considered and it is shown that it is well defined for a particular class of Π1 theories.
Abstract: We consider one possible interpretation of the 'least informative model' of a relational and finite theory and show that it is well defined for a particular class of Π1 theories. We conjecture that it is always defined for Π1 theories.

Journal ArticleDOI
31 Dec 2010
TL;DR: Exergaming : a future of mixing entertainment and exerciseassisted by mixed reality agents, published in Computers in Entertainment (CIE) Magazine, 8 (4):Publisher ACMLink topublisher'sversionhttp://dx.doi.org/10.1145/1921141.1921147This item'srecord/moreinformationhttp://hdl.handle.net/10197/2794RightsThis is the author's version of the work.
Abstract: TitleExergaming : a future of mixing entertainment and exerciseassisted by mixed reality agentsAuthor(s)Gorgu, Levent; Campbell, Abraham G.; Dragone, Mauro;O'Hare, G. M. P. (Greg M. P.)PublicationDate2010-12PublicationinformationACM Computers in Entertainment (CIE) Magazine, 8 (4):Publisher ACMLink topublisher'sversionhttp://dx.doi.org/10.1145/1921141.1921147This item'srecord/moreinformationhttp://hdl.handle.net/10197/2794RightsThis is the author's version of the work. It is posted here bypermission of ACM for your personal use. Not forredistribution. The definitive version was published inComputers in Entertainment (CIE) VOL8, ISS4 (December2010) http://doi.acm.org/10.1145/1921141.1921147.Permission to make digital or hard copies of part or all of thiswork for personal or classroom use is granted without feeprovided that copies are not made or distributed for profit orcommercial advantage and that copies bear this notice and thefull citation on the first page. Copyrights for components ofthis work owned by others than ACM must be honored.Abstracting with credit is permitted. To copy otherwise, torepublish, to post on servers, or to redistribute to lists, requiresprior specific permission and/or a fee. Request permissionsfrom Publications Dept., ACM, Inc., fax +1 (212) 869-0481, orpermissions@acm.org

Book ChapterDOI
30 Jun 2010
TL;DR: A theory of (first-order) definability in the subword partial order in parallel with similar theories for the h-quasiorder of finite k-labeled forests and for the infix order shows that any element is definable, and the first-order theory of the structure is atomic and computably isomorphic to theFirst-order arithmetic.
Abstract: We develop a theory of (first-order) definability in the subword partial order in parallel with similar theories for the h-quasiorder of finite k-labeled forests and for the infix order. In particular, any element is definable (provided that words of length 1 or 2 are taken as parameters), the first-order theory of the structure is atomic and computably isomorphic to the first-order arithmetic. We also characterize the automorphism group of the structure and show that any arithmetical predicate invariant under the automorphisms of the structure is definable in the structure.

Journal ArticleDOI
30 Dec 2010
TL;DR: An object-oriented, Java-based framework for the integration and transformation of MPEG4 standards-compliant animation streams known as Charisma is described, designed for use with modern games animation systems; this article illustrates the application of this framework on top of the authors' Java/OpenGL-based games engine framework known as Homura.
Abstract: The MPEG-4 standards define a technique for 3D facial and body model animations (FAPS/BAPS respectively), as seen in animation systems such as Greta. The way this technique works is in contrast to the set of animation techniques currently used within modern games technologies and applications, which utilize more advanced, expressive animation systems such as Skeletal, Morph Target, and Inverse Kinematics. This article describes an object-oriented, Java-based framework for the integration and transformation of MPEG4 standards-compliant animation streams known as Charisma. Charisma is designed for use with modern games animation systems; this article illustrates the application of this framework on top of our Java/OpenGL-based games engine framework known as Homura.

Book ChapterDOI
Yuri I. Manin1
30 Jun 2010
TL;DR: It is argued that partial recursive functions that according to Church’s thesis exhaust the universe of (semi)computable maps are generally not everywhere defined due to potentially infinite searches and loops and can be addressed in the same way as Feynman divergences.
Abstract: Introduction. The main observable quantities in Quantum Field Theory, correlation functions, are expressed by the celebrated Feynman path integrals. A mathematical definition of them involving a measure and actual integration is still lacking. Instead, it is replaced by a series of ad hoc but highly efficient and suggestive heuristic formulas such as perturbation formalism. The latter interprets such an integral as a formal series of finite–dimensional but divergent integrals, indexed by Feynman graphs, the list of which is determined by the Lagrangian of the theory. Renormalization is a prescription that allows one to systematically “subtract infinities” from these divergent terms producing an asymptotic series for quantum correlation functions. On the other hand, graphs treated as “flowcharts”, also form a combinatorial skeleton of the abstract computation theory. Partial recursive functions that according to Church’s thesis exhaust the universe of (semi)computable maps are generally not everywhere defined due to potentially infinite searches and loops. In this paper I argue that such infinities can be addressed in the same way as Feynman divergences. More details can be found in [9,10].

Journal ArticleDOI
30 Dec 2010
TL;DR: The steps taken to consult with families affected by TBI to understand the difficulties teenagers commonly face when they live with a brain-injured parent are described, and to weave some of these difficulties into a pedagogical drama that can be played as an interactive game.
Abstract: Traumatic brain injury (TBI) is a leading cause of long-term disability and death worldwide. This article describes an ongoing research project to design, develop, and evaluate interactive learning simulations that integrate educational materials for uninjured teenagers who have a parent with a TBI. By immersing players in an interactive environment that resembles the gaming world with which most teenagers are familiar, these simulations are designed to help players develop knowledge and skills in circumstances approximating real-life settings. We describe the steps we took, both to consult with families affected by TBI to understand the difficulties teenagers commonly face when they live with a brain-injured parent, and to weave some of these difficulties into a pedagogical drama that can be played as an interactive game.

Journal ArticleDOI
30 Jun 2010
TL;DR: It is proved that each superlow ML-random set already satisfies a stronger randomness notion called balanced randomness, which implies that for each computable approximation and each constant c, there are infinitely many n such that Zs ↑n changes more than c2n times.
Abstract: Consider a Martin-Lof random Δ20 set Z. We give lower bounds for the number of changes of Zs ↑n for computable approximations of Z. We show that each nonempty Π10 class has a low member Z with a computable approximation that changes only o(2n) times. We prove that each superlow ML-random set already satisfies a stronger randomness notion called balanced randomness, which implies that for each computable approximation and each constant c, there are infinitely many n such that Zs ↑n changes more than c2n times.

Journal ArticleDOI
01 Dec 2010
TL;DR: This article presents LightTracker, an open-source toolkit for vision-based multi-touch setups that can dynamically create and manipulate the image processing pipeline at runtime and presents implementation details such as the plug-in system and the multithreaded architecture.
Abstract: In this article we present LightTracker -- an open-source toolkit for vision-based multi-touch setups. Using this toolkit, we can dynamically create and manipulate the image processing pipeline at runtime. After presenting various new requirements derived from hardware configurations as well as literature review, features and shortcomings of available tracking solutions are discussed and compared to our proposed toolkit. This is followed by a detailed description of the toolkit’s functionality, including the filter chain and the improved calibration module. We also present implementation details such as the plug-in system and the multithreaded architecture. To illustrate the advantages of the toolkit, an interactive gaming couch table based on LightTracker is introduced.

Book ChapterDOI
30 Jun 2010
TL;DR: This paper presents a new O(Δ3m2(mΔ + n3)) time algorithm for this particular task for a m×n binary matrix with at most Δ 1-entries per row, thereby improving the O( Δ3m1(mn - n3) time algorithm of Dom et al.
Abstract: A binary matrix has the Consecutive Ones Property (C1P) if its columns can be ordered in such a way that all 1s on each row are consecutive. Algorithmic issues of the C1P are central in computational molecular biology, in particular for physical mapping and ancestral genome reconstruction. In 1972, Tucker gave a characterization of matrices that have the C1P by a set of forbidden submatrices, and a substantial amount of research has been devoted to the problem of efficiently finding such a minimum size forbidden submatrix. This paper presents a new O(Δ3m2(mΔ + n3)) time algorithm for this particular task for a m×n binary matrix with at most Δ 1-entries per row, thereby improving the O(Δ3m2(mn + n3)) time algorithm of Dom et al. [17].

Journal ArticleDOI
31 Dec 2010
TL;DR: Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies show this notice on the first page or initial screen of a display.
Abstract: Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies show this notice on the first page or initial screen of a display along with the full citation. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works requires prior specific permission and/or a fee. Permissions may be requested from Publications Dept., ACM, Inc., 2 Penn Plaza, Suite 701, New York, NY 10121-0701 USA, fax +1 (212) 869-0481, or permissions@acm.org. ©2010 ACM 1544-3574/2010/12-ART25 $10.00 DOI: 10.1145/1921141.1921145 http://doi.acm.org/10.1145/1921141.1921145