Jin Akiyama - Böcker

This book constitutes the thoroughly refereed post-conference proceedings of the 21st Japanese Conference on Discrete and Computational Geometry and Graphs, JCDCGGG 2018, held in Quezon City, Philippines, in September 2018. The total of 14 papers included in this volume was carefully reviewed and selected from 25 submissions.

This book, LNCS 14364, constitutes the refereed proceedings of the 24th Japanese Conference on Discrete and Computational Geometry and Graphs, JCDCGGG 2022, held virtually during September 9-11, 2022. The 22 full papers included in this volume were carefully reviewed and selected from 35 submissions.

This book constitutes the thoroughly refereed post-conference proceedings of the 16th Japanese Conference on Discrete and computational Geometry and Graphs, JDCDGG 2013, held in Tokyo, Japan, in September 2013.The total of 16 papers included in this volume was carefully reviewed and selected from 58 submissions. The papers feature advances made in the field of computational geometry and focus on emerging technologies, new methodology and applications, graph theory and dynamics.

This book constitutes the thoroughly refereed post-conference proceedings of the 18th Japanese Conference on Discrete and Computational Geometry and Graphs, JDCDGG 2015, held in Kyoto, Japan, in September 2015. The total of 25 papers included in this volume was carefully reviewed and selected from 64 submissions.

Since it was ?rst organized in 1997, the Japan Conference on Discrete and C- putational Geometry (JCDCG) continues to attract an international audience. The ?rst ?ve conferences of the series were held in Tokyo, the sixth in Manila, Philippines. This volume consists of the refereed papers presented at the seventh conference, JCDCG 2002, held in Tokai University, Tokyo, December 6-9, 2002. An eighth conference is planned to be held in Bandung, Indonesia. The proceedings of JCDCG 1998 and JCDCG 2000 were published by Springer-Verlag as part of the series Lecture Notes in Computer Science: LNCS volumes 1763 and 2098, respectively. The proceedings of JCDCG 2001 were also published by Springer-Verlag as a special issue of the journal Graphs and C- binatorics, Vol. 18, No. 4, 2002. The organizers are grateful to Tokai University for sponsoring the conf- ence. They wish to thank all the people who contributed to the success of the conference, in particular, Chie Nara, who headed the conference secretariat, and the principal speakers: Takao Asano, David Avis, Greg N. Frederickson, Ferran Hurtado, Joseph O'Rourke, J' anos Pach, Rom Pinchasi, and Jorge Urrutia.

This volume consists of the refereed papers presented at the Indonesia-Japan Joint Conference on Combinatorial Geometry and Graph Theory (IJCCGGT 2003), held on September 13-16, 2003 at ITB, Bandung, Indonesia. This conf- ence can also be considered as a series of the Japan Conference on Discrete and Computational Geometry (JCDCG), which has been held annually since 1997. The ?rst ?ve conferences of the series were held in Tokyo, Japan, the sixth in Manila, the Philippines, in 2001, and the seventh in Tokyo, Japan in 2002. The proceedings of JCDCG 1998, JCDCG 2000 and JCDCG 2002 were p- lished by Springer as part of the series Lecture Notes in Computer Science: LNCS volumes 1763, 2098 and 2866, respectively. The proceedings of JCDCG 2001 were also published by Springer as a special issue of the journal Graphs and Combinatorics, Vol. 18, No. 4, 2002. TheorganizersaregratefultotheDepartmentofMathematics,InstitutTek- logi Bandung (ITB) and Tokai University for sponsoring the conference. We also thank all program committee members and referees for their excellent work. Our big thanks to the principal speakers: Hajo Broersma, Mikio Kano, Janos Pach andJorgeUrrutia.Finally,ourthanksalsogoestoallourcolleagueswhoworked hard to make the conference enjoyable and successful.August 2004 Jin Akiyama Edy Tri Baskoro Mikio Kano Organization The Indonesia-Japan Joint Conference on Combinatorial Geometry and Graph Theory (IJCCGGT) 2003 was organized by the Department of Mathematics, InstitutTeknologiBandung(ITB)IndonesiaandRIED,TokaiUniversity,Japan.

This volume consists of the refereed proceedings of the Japan Conference on Discrete and Computational Geometry (JCDCG 2004) held at Tokai University in Tokyo, Japan, October, 8-11, 2004, to honor Jan ' os Pach on his 50th year. J' anos Pach has generously supported the e?orts to promote research in discrete and computational geometry among mathematicians in Asia for many years. The conference was attended by close to 100 participants from 20 countries. Since it was ?rst organized in 1997, the annual JCDCG has attracted a growing international participation. The earlier conferences were held in Tokyo, followed by conferences in Manila, Philippines, and Bandung, Indonesia. The proceedings of JCDCG 1998, 2000, 2002 and IJCCGGT 2003 were published by SpringeraspartoftheseriesLectureNotesinComputerScience(LNCS)volumes 1763, 2098, 2866 and 3330, respectively, while the proceedings of JCDCG 2001 were also published by Springer as a special issue of the journal Graphs and Combinatorics, Vol. 18, No. 4, 2002.The organizers of JCDCG 2004 gratefully acknowledge the sponsorship of Tokai University, the support of the conference secretariat and the partici- tion of the principal speakers: Ferran Hurtado, Hiro Ito, Alberto M' arquez, Ji? r' ? Matou? sek, Ja 'nos Pach, Jonathan Shewchuk, William Steiger, Endre Szemer' edi, G' eza T' oth, Godfried Toussaint and Jorge Urrutia.

TheJapanConferenceonDiscreteandComputationalGeometry(JCDCG)has beenheldannuallysince1997. Oneofthegoalsofthisconferenceseriesistobring togetherJapaneseresearchersfrombothacademiaandindustrywithresearchers inthese?eldsfromabroadtosharetheirrecentresults. JCDCG2000washeld22-25November2000atTokaiUniversityinTokyo inconjunctionwiththecelebrationofWorldMathematicsYear2000. Atotalof 120participantsfrom20countriesattended. Thisvolumeconsistsofthepapers presentedatJCDCG2000,whichhavebeenrefereedandrevised. Somepapers whichappearinshortforminthisvolumealsoappearinfullerexpandedversions injournalsdedicatedtocomputationalgeometry. Theorganizersoftheconferencethanktheprincipalspeakersfortheir- terestandsupport:ImreBarany,ErikD. Demaine,GregN. Fredrickson,Gyula Karolyi,NaokiKatoh,DavidKirkpatrick,JosephO'Rourke,JanosPach,Jozsef Solymosi,WilliamSteiger,JorgeUrrutia,andAllanWilks. Theythankthe- jorsponsorsfortheirgenerouscontribution:TheResearchInstituteofEdu- tionalDevelopmentofTokaiUniversity,theMinistryofEducationofJapan(for thegrant-in-aidtoA. Saito(A):10304008),andTokaiEducationInstruments Co. ,Ltd.April2001 TheEditors, JinAkiyama MikioKano MasatsuguUrabe OrganizingCommittee Chairs:JinAkiyamaandMikioKano Members: TetsuoAsano,DavidAvis,VasekChvatal,KiyoshiHosono,HiroshiImai, TakakoKodate,JosephO'Rourke,ToshinoriSakai,XuehouTan,Morimasa Tsuchiya,MasatsuguUrabe,andJorgeUrrutia. TableofContents Papers DudeneyDissectionsofPolygonsandPolyhedrons-ASurvey-...1 J. AkiyamaandG. Nakamura UniversalMeasuringDeviceswithoutGradations...31 J. Akiyama, H. Fukuda,G. Nakamura, T. Sakai, J. Urrutia, andC. Zamora-Cura ANoteonthePurelyRecursiveDissectionforaSequentially n-Divisible Square ...41 J. Akiyama, G. Nakamura, A. Nozaki, and K. Ozawa SequentiallyDivisibleDissectionsofSimplePolygons ...53 J. Akiyama, T. Sakai, andJ. Urrutia PackingConvexPolygonsintoRectangulerBoxes ...67 H. AltandF. Hurtado OntheNumberofViewsofPolyhedralScenes ...81 B. Aronov, H. Br. onnimann,D. Halperin,andR. Schi?enbauer ProblemsandResultsAroundtheErdos-Szek ? eresConvex PolygonTheorem ...91 I. Bar ' an ' y andG. Kar ' olyi OnFindingMaximum-CardinalitySymmetricSubsets ...106 P. Brass FoldingandUnfoldingLinkages,Paper,andPolyhedra ...113 E. D. Demaine OntheSkeletonoftheMetricPolytope ...125 A. Deza,K. Fukuda,D.Pasechnik, andM. Sato GeometricDissectionsThatSwingandTwist ...137 G. N. Frederickson OnConvexDecompositionsofPoints ...149 K. Hosono, D. Rappaport, andM. Urabe VolumeQueriesinPolyhedra ...156 J. IaconoandS. Langerman VIII Table ofContents SumofEdgeLengthsofaGraphDrawnonaConvexPolygon ...160 H. Ito,H. Uehara, andM. Yokoyama OnDoubleBoundGraphswithRespecttoGraphOperations ...167 S. Iwai,K. Ogawa,andM. Tsuchiya GeneralizedBalancedPartitionsofTwoSetsofPointsinthePlane ...176 A. KanekoandM. Kano OnPathsinaCompleteBipartiteGeometricGraph ...187 A. KanekoandM. Kano ApproximatingUniformTriangularMeshesforSpheres ...192 N. Katoh,H. Kojima, andR. Taniguchi TheConstructionofDelaunayDiagramsbyLobReduction ...205 P. Kau?mannand J. C. Spehner GeometricTransformationsinPlaneTriangulations ...217 K. Kawarabayashi, A. Nakamoto, Y. Oda, andM. Watanabe SeparationSensitiveKineticSeparationStructuresforConvexPolygons . . 222 D. Kirkpatrick andB. Speckmann OnAcuteTriangulationsofQuadrilaterals ...237 H. Maehara IntersectingRedandBlueLineSegmentsinOptimalTimeandPrecision . 244 A. MantlerandJ. Snoeyink TightErrorBoundsofGeometricProblemsonConvexObjectswith ImpreciseCoordinates ...252 T. NagaiandN.Tokura TriangleContactSystems,OrthogonalPlanePartitionsandtheirHitGraphs 264 A. Nakamoto NoteonDiagonalFlipsandChromaticNumbersofQuadrangulationson ClosedSurfaces ...274 A. NakamotoandS. Negami AnExtensionofCauchy'sArmLemmawithApplicationtoCurve Development ...280 J. O'Rourke OntheComplexityoftheUnionofGeometricObjects ...292 J. Pach Table of Contents IX StructureTheoremsforSystemsofSegments ...308 J. Pach andJ. Solymosi 3-dimensionalSingleActiveLayerRouting ...

This book constitutes the thoroughly refereed post-conference proceedings of the Second Japanese Conference on Discrete and Computational Geometry, JCDCG8, held in Tokyo, Japan, in December 1999. The 27 revised full papers presented were carefully reviewed and selected for inclusion in the post-conference proceedings. Among the topics addressed are approximation, convex hulls, lattice computations, tilings, graph computations, Voronoi diagrams, clustering, graph drawing, diagram design, and illumination problems.

This book constitutes the thoroughly refereed post-proceedings of the 7th China-Japan Conference on Discrete Geometry, Combinatorics and Graph Theory, CJCDGCGT 2005, held in Tianjin, China, as well as in Xi'an, China, in November 2005. The 30 revised full papers address all current issues in discrete algorithmic geometry, combinatorics and graph theory.

This book chronicles the development of graph factors and factorizations. It pursues a comprehensive approach, addressing most of the important results from hundreds of findings over the last century. One of the main themes is the observation that many theorems can be proved using only a few standard proof techniques. This stands in marked contrast to the seemingly countless, complex proof techniques offered by the extant body of papers and books. In addition to covering the history and development of this area, the book offers conjectures and discusses open problems. It also includes numerous explanatory figures that enable readers to progressively and intuitively understand the most important notions and proofs in the area of factors and factorization.

This book constitutes the thoroughly refereed post-conference proceedings of the China-Japan Joint Conference on Computational Geometry, Graphs and Applications, CGGA 2010, held in Dalian, China, in November 2010. The 23 revised full papers presented were carefully selected during two rounds of reviewing and improvement from numerous submissions. All aspects of computational and discrete geometry, graph theory, graph algorithms, and their applications are covered.

This book constitutes the refereed proceedings of the Thailand-Japan Joint Conference on Computational Geometry and Graphs, TJJCCGG 2012, held in Bangkok, Thailand, in December 2012.The 15 original research papers presented were selected from among six plenary talks, one special public talk and 41 talks by participants from about 20 countries around the world. TJJCCGG 2012 provided a forum for researchers working in computational geometry, graph theory/algorithms and their applications.

This book is written in a style that uncovers the mathematical theories buried in our everyday lives such as examples from patterns that appear in nature, art, and traditional crafts, and in mathematical mechanisms in techniques used by architects.

Math Wonderland is a museum of interactive mathematical models in Hokkaido, Japan, founded by one of the authors, Jin Akiyama, in 2003. The models in Wonderland, many of which have been exhibited all over Japan and in cities around the world, are meant to help children and young adults discover and experience the wonders of mathematics.This book is centered around the experiences of three fictional middle-school students during a visit to Wonderland. They spend a day in Wonderland, handling the interactive models and participating in the activities offered there. At the end of the day, they leave with a genuine appreciation of mathematics gained from witnessing its beauty, applicability and inevitability.The book is an important contribution to the genre because it presents mathematics and models that have never before appeared in books in the same category: reversible solids, plane tiling with developments of tetrahedrons, and double-packable solids, which are derived from the authors' own research papers published in mathematics journals. It is designed to entertain, inform and even teach some mathematics. Although it is targeted at young adults, parents and teachers may learn something from the book as well.