An XML Representation of the Octgrid for the Rectangular Dissections

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1 2016 4th Intl Conf on Applied Computing and Information Technology/3rd Intl Conf on Computational Science/Intelligence and Applied Informatics/1st Intl Conf on Big Data, Cloud Computing, Data Science & Engineering An XML Representation of the Octgrid for the Rectangular Dissections Koushi Anzai Department of Economics Kanto Gakuen University Ohta, Gunma, , Japan Takeo Yaku Department of Information Science Nihon University Setagaya, Tokyo, , Japan Takaaki Goto Department of Distribution and Logistics Systems Ryutsu Keizai University Ryugasaki, Ibaraki, , Japan Youzou Miyadera Division of Natural Science Tokyo Gakugei University Koganei, Tokyo, , Japan Ken Yokota Department of Information Science Nihon University Setagaya, Tokyo, , Japan Abstract This paper proposes an XML representation of octgrid completely. Octgrid is a data structure based on octal grid graphs for heterogeneous rectangular dissections. This model is represented by a list structure called H3-Code. The file format of H3-Code is a plain text file that consists of a plurality of space separated field. Therefore we introduced the XML representation called H14-Code. Keywords octgrid; heterogeneous rectangular dissections; XML; spreadsheet; I. INTRODUCTION H14-Code is the specification of data structures and data format for developing table processing systems. H14-Code represents the list-type data structure called octgrid in XML. H14-Code is based on the H3-Code [2, 5]. The feature of H14-Code is the XML representation for the list-type data structure. Since you can use existing XML technology by representing the list-type data structure in XML, you can expect to build easily the processing system that applies the list-type data structure. However, the XML representation which is proposed by Shiono et al [3, 4 ] requires a specific order of cells to display it. According to previous studies [1, 6, 9], "octgrid" list structure to represent a heterogeneous rectangular dissections has been proposed. Octgrids are octal degree heterogeneous grid graphs. Each node of octgrid correspond to the rectangle of the dissections. The relationship with the adjacent node are held by the edges of eight directions. Therefore, It can make relation between the two rectangles which is splitted by another heterogeneous rectangle. First, we survey octgrid that represent heterogeneous rectangular dissections. Next, we introduce a new XML representation for octgrid. II. OCTGRIDS FOR THE RECTANGULAR DISSECTIONS A. The Octgrid Model [1, 9] A rectangular dissection is a set of rectangles, the sides of which are parallel, such that the area is covered by the union of all rectangles with no intersection. Figure 1 shows each of these four walls (left) and an example of rectangular dissection (right). Fig. 1. Each of these four walls (left) and an example of rectangular dissection (right) [10] The octgrid G for a rectangular dissection D is defined as follows. Definition 2.1 Consider D to be a rectangular dissection. G D is an octgrid corresponding to D if and only if D is represented as a multiedge undirected graph where : the set of vertices that represents cells in D : defined by the following Rules 1 4. is defined by the following Rules 1 4. : the set of attributes are defined for by /16 $ IEEE DOI /ACIT-CSII-BCD

2 <Rule 1> If and there is no cell between c and d having an equal north wall, then In this case, is called a north wall edge (see Figure 2). <Rule 2> If and there is no cell between c and d having an equal south wall, then In this case, is called a south wall edge (see Figure 3). <Rule 3> If and there is no cell between c and d having an equal east wall, then In this case, is called a east wall edge (see Figure 4). <Rule 4> If and there is no cell between c and d having an equal west wall, then In this case, is called a west wall edge (see Figure 5). Fig. 2. Illustration of Rule 1. [7] Fig. 3. Illustration of Rule 2. [7] Fig. 4. Illustration of Rule 3. [7] Fig. 5. Illustration of Rule 4. [7] Definition 2.2 G is an octgrid if and only if there is a rectangular dissection D such that G is an octgrid corresponding to D. Figure 6 shows an example of a heterogeneous rectangular dissection including inner cells and perimeter cells (left) and its corresponding octgrid (right). Fig. 6. Heterogeneous rectangular dissection (left) and corresponding octgrid (right) [10] B. Octgrid Implementation (H3-Code) For Octgrid implementation, a file format called H3-Code is proposed [2, 5], which is a list structure as shown in Figure 7. Fig. 7. Fields of a cell (left) and the whole structure of an H3-Code (right) [2] III. XML REPRESENTATION FOR OCTDRID (H14-CODE OVER VIEW)[8] In this section, we introduce an XML representation for octgrid easily. The XML notation which is proposed by Shiono et al. requires a specific order of cells to display it. But, it can be displayed directly with some appropriate XSL style sheet. Meanwhile, since our XML notation is converted into another XML notation for display by another process, our XML notation does not require any particular order of cells. We will show an algorithm for the process. First, each node of octgrid consists of the following elements (See Figure 7) links to the cell around wwe_upper, ewe_upper, wwe_lower, ewe_lower, nwe_left, swe_left, nwe_right, swe_right 2. Additional information about the s of the cell cell_id, north_wall (information for the north wall position), south_wall, west_wall, east_wall, link(location for the s of the cell), align, epoint Next, we define XML representation for each cell as follows. <cell> <wwe_upper>~</wwe_upper> <swe_right>~</swe_right> <cell_id>~</cell_id> <_lnk>~</ _lnk > </cell> We define the following notation as a whole by adding other information and header information. The cell tag is repeated as many times as necessary. 39

3 <?xml version= 1.0?> <H14Code> <header> <version>~</version> </header> <HLTC> <cell>~</cell> <cell>~</cell> </HLTC> <HCContent>~</HCContent> </H14Code> IV. H14-CODE In this section, we introduce H14-Code completely. We define the XML representation for octgrid by EBNF notation. H14-Code is consists of header part, HLTC part, and HCContent part. <H14-Code-Syntax> ::= "<?xml version = \"1.0\"?>" "<H14Code>" <header-section> <HLTC-section> <HCContent-section> "</H14Code>" ; The following items are described in the header section. 1. version of H14-Code 2. size of row 3. size of column 4. number of s 5. document title 6. author(s) 7. date 8. document version TABLE I. HEADER SECTION item significance specification restriction h_version version of text - H14-Code row row size integer - column column size integer - s number of integer - s title document text - title author author(s) text - date date text - doc_version document version text - <header-section> ::= "<header>" "<h_version>".+ "</h_version>" "<row>" [0-9]+ "</row>" "<column>" [0-9]+ "</column>" "<s>" [0-9]+ "</s>" "<title>".+ "</title>" "<author>".+ "</author>" "<date>".+ "</date>" "<doc_version>".+ "</doc_version>" "</header>" ; The following items are described in the HLTC (HList for Table Cell) section. 1. invisible cell (perimeter cell) 2. visible cell <HLTC-section> ::= "<HLTC>" "<perimeter>" <cells> "</perimeter>" "<visible>" <cells> "</visible>" "</HLTC>" ; <cells> ::= <cell> <cell> <cells> ; <cell> ::= "<cell>" "<cell_id>" [0-9]+ "</cell_id>" "<wwe_upper>" [0-9]+ "</wwe_upper>" "<wwe_lower>" [0-9]+ "</www_lower>" "<ewe_upper>" [0-9]+ "</ewe_upper>" "<ewe_lower>" [0-9]+ "</ewe_lower>" "<nwe_left>" [0-9]+ "</nwe_left>" "<nwe_right>" [0-9]+ "</nwe_right>" "<swe_left>" [0-9]+ "</swe_left>" "<swe_right>" [0-9]+ "</swe_right>" "<east_wall>" [0-9]+ "</east_wall>" "<west_wall>" [0-9]+ "</west_wall>" "<south_wall>" [0-9]+ "</south_wall>" "<north_wall>" [0-9]+ "</north_wall>" "<_lnk>" [0-9]+ "</_lnk>" "<align>" [0-3] "</align>" "</cell>" ; The following items are described in the HCContent (Contents list for H14-Code) section. 40

4 TABLE II. HCCONTENT SECTION item significance specification restriction _id _type object identifier data type of itself or link for the <HCContent-section> ::= integer >=1 integer 1: text 100 : HTML 101 : RTF 102 : image text (double quote) unique number - link for the other file, keyword link is required (ex) link:./sample.jpg "<HCContent>" "</HCContent>" "<HCContent>" <s> "</HCContent>" ; <s> ::= <> <> <s> ; <> ::= "<>" "<_id>" [0-9]+ "</_id>" "<_type> "[0-9]+ "</_type>" "<object>".+ "</object>" "</>" ; V. CONVERSION ALGORITHM In order to display the XML in a browser, it must be arranged in the same order as each tag in HTML that corresponds each tag of XML. On the other hand, the XML tags in the H14-Code may not aligned in this order. Therefore, in order to display the rectangular dissection corresponding to the given H14-Code, we need an algorithm that adds some attributes for the actual display and rearranges the XML tags of the H14-Code in this order. The XML code (viewable XML) obtained by this algorithm is converted to a HTML in the browser with a suitable XSLT program. Algorithm H14-Code_to_viewableXML INPUT H14-Code OUTPUT viewable XML code METHOD Let s be the perimeter cell in the upper left corner of a rectangular dissection. FOR (c := s ; c!= NULL ; c := c.wwe_lower) { PUT "<row>" ; FOR (d := c ; d!= NULL ; d := d.nwe_right) { PUT "<cell>" ; celltype = 0 ; IF d is a perimeter cell THEN PUT celltype, s of d ELSE { GET rowspan, colspan from 4 walls location ; celltype = 1 ; PUT celltype ; PUT contens of d and some attributes (rowspan, colspan, etc) ; PUT "</cell>" ; PUT "</row>" ; Algorithm viewablexml_to_html INPUT viewable XML code OUTPUT HTML METHOD <?xml version = "1.0"?> <xsl:stylesheet xmlns:xsl = " version = "1.0"> <xsl:output method = "html" /> <xsl:template match = "/"> <html> <head> <title> <xsl:value-of select = "H14CodeTABLE/title" /> </title> </head> <body> <h1> <xsl:value-of select = "H14CodeTABLE/title" /> </h1> <table border="0" cellspacing="3" cellpadding="10"> <xsl:apply-templates select = "H14CodeTABLE" /> </table> </body> </html> </xsl:template> <xsl:template match = "H14CodeTABLE" > <xsl:for-each select = "row" > <tr> 41

5 <xsl:for-each select = "cell" > <xsl:choose> <xsl:when test = "celltype=0" > <td> </td> <!-- invisible space mark --> </xsl:when> <xsl:when test = "celltype=1" > <xsl:element name="td"> <xsl:attribute name="bgcolor"> silver <xsl:attribute name="rowspan"> <xsl:value-of select = "rowspan" /> <xsl:attribute name="colspan"> <xsl:value-of select = "colspan" /> <xsl:value-of select = "" /> </xsl:element> </xsl:when> <xsl:otherwise > </xsl:otherwise > </xsl:choose> </xsl:for-each> </tr> </xsl:for-each> </xsl:template> </xsl:stylesheet> Figure8 shows the result of algorithm viewablexml_to_ HTML XSLT program on the web browser. This table represents the structure for figure 6. VI. CONCLUSION In this paper, we surveyed an octgrid graph model. Furthermore, we have introduced an XML representation for the octgrid graph completely. This XML representation we proposed is not able to display the table directly in the web browser. In order to display on the web browser, you need a program to output the cell tags in the same order as the HTML TABLE tags. We have shown two algorithms for that. As future works, we would like to establish an H14-Code development foundation that is based on standard technologies such as XML parsers and RDBMS. [8] REFERENCES [1] T. Yaku, Representation of Heterogeneous Tessellation Structures by Graphs, Working Group of Automata and Its Applications Research Report 2001, [2] Tadaaki Kirishima, Tomoe Motohashi, Kensei Tsuchida, Takeo Yaku, Table Processing based on Attribute Graphs, Proc. IASTED SEA 2002, pp [3] Yasunori Shiono, Tomokazu Arita, Tadaaki Kirishima, Kensei Tsuchida, Takeo Yaku, XML Data Formats for General Tabular Forms, Proc. the 22nd Conf. Japan Society for Software Science and Technology (JSSST), 7D-3, [4] Y. Shiono, K. Tsuchida and T. Yaku, H10-Code, Working Group of Automata and Its Applications Research Report 2006, Specification_1_00_english.odt [5] T. Arita and T. Yaku, H3Code version 2.3, Working Group of Automata and Its Applications Research Report 2006, waap-rr/waap-rr /index.html [6] Takeo Yaku, Koichi Anada, Koushi Anzai, Shinji Koka, Kensei Tsuchida, 8k-ary Grid Graph Modeling of the Rectangular Dissections, Proc. Int l Conf. Modeling, Sim. and Vis. Methods, pp , 2012 [7] Koichi Anada, Shinji Koka, Akihito Kubota, Yuki Shindo, and Takeo Yaku, The Number of Cells in Regions Shifted on 2D Images Represented by Raster Data with Heterogeneous Parts, Proc. 14th IEEE/ACIS (SNPD), pp , [8] Koushi Anzai, Koichi Anada, Youzou Miyadera, Takeo Yaku, Ken Yokota, A Consept of the Editing for Spreadsheets Based on Octgrids and SQL, Proc. 27th International Conference on Computer Applications in Industry and Engineering (CAINE2014) pp , 2014 [9] Takeo Yaku, Kouichi Anada, Koushi Anzai, Shinji Koka, Youzou Miyadera, and Kensei Tsuchida, 8k-ary Grid Graph Models of Tabular Forms, Lecture Notes in Computer Science 8373 (Specification, Algebra and Software 2014), [10] Taiyou Kikuchi, Koichi Anada, Shinji Koka, Youzou Miyadera, Takeo Yaku, A data structure for triangular dissection of multi-resolution images, Proc. 15th IEEE/ACIS International Conference on SNPD, 2014, Fig. 8. Excution example for the algorithm viewablexml_to_html XSLT program 42