DocEng2011 Bilauca Healy - Building Table Formatting Tools

DocEng2011, September 19– 22, 2011, Mountain View, California

Building
Table Formatting Tools
Mihai Bilauca

Patrick Healy

Department of Computer Science and Information Systems
University of Limerick, Ireland

Supported by Science Foundation Ireland under the research programme 01/P1.2/C009,
Mathematical Foundations, Practical Notations, and Tools for Reliable Flexible Software.

Building Table Formatting Tools
Why this paper?
• Tables are widely used for presenting logical
relationships between data items;
• Widely spread WYSIWYG tools only control
presentation parameters;
• Existing tools have limitations;
• Authoring tables is hard, time consuming and error
prone;

Slide 2 of 48

Overview
A) A review of logical table models;
B) Table Drawing Tool Prototype: Typographical issues;
C) Automated table layout optimization for tables with
spanning cells:

Report experimental results for large tables

Comparison with previous models;

A simplified solution for nested tables;
A) Conclusions

Slide 3 of 48

Logical table models


Slide 4 of 48

1985 Beach
• An for Tioga DS that formats itself based on given dimensions
• A “grid” with table topology and table geometry
1989 Cameron
• Identifies 3 mental processes: structure, content & visual editing
1989 Vanoirbeek
• a multidimensional collection of logically connected data items
• each dimension is divided in rubrics to classify data items
• merged items where an item is connected to multiple rubrics
• defines tables in a language based on attribute grammars


Slide 5 of 48

1996 Wang
• layout structure (topology & typographic style)
• logical structure: a mathematical model based on unordered
sets
• identified operations at table, category and label level
2010 Parnas
• meaningful expressions which can be evaluated and validated
• indexation separates table semantics from appearance
• An indexed set of grids < GS, I, x > and each grid is an indexed
set of expressions
• A grid < SetExp, J, y > is a set of expressions SetExp, an indexed
set J and a mapping y between SetExp and J

Slide 6 of 48

Table Drawing Tool Prototype:
Typographical issues;


Slide 7 of 48

Table Drawing Tool - TDT
• Part of a larger project developed at University of Limerick
Ireland, a tabular expressions tool:
–
–
–
–

Table Input Tool;
Kernel;
Evaluation module;
Table Drawing Tool;

• concerned only with drawing tables on a rendering device
depending on the table layout using a layout optimizer;
• current version supports rectangular tables which can be
rendered in PDF using a layout optimizer based on IBM ILOG
OPL;


Slide 8 of 48

TDT Circular layout?

Table 1 is represented with both rectangular and a circular layout


Slide 9 of 48

TDT Device
The device is an abstract object that must provide functions to:
• open and close the device;
• set colours, fill colours, line styles;
• font settings (font family, style, size);
• vertical and horizontal alignment;
• text spacing (word, character and line spacing);
• draw curves (bezier);
• support for images;
• support for paging the content;
The device must return measurement units in the TDT coordinate
system;


Slide 10 of 48

TDT Hierarchical model
A table layout tool needs to be as powerful as a page
layout tool
• TDT implements a hierarchical structure of containers
(similar to the CSS)
• It is each container’s responsibility to format itself
• Each container must implement computeLayout and render
on device functions
• For drawing tables TDT implements a box model;
Support for
• Hierarchical propagation of typographical parameters
• Layered control of typographical parameters


Slide 11 of 48

TDT The Box model

For drawing tables TDT implements a box model (similar to CSS)


Slide 12 of 48

TDT Typographical issues
• table layout: a caption and a layout (rectangular, circular,
custom)
• caption: label, number and caption text; Global numbering
styles must be defined; example: Table A.12 Test data
• laying containers: fixed and floating positioning. lay floating
(nonfixed) containers on lines; complexity is increased with
fixed position containers
• lines: styles and joins: pattern, line cap, line join and miter
limit; The pattern is defined as a dash array and a phase
• margins: add or merge adjacent margins?

Slide 13 of 48

TDT Typographical issues
• coordinates space: TDT uses a coordinate system with points
(1/72 inch)
• text direction: right-to-left, top-to-bottom
• equations: TDT uses WebEQ to render MathML expressions
• images: conversion from pixels in the units of the coordinate
system;
• borders: without a clear definition of the lines styles, dealing
with borders can be a major cause of frustration:
– border space;
– border alignment;
– border priority;

Slide 14 of 48

Border conflicts in Open Office


Slide 15 of 48

Automated table layout optimization


Slide 16 of 48

Table layout optimization
• For applications where finding the layout with the
minimum height for a given width is important;
• Because it is exact (not based on heuristics);
• Priority should be given to user constraints imposed
by space limitations or other aesthetic criteria;


Slide 17 of 48

The Table Layout Problem
Find a layout λ of a table ℑ with minimum
such that

height (λ )

width(λ ) < W
W – a given page width


Slide 18 of 48

Definitions (Anderson and Sobti)
ℑ , m x n table, m rows, n columns, λ

is a layout of ℑ

k
k
Ci , j : {( wij , hij ) | 1 ≤ k ≤ K ij }

is the set of configurations for cell i,j with

1 ≤ ki , j ≤ K ij the index of the configuration selected from Ci,j
m

height (λ ) = ∑ hi
i =1

n

width(λ ) = ∑ w j
j =1

where hi = max(hi,j) for each row i, wj = max(wi,j) for each column j
ki , j
i, j

hi , j = h

ki , j
i, j

wi , j = w

Slide 19 of 48

Cell configurations
Example:
k
k
Ci , j : {(hij , wij ) | 1 ≤ k ≤ K ij }
Cell configurations for cell i,j
this blue sky


this blue
sky

this
blue
sky

Slide 20 of 48

IP definition – simple tables
m

n

minimize∑ max hi , j ,k ⋅ xi , j ,k
i =1

j =1

subject to
n

1)

m

∑ max w
i =1

j =1

2)
where

∑x

i , j ,k

i , j ,k

⋅ xi , j ,k ≤ W

= 1,

x ∈ {0,1}
1 ≤ ki , j ≤ K i , j
Slide 21 of 48

IP – Tables with spanning cells
The height and width of a spanning cell i,j is

1)

2)

S

h
i, j

S

w
i, j

hi , j =
wi , j =

i + S ih, j

∑h

r

r =i

j + S iwj
,

∑w
c= j

c

the number of additional rows spanned by cell i,j
the number of additional columns spanned by cell i,j


Slide 22 of 48

Tables with spanning cells
Two cases:

A) cell 1,1 spans wide
columns


B) cell 1,1 spans narrow columns

Slide 23 of 48

A cell spanning narrow columns requires “glue”

“Glue” is a concept similar to the “glue” introduced by Knuth
- it stretches and shrinks as required;
- its value can be further constraint;


Slide 24 of 48

For a spanning cell i,j the equations 1) and 2) become:

1)

2)

g

hi , j =
wi , j =

i + S ih, j

∑ (h

r

r =i

j + S iwj
,

∑ (w
c= j

c

+g )
h
r

+g )

h
r

the vertical glue for row r

w
c

w
c

the horizontal glue for column c

g


Slide 25 of 48

a)

hi , j = ∑ hi , j ,k ⋅ xi , j ,k

m

c)

i =1

k

b)

wi , j = ∑ wi , j ,k ⋅ xi , j ,k

n

d)

where

x, y, z ∈ {0,1}

h ∈ Hi ,

r
i

wj = ∑ w ⋅ z
j =1

k

r
i

hi = ∑ h ⋅ y
r
i

c
j

c
j

w ∈W j
c
j

1 ≤ k ≤ Ci , j , 1 ≤ c ≤ W j ,

1 ≤ r ≤ Hi
Slide 26 of 48

IP definition – simple tables
m

minimize∑ hir ⋅ yir + g ih
i =1

subject to
n

1)

wcj ⋅ z cj + g w ≤ W
∑
j

4)*

j =1

2)

3)

hi , j ≤
wi , j ≤

i + S ih, j

(hr + g rh )
∑
( wc + g cw )
∑

i , j ,k

= 1, ∀i, j

m

5)

r =i

j + S iwj
,

∑x

yir = 1
∑
i =1
n

6)

z cj = 1
∑
j =1

c= j

* dummy cells (0,0) are inserted for spanned cells

Slide 27 of 48

Table Layout problem is NP-complete
Demonstrated by:
• 1996 Wang - demonstration using large
integers;
• 1999 Anderson and Sobti - using
reductions of the clique problem to the
table layout, on simple tables.


Slide 28 of 48

OPL
OPL – Optimization Programming Language
designed for solving combinatorial optimization
problems.
• support for:
– MIP and constraint programming including search specification;
– logical and higher order constraints;
– support for scheduling and resource allocation applications;

• shares structure and syntax features with mathematical
programming languages such as AMPL or GAMS
• problems can be formulated in a language similar to their
algebraic notation


Slide 29 of 48

OPL Keywords
dvar – decision variable. The purpose of an OPL

model is to find values for the decision variables
such that all constraints are satisfied
dexpr - to express decision variables in a more

compact way
{dataType} - set of type dataType
<x,y> - represents a tuple value;

Slide 30 of 48

TSC Model - Data types
tuple Conf {int w; int h;}
tuple CellConf {int i; int j; Conf c;}
int pageW;
// page width
{CellConf} configs; // set of cell configurations
sample data: configs = {<0,0, <127,10>>, <0,0, <92,20>>,
<0,1, <75,20>>,<0,2, <65,10>>,…,}

{Cell} cells = {<i,j> | <i,j,k> in configs}
{int} rows = {i | <i,j> in cells}
{int} cols = {j | <i,j> in cells}

Slide 31 of 48

TSC model - Additional data
// for each column j, the set of possible widths
{Pair} colWset = {<j, k.w> | <i,j,k> in configs:
Sw[<i,j>==0};
// for each row i, the set of possible heights
{Pair} rowHset = {<i, k.h> | <i,j,k> in configs:
Sh[<i,j>==0};


Slide 32 of 48

TSC model – Decision variables
Decision variables: x,y,z
// cell configuration selector
dvar int x[configs] in 0..1
// row height/colum width selectors
dvar int y[rowHset] in 0..1
dvar int z[colWset] in 0..1
// glue
dvar int Gh[rows] in 0..maxint
dvar int Gw[columns] in 0..maxint


Slide 33 of 48

TSC model – Expressions
// cell width
dexpr int cellW[<i,j> in cells] =
sum(<i,j,k> in configs) x[<i,j,k>] * k.w;
// row height
dexpr int rowH[i in rows] =
sum(<i,h> in rowHset) y[<i,h>] * h;
// column width
dexpr int colW[j in cols] =
sum(<j,w> in colWset) z[<j,w>] * w;
// table height/width
dexpr int tableH = sum(i in rows) rowH[i];
dexpr int tableW = sum(j in cols) colW[j];


Slide 34 of 48

TSC Model - Constraints
minimize tableH;
constraints
{
ct1:
tableW <= pageW;
ct4: // select only one cell configuration
forall(i in rows,j in cols)
sum(<i,j,k> in configs) x[<i,j,k>] == 1;
ct4-1: // select only one row height
forall(i in rows)
sum(<i,k> in rowHset) y[<i,k>] == 1;
ct4-2: // select only one column width
forall(j in cols)
sum(<j,k> in colWset) z[<j,k>] == 1;

}


Slide 35 of 48

TSC Model - Constraints
constraints{
…
ct3: // select correct value for cell height
forall(i in rows,j in cols)
if (Sh[<i,j>] > 0)
cellH[<i,j>] <= sum(row in i..i+Sh[<i,j>])
(rowH[row] + Gh[row]);
else
cellH[<i,j>] <= rowH[i];
…
} //select only one cell configuration


Slide 36 of 48

TSC Model – Glue distribution
dexpr int glueW[<i,j,s> in colSpan] =
cellW[<i,j>] − sum(col in j..j+s) colW[col] ;
constraints{
…
glueW is equally distributed
to all s columns spanned by cell i, j.
forall(<i,j,s> in colSpan)
forall(col in j . . j+s )
Gw[col] <= glueW[<i,j,s>] / (s+1);
…
}


Slide 37 of 48

TSC Model - Experimental results

Running time for a 30x30 table
and up to 6 words per cell.


Slide 38 of 48


Slide 39 of 48

Sample output


Slide 40 of 48

Sample output – Nested tables


Slide 41 of 48

Sample output – Large Table


Slide 42 of 48

Conclusions
•

Building table tools is hard because tables can
contain any type of objects: text, images,
mathematical expressions and even other tables;

•

Operations at the table structure level are hard and
prone to errors. WYSIWYG tools are concerned
with presentation only;

•

Using a flexible presentation model such as the
hierarchical model with box elements raises a
number of problems which need to be addressed;


Slide 43 of 48

Conclusions
•

The TSC model is faster than our previous models:
we now report on larger tables 3600 cells (60x60);

•

Computing text configurations (the paragraphing
problem) is critical for this model

•

We can constrain “the glue” for tables with
spanning cells;

•

We have suggested a possible (simplified)
approach for solving the layout with nested tables;


Slide 44 of 48

Future work
To develop a model for tables with
• nested tables;
• other user constraints, i.e. constraints on group of
rows/columns;


Slide 45 of 48

Acknowledgements

We would like to express our gratitude to
Prof. David Parnas
for motivating much of this work


Slide 46 of 48

Acknowledgements

We would like to thank
Kim Marriott and Graeme Gange
for their valuable feedback


Slide 47 of 48


Questions ?

www.tabularlayout.org


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