Visualizing Evaluation Structures 
 using Layered Graph Drawings Yosuke Onoue1), Nobuyuki Kukimoto1), Naohisa Sakamoto2), Kazuo Misue3), and Koji Koyamada1) 1) Kyoto University 2) Kobe University 3) University of Tsukuba 

Introduction 

Background • The evaluation grid method (EGM) have been used to support product planning in Japan [Sanui 1996] • EGM is a qualitative research method based on semi-structured interviews • Researchers analyze evaluation structures
 that are results of EGM to understand 
 consumer needs J. Sanui, “Visualization of users’ requirements: Introduction of Evaluation Grid Method,” Proc. 3rd Des. Decis. Support Syst. Archit. Urban Plan. Conf., pp. 365–374, 1996. 

Evaluation Structures • Networks extracted from interviews based on EGM • Evaluation structures are represented as directed acyclic graphs (DAG) The majority of evaluation structure diagrams in the literature are not automatically laid out (user-produced) ➡ We apply Sugiyama framework for automatic layout An evaluation structure for the concept of “comfortable research environment” Q: Why is “comfortable temperature” better for you ? A. Because I can concentrate. $BVTF &⒎FDU 

Sugiyama Framework • Layered graph drawing method for directed graphs [Sugiyama 1981] • 4 steps for Sugiyama framework Manual Layout (by hand) Automatic Layout (Sugiyama framework) Gaps 1. Cycle removal 2. Layer assignment 3. Crossing reduction 4. Position assignment There are gaps between user-produced layout and automatic layout ➡ To resolve the gaps, we develop a novel layer assignment method K. Sugiyama, S. Tagawa, and M. Toda, “Methods for Visual Understanding of Hierarchical System Structures,” IEEE Trans. Syst. Man. Cybern., vol. 11, no. 2, pp. 109–125, 1981. 

Layer Assignment • Layers of each vertex are determined
 in the layer assignment step • Existing layer assignment methods • longest-path method • network-simplex-layering method • ULair
 … P. Healy and N. S. Nikolov, “Hierarchical Drawing Algorithms,” in Handbook of Graph Drawing and Visualization, CRC Press, 2013, pp. 409–454. from [Healy 2013] 

Motivation • Visualization approaches for the evaluation structures are not enough • It takes too much time to produce manual layout • We apply Sugiyama framework to realize the effective analysis of evaluation structures • To resolve the gaps between user-produced layout and automatic layout, we propose a novel layer assignment method for Sugiyama framework 

Proposed Method 

Our Approach Layer assignment problem
 for network-simplex-layering Direct formulation Equivalent transformation Proposed layer assignment problem Add requirements
 for evaluation structures [ PG] : minimize X (u,v)2A wuv( yv yu) subject to yv yu uv, 8 ( u, v ) 2 A, yv 2 Z+, 8v 2 V. [ PQ] : minimize X (u,v)2A wuv( yv yu) 2 subject to yv yu uv, 8 ( u, v ) 2 A, yv = 0 , 8v 2 V0, yv = L, 8v 2 VL, yv 2 Z+, 8v 2 V. [PL] : minimize X (u,v)2A wuv X k2Kuv k 2 xuvk subject to X k2Kuv kxuvk yv + yu = 0, 8 (u, v) 2 A, X k2Kuv xuvk = 1, 8 (u, v) 2 A, yv = 0, 8 v 2 V0, yv = L, 8 v 2 VL, yv 2 Z+ , 8 v 2 V, xuvk 2 { 0, 1 } , 8 (u, v) 2 A, 8 k 2 Kuv. Apply optimization solver 

Layer Assignment Problem • The layer assignment problem that minimizes total edge span is formulated as an integer linear programing (ILP) problem [Gansner 1993] We modify this formulation to add requirements for visualizing evaluation structures [ PG] : minimize X (u,v)2A wuv( yv yu) subject to yv yu uv, 8 ( u, v ) 2 A, yv 2 Z+, 8v 2 V. G] : nimize X (u,v)2A wuv( yv yu) ject to yv yu uv, 8 ( u, v ) 2 A, yv 2 Z+, 8v 2 V. wuv 8(u, v) 2 A uv 8(u, v) 2 A A ✓ V ⇥ V V A set of vertices A set of arcs yv 8v 2 V Layers of vertices to be determined Z+ A set of non-negative integers Weights of arcs Minimum edge spans of arcs 

Requirements for Visualizing Evaluation Structures 1. Alignment constraints for source and sink vertices 1. Source vertices should have the lowest layer
 2. Sink vertices should have the highest layer
 
 2. Balance of arc lengths yv = 0, 8v 2 V0 yv yu, 8v 2 VL, 8u 2 V Arc lengths are not balanced Network-simplex-layering
 with requirement 1 yv = L, 8v 2 VL L The maximum height 

Problem Formulation • We modified original layer assignment problem in two points The layer assignment problem for evaluation structures are 
 formulated as an integer quadratic programming (IQP) problem balance of arc lengths alignment conditions for 
 source and sink vertices [ PQ] : minimize X (u,v)2A wuv( yv yu) 2 subject to yv yu uv, 8 ( u, v ) 2 A, yv = 0 , 8v 2 V0, yv = L, 8v 2 VL, yv 2 Z+, 8v 2 V. ze X (u,v)2A wuv( yv yu) 2 to yv yu uv, 8 ( u, v ) 2 A, yv = 0 , 8v 2 V0, yv = L, 8v 2 VL, yv 2 Z+, 8v 2 V. 

ILP Transformation • IQPs are difficult mathematical optimization problems • We equivalently transform [PQ ] to an ILP ILPs and IQPs can be solved using general mathematical optimization solver [ PQ] : minimize X (u,v)2A wuv( yv yu) 2 subject to yv yu uv, 8 ( u, v ) 2 A, yv = 0 , 8v 2 V0, yv = L, 8v 2 VL, yv 2 Z+, 8v 2 V. ze X (u,v)2A wuv( yv yu) 2 to yv yu uv, 8 ( u, v ) 2 A, yv = 0 , 8v 2 V0, yv = L, 8v 2 VL, yv 2 Z+, 8v 2 V. [PL] : minimize X (u,v)2A wuv X k2Kuv k 2 xuvk subject to X k2Kuv kxuvk yv + yu = 0, 8 (u, v) 2 X k2Kuv xuvk = 1, 8 (u, v) 2 A, yv = 0, 8 v 2 V0, yv = L, 8 v 2 VL, yv 2 Z+ , 8 v 2 V, xuvk 2 { 0, 1 } , 8 (u, v) 2 A, 8 k 2 Kuv [PL] : minimize X (u,v)2A wuv X k2Kuv k 2 xuvk subject to X k2Kuv kxuvk yv + yu = 0, 8 (u, v) 2 A, X k2Kuv xuvk = 1, 8 (u, v) 2 A, yv = 0, 8 v 2 V0, yv = L, 8 v 2 VL, yv 2 Z+ , 8 v 2 V, xuvk 2 { 0, 1 } , 8 (u, v) 2 A, 8 k 2 Kuv. X k2Kuv kxuvk = yv yu Kuv = { uv, · · · , L} X k2Kuv xuvk = 1 xuvk 2 {0 , 1} where 

Evaluation 

Evaluation Criteria • Can the proposed method generate a layout that satisfies the provided aesthetics?
 → This is satisfied because the layer assignment problem is exactly solved • Does the proposed method efficiently generate a layout?
 → Computational experiments • Are the provided aesthetics, such as the arc balance and constraints against the source and sink vertices, appropriate for EGM?
 → Application example and user study 

Computational Time %BUB c7c c"c - $PNQVUBUJPOBM
UJNF
 TFDPOET <12> <1-> "      #      $      %      &      '      (      )      *      +      ,      -      [PL ] < [PQ ] for middle and large scale instances Environment:
 Intel 1.8GHz processor 4GB RAM Linux OS Gurobi Optimizer 5.6 [PQ ] could not be solved for large scale instances 

Drawing Results 

User Study • Method: Scheffeé's pairwise comparison • Participants: 12 EGM users • Objectives: 5 layer assignment methods 

User Feedback • Comparing vertices becomes easy because the source and the sink vertices are placed on the same layer. • The drawing result is visible because blank space is small and the vertices are well balanced. • The number of arc crossings appears to be small. • The interview results are correctly reflected with the proposed method; therefore, a misunderstanding is unlikely to occur. 

Discussion • Computational Time • The layer assignment problem for evaluation structures are efficiently solved by transforming into ILP • User Study • The proposed method is preferable for EGM users → The effectiveness of the proposed method is validated through the evaluation 

Conclusion 

Conclusion & Future Work • We applied Sugiyama framework to visualize evaluation structures • ILP formulation of layer assignment for evaluation structures • Solving the layer assignment problem using optimization solver • Preferable layout for EGM users • Future work • Approximate methods for the layer assignment problem • Evaluation from the viewpoint of user tasks. 

Thank you ! 

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