OFFICE OF SMALL BUSINESS PROGRAMS Visit Our Small Business Office Web Site at: .
IT’S A SMALL OFFICE… The evolution of office artifacts and the small-world phenomenon BY: JOSH...
-
date post
20-Dec-2015 -
Category
Documents
-
view
218 -
download
2
Transcript of IT’S A SMALL OFFICE… The evolution of office artifacts and the small-world phenomenon BY: JOSH...
IT’S A SMALL OFFICE…
The evolution of office artifacts and the small-world phenomenon
BY: JOSH BYERS & MATT SHIRLEY
References
• Watts, Duncan J. Small Worlds: The Dynamics of Networks
between Order and Randomness. Princeton: Princeton
University Press, 1999.
• Winter 2001 STAPLES Mail-Order Catalog
• www.santafe.edu/sfi/publications/bulletins/bulletinfall99/work…
inprogress/smallworld.html
• www.cs.cornell.edu
• www.cs.colorado.edu
• www.imagix.com
• www.wfs.org
Artifact Systems Reengineering(Background)
• Offers an approach which draws on the characteristics of “artifacts”
or components of legacy systems to develop a new, more evolved
and efficient system
• Artifacts take much of their significance from the social world.
At the same time they mediate our interaction with that world.
• Is there a way to study and make use of this phenomenon?
It’s a Small World…(Background)
• Six Degrees of Separation (The Kevin Bacon Game)
• The Triangle Inequality: states that if three points (a, b and c) are
anywhere in the same space, then they can be connected via the
three sides of a triangle, and the length of those sides must obey
the inequality d(a,c) < d(a,b) + d(b,c).
• Small World “violation”: It is quite possible for person A to
know both person B and C, yet for B and C to be not even remotely
familiar with each other.
• Does this apply to the relationships between artifacts?
It’s a Small World…(Background)
• Terms Identified: – vertex. Vertices are office products.
V(G) – vertex set of G.
E(G) – edge list of G. Edges are points of connectivity on G.
n – order of graph G = number of vertices in set
M – size of G = number of edges in E(G)
k – average degree of graph
(G) – neighborhood of a vertex, all adjacent vertices
– clustering coefficient, vertex adjacency for vertex
L(G) – characteristic path length. Shortest distance between vertices.
It’s a Small World…(Background)
• Graph Restrictions1. Undirected. Edges exert no direction, relationship is symmetrical.
2. Unweighted. Edges do not have a priori strength.
3. Simple. Multiple edges are not allowed between any one or two vertices.
4. Sparse. Maximum size, M = n(n-1)/2. Here, M<<n(n-1)/2.
5. Connected. Any vertex can be reached by another by traversing a path
consisting of a finite number of edges.
• Characteristic path length, L, is the median of the means of the
shortest path length connecting each vertex V(G) to all others.1. Calculate d(,j) j V(G) and find for each . L is median of { }.
“Substitutions”
• Artifacts which perform “complimentary” functions may become
substitutes for artifacts that performed similar functions in the past
• Substitution is inevitable as systems become more integrated
• Substitution is a slow process
• Office Examples:
-- Computer/Printer for typewriter
-- Hand-held computers for organizers
-- E-mail for intra-office memos
Scope
• The artifacts of an office system: Past (1970), Present (2000) and Future (2020)
• Defined types of interaction that office artifacts may share:-- Type A: sharing component(s)-- Type B: sharing basic function(s)-- Type C: exchange of information (physical)-- Type D: exchange of information (remote)-- Type E: exchange of material (physical)-- Type F: exchange of energy (physical)-- Type G: exchange of energy (remote)
Hypothesis
THE SMALL WORLD PHENOMENOM CAN EXPLAIN THE
RELATIONSHIPS BETWEEN VARIOUS OFFICE
ARTIFACTS/SYSTEMS. MORE SPECIFICALLY, THE
SHARING OF FUNCTIONS IN A NETWORK OF OFFICE
ARTIFACTS (IN A GIVEN PERIOD) RELATE TO EACH
OTHER SIMILARLY TO THE SHARING OF
ACQUAINTANCES IN A SOCIAL SYSTEM
Methodology
• Identified office functions to be examined
• Chose various artifacts from three different periods of time that
perform those functions
• Construct adjacency matrix M(G) of (n x n) artifacts for each
period for each type of interaction (Type A, Type B, Type C, etc…)
• Assign binary value of 0 or 1 to describe the Type __ interactions
between artifacts in the matrix
Methodology (cont…)
• Compute the “clustering coefficient” for each type of interaction
in each time period
• Compare these matrices/graphs and coefficients to both the
“caveman-world” graph and the “spatial” graph
• How do they relate? Does it change over time? Does the small
world phenomenon apply?
Assumptions (1 of 7)
• Type A Interactions (Sharing Components)
- either share the same component physically (such as two
machines running off of one battery) or having same
components as another artifact, but with no interaction
between the artifacts themselves
- two pens both have ink but do not share the same ink
Assumptions (2 of 7)
• Type B Interactions (Sharing Basic Functions)
- the same basic function as another artifact at any level of
abstraction
- a ball point pen and a felt tip marker have a type B interaction
Assumptions (3 of 7)
• Type C Interactions (Physical Exchange of Information)
- a physical product of information passes from one artifact
to another
- a printer prints a document and a fax machine sends it out
Assumptions (4 of 7)
• Type D Interactions (Remote Exchange of Information)
- any transmission of data from one artifact to another that
requires no further processing at its destination
- email, or a computer forces information to a fax machine
Assumptions (5 of 7)
• Type E Interactions (Exchange of Material)
- an artifact leaves residue, transfers any material or can be
stored in another artifact
- a pen leaves ink on paper and transfers the ink
Assumptions (6 of 7)
• Type F Interactions (Physical Exchange of Energy)
- if two artifacts can be electrically connected to each other,
including sharing multiple connectors
- a keyboard and a computer motherboard
Assumptions (7 of 7)
• Type G Interactions (Remote Exchange of Energy)
- any exchange of electricity or information between two
artifacts that have no physical contact between each other
- PDAs checking email through a cellular phone connection
Adjacency Matrix (example)
CategoryCopy Paper
Laser Paper
Ink-J et Paper
Multi-Use Paper
Fax Paper
Notebooks
Message Pads
Ink-J et Cartridges
Laser Cartridges
Fax Cartridges
Copier Toner
Printer Ribbons
Typewriter Ribbons
Correction Tape
Correction Film
Correction Fluid
Correction Pens
Ballpoint Pens
Retractable Ballpoint Pens
Rollerball Pens
Mechanical Pencils
Pencil Sharpeners
Markers
Highlighters
Paper Supplies
Cartridges, Toners, Ribbons
Writing Instruments
Past Office Artifacts
• Type A interaction-- M = 41-- k = 0.661 LA-past = 11.64-- = 0.0054 = 0.0090
• Type B interaction-- M = 117-- k = 1.887 LB-past = 7.59-- = 0.0155 = 0.0292
• Type C interaction-- M = 126-- k = 2.032 LC-past = 6.79-- = 0.0167 = 0.0092
Past Office Artifacts
• Type D interaction-- M = 0-- k = 0.000 LD-past =-- = 0.0000 = 0.0000
• Type E interaction-- M = 299-- k = 4.823 LE-past = 3.06-- = 0.0395 = 0.0215
• Type F interaction-- M = 145-- k = 2.339 LF-past = 5.67-- = 0.0192 = 0.0143
Past Office Artifacts
• Type G interaction-- M = 0-- k = 0.000 LF-past =-- = 0.0000 = 0.0000
• Overall-- M = 728-- k = 11.742 Lpast = 1.96-- = 0.0962
Present Office Artifacts
• Type A interaction-- M = 61-- k = 0.726 LA-present = 22.66-- = 0.0044 = 0.0097
• Type B interaction-- M = 190-- k = 2.262 LB-present = 6.28-- = 0.0136 = 0.0247
• Type C interaction-- M = 148-- k = 1.762 LC-present = 9.05-- = 0.0106 = 0.0114
Present Office Artifacts
• Type D interaction-- M = 26-- k = 0.310 LD-present = 4.37-- = 0.0019 = 0.0033
• Type E interaction-- M = 520-- k = 6.191 LE-present = 2.81-- = 0.0373 = 0.0220
• Type F interaction-- M = 222-- k = 2.643 LF-present = 5.27-- = 0.0159 = 0.0131
Present Office Artifacts
• Type G interaction-- M = 43-- k = 0.512 LG-present = 7.65-- = 0.0031 = 0.0039
• Overall-- M = 1210-- k = 14.405 LPresent = 1.92-- = 0.0868
Future Office Artifacts
• Type A interaction-- M = 70-- k = 0.833 LA-future = 28.10-- = 0.0050 = 0.0088
• Type B interaction-- M = 239-- k = 2.845 LB-future = 4.90-- = 0.0171 = 0.0263
• Type C interaction-- M = 125-- k = 1.488 LC-future = 12.89-- = 0.0090 = 0.0079
Future Office Artifacts
• Type D interaction-- M = 34-- k = 0.405 LD-future = 5.67-- = 0.0024 = 0.0041
• Type E interaction-- M = 495-- k = 5.893 LE-future = 2.89-- = 0.0355 = 0.0312
• Type F interaction-- M = 269-- k = 3.202 LF-future = 4.40-- = 0.0193 = 0.0169
Future Office Artifacts
• Type G interaction-- M = 55-- k = 0.655 LG-future = 12.10-- = 0.0039 = 0.0045
• Overall-- M = 1287-- k = 15.321 Lfuture = 1.88-- = 0.0923
Trends
• Past to Present1. M increased for all interactions because n increased from 124 to 168
2. k for each interaction category increased except Type C & E
3. overall decreased (less connected) but L decreased also
• Present to Future1. Remote interactions assumed more critical role in office interactions
2. k trend continues throughout interaction types
3. More connected matrices (increased M, static n) yield higher order
graph with higher and shorter L.
Trends (cont.)
• Interaction between vs. interaction within categories:
-- There is an inverse relationship between the for an
entire interaction and the for that same interaction
-- For example, a higher for the interaction than the
for that same interaction means that the interaction between
categories was lower than the interaction within categories
(Type A and B interations in the past, Type A, B, D and G in
the present and future)
-- Also applies vice versa
Trends: Clustering Coefficients
00.0050.010.0150.020.0250.030.0350.040.045
typeA
typeB
typeC
typeD
typeE
typeF
typeG
PastPresentFuture
Trends: Characteristic Path Length
0
5
10
15
20
25
30
typeA
typeB
typeC
typeD
typeE
typeF
typeG
PastPresentFuture
Caveman Graph
Spatial Graph
• Note: the office world is non-uniform
Relational Graph
• interpolate between ordered and random limits (Caveman vs. Spatial)• the probability of two vertices sharing a common edge depends only upon pre-existing conditions• Relational graphs admit a particular class of graphs (small-world) that share L with equivalent random graphs but with much greater clustering (~ )
Caveman SpatialOur real-world graph
Conclusions*
• Various interactions between office artifacts translate into a relational graph
• Office artifacts interact more as time progresses
• These increases in interaction between office systems yield a
decreased characteristic path length
• The small-world phenomenon more accurately describes the
office world as time progresses*See also “Trends”
Qualitative Comments (1 of 2)
• L, characteristic path length, is only a valid statistic for
sufficiently connected graphs such that:
M > 62 in the past, &
M > 84 in the present and future
• Automate spreadsheet adjacency matrix production and construct
macros to apply binary bridge values of “1” from one workbook
to another
Qualitative Comments (2 of 2)
• Develop a macro to determine
• Construct the relational graph to compare with caveman and spatial graphs
• Develop a method of mediating or minimizing the effect that comes from different numbers of artifacts in each time period
Total and Complete Confusion?
Questions?