I efteråret 2007 og foråret 2008 underviste jeg på ITU-kurset Social Software: Design og implementering.
Se http://mortengade.dk/2009/social-software-et-semesters-undervisning-i-en-post
Se http://social08.pbwiki.com
Oplæg holdt ved MOC's gåhjem-møde om Typo3 NEOS. Jeg blev bedt om at vurdere fremtiden for CMS set fra et kommunikations- og brandingsynspunkt. Min overordnede pointe er, at der er for ensidigt fokus på at få indholdet på nettet - og at fremtiden må være større fokus på at producere bedre indhold.
ITU - Social software: 18 StoresamarbejderMorten Gade
I efteråret 2007 og foråret 2008 underviste jeg på ITU-kurset Social Software: Design og implementering.
Se http://mortengade.dk/2009/social-software-et-semesters-undervisning-i-en-post
Se http://social08.pbwiki.com
Oplæg holdt ved MOC's gåhjem-møde om Typo3 NEOS. Jeg blev bedt om at vurdere fremtiden for CMS set fra et kommunikations- og brandingsynspunkt. Min overordnede pointe er, at der er for ensidigt fokus på at få indholdet på nettet - og at fremtiden må være større fokus på at producere bedre indhold.
ITU - Social software: 18 StoresamarbejderMorten Gade
I efteråret 2007 og foråret 2008 underviste jeg på ITU-kurset Social Software: Design og implementering.
Se http://mortengade.dk/2009/social-software-et-semesters-undervisning-i-en-post
Se http://social08.pbwiki.com
Hvad er en digital forretningsmodel? Hvilke findes der? Hvordan udvikler jeg min virksomheds digitale forretningsmodel? Hvilke metoder kan jeg bruge?
Oplæg for MBA-uddannelsen MMT 21. april 2017.
Digital strategi - DKF kursus - marts 2016Morten Gade
Fokuser den digitale indsats og undgå spredt fægtning. Få sammenhæng mellem analyse, retning og handling. Skab dynamik på tværs af funktioner, hensyn og behov. Undgå de værste faldgruber, træf de rigtige beslutninger og skab de bedste resultater - på kort og lang sigt.
Dette kursus giver dig indsigt og overblik, en opdateret værktøjskasse, effektive staldtips, do’s og dont’s og ganske enkelt 1:1 sparring så du kan komme effektivt videre selv.
Kontrapunkt wake up call:
En god strategi er et værktøj, som du bruger til at træffe de bedste beslutninger – på kort og langt sigt. Den hjælper dig til at indfri din organisations potentiale ved at skabe sammenhæng og dynamik.
Medlemsorganisationens muligheder ved digitalt servicedesignMorten Gade
Fra Groupcare konferencen "Den digitale medlemsorganisation"
Morten Gade, partner og head of digital hos Kontrapunkt og tidligere digital chef i FDB/COOP, vil på baggrund af sine mange år som rådgiver og digital chef fortælle om, hvordan man med digitalt servicedesign får organisationens forskellige touch points og processer til at hænge sammen, når man som medlemsorganisation har et langsigtet syn på sine kunder/medlemmer.
Lav en digital strategi, der giver resultaterMorten Gade
En digital strategi er ikke bare en strategi for digital kommunikation og markedsføring, ligesom det heller ikke bare er en it-strategi. Den digitale strategi bryder på alle mulige måder ind i menneskers hverdag og arbejdsrutiner.
Oplæg holdt i regi af Kommunikationsforum
September 2015
Morten Gade / Kontrapunkt
Presentation for T3con, the 10th international Typo3 conference on how we need to develop content management systems from being all about publishing and management - to being tools for unleashing creativity.
There's a write up of the talk here: https://medium.com/@mortengade/we-need-a-content-facilitation-system-da7c2420993d
Business Models:
- Runthrough of Osterwalder and Pigneurs "Business Model Canvas"
- 40 examples of online business models
Lecture at ITU class "Concept Development with Industry", February 15.
Videoerne er desværre ikke med i præsentationen på Slideshare. Når der kommer et link til 23's videooptagelser af Videoday supplerer jeg med et link her.
I efteråret 2007 og foråret 2008 underviste jeg på ITU-kurset Social Software: Design og implementering.
Se http://mortengade.dk/2009/social-software-et-semesters-undervisning-i-en-post
Se http://social08.pbwiki.com
ITU - Social software: 20 DemokratiseringMorten Gade
I efteråret 2007 og foråret 2008 underviste jeg på ITU-kurset Social Software: Design og implementering.
Se http://mortengade.dk/2009/social-software-et-semesters-undervisning-i-en-post
Se http://social08.pbwiki.com
I efteråret 2007 og foråret 2008 underviste jeg på ITU-kurset Social Software: Design og implementering.
Se http://mortengade.dk/2009/social-software-et-semesters-undervisning-i-en-post
Se http://social08.pbwiki.com
Search and Society: Reimagining Information Access for Radical FuturesBhaskar Mitra
The field of Information retrieval (IR) is currently undergoing a transformative shift, at least partly due to the emerging applications of generative AI to information access. In this talk, we will deliberate on the sociotechnical implications of generative AI for information access. We will argue that there is both a critical necessity and an exciting opportunity for the IR community to re-center our research agendas on societal needs while dismantling the artificial separation between the work on fairness, accountability, transparency, and ethics in IR and the rest of IR research. Instead of adopting a reactionary strategy of trying to mitigate potential social harms from emerging technologies, the community should aim to proactively set the research agenda for the kinds of systems we should build inspired by diverse explicitly stated sociotechnical imaginaries. The sociotechnical imaginaries that underpin the design and development of information access technologies needs to be explicitly articulated, and we need to develop theories of change in context of these diverse perspectives. Our guiding future imaginaries must be informed by other academic fields, such as democratic theory and critical theory, and should be co-developed with social science scholars, legal scholars, civil rights and social justice activists, and artists, among others.
Neuro-symbolic is not enough, we need neuro-*semantic*Frank van Harmelen
Neuro-symbolic (NeSy) AI is on the rise. However, simply machine learning on just any symbolic structure is not sufficient to really harvest the gains of NeSy. These will only be gained when the symbolic structures have an actual semantics. I give an operational definition of semantics as “predictable inference”.
All of this illustrated with link prediction over knowledge graphs, but the argument is general.
Hvad er en digital forretningsmodel? Hvilke findes der? Hvordan udvikler jeg min virksomheds digitale forretningsmodel? Hvilke metoder kan jeg bruge?
Oplæg for MBA-uddannelsen MMT 21. april 2017.
Digital strategi - DKF kursus - marts 2016Morten Gade
Fokuser den digitale indsats og undgå spredt fægtning. Få sammenhæng mellem analyse, retning og handling. Skab dynamik på tværs af funktioner, hensyn og behov. Undgå de værste faldgruber, træf de rigtige beslutninger og skab de bedste resultater - på kort og lang sigt.
Dette kursus giver dig indsigt og overblik, en opdateret værktøjskasse, effektive staldtips, do’s og dont’s og ganske enkelt 1:1 sparring så du kan komme effektivt videre selv.
Kontrapunkt wake up call:
En god strategi er et værktøj, som du bruger til at træffe de bedste beslutninger – på kort og langt sigt. Den hjælper dig til at indfri din organisations potentiale ved at skabe sammenhæng og dynamik.
Medlemsorganisationens muligheder ved digitalt servicedesignMorten Gade
Fra Groupcare konferencen "Den digitale medlemsorganisation"
Morten Gade, partner og head of digital hos Kontrapunkt og tidligere digital chef i FDB/COOP, vil på baggrund af sine mange år som rådgiver og digital chef fortælle om, hvordan man med digitalt servicedesign får organisationens forskellige touch points og processer til at hænge sammen, når man som medlemsorganisation har et langsigtet syn på sine kunder/medlemmer.
Lav en digital strategi, der giver resultaterMorten Gade
En digital strategi er ikke bare en strategi for digital kommunikation og markedsføring, ligesom det heller ikke bare er en it-strategi. Den digitale strategi bryder på alle mulige måder ind i menneskers hverdag og arbejdsrutiner.
Oplæg holdt i regi af Kommunikationsforum
September 2015
Morten Gade / Kontrapunkt
Presentation for T3con, the 10th international Typo3 conference on how we need to develop content management systems from being all about publishing and management - to being tools for unleashing creativity.
There's a write up of the talk here: https://medium.com/@mortengade/we-need-a-content-facilitation-system-da7c2420993d
Business Models:
- Runthrough of Osterwalder and Pigneurs "Business Model Canvas"
- 40 examples of online business models
Lecture at ITU class "Concept Development with Industry", February 15.
Videoerne er desværre ikke med i præsentationen på Slideshare. Når der kommer et link til 23's videooptagelser af Videoday supplerer jeg med et link her.
I efteråret 2007 og foråret 2008 underviste jeg på ITU-kurset Social Software: Design og implementering.
Se http://mortengade.dk/2009/social-software-et-semesters-undervisning-i-en-post
Se http://social08.pbwiki.com
ITU - Social software: 20 DemokratiseringMorten Gade
I efteråret 2007 og foråret 2008 underviste jeg på ITU-kurset Social Software: Design og implementering.
Se http://mortengade.dk/2009/social-software-et-semesters-undervisning-i-en-post
Se http://social08.pbwiki.com
I efteråret 2007 og foråret 2008 underviste jeg på ITU-kurset Social Software: Design og implementering.
Se http://mortengade.dk/2009/social-software-et-semesters-undervisning-i-en-post
Se http://social08.pbwiki.com
Search and Society: Reimagining Information Access for Radical FuturesBhaskar Mitra
The field of Information retrieval (IR) is currently undergoing a transformative shift, at least partly due to the emerging applications of generative AI to information access. In this talk, we will deliberate on the sociotechnical implications of generative AI for information access. We will argue that there is both a critical necessity and an exciting opportunity for the IR community to re-center our research agendas on societal needs while dismantling the artificial separation between the work on fairness, accountability, transparency, and ethics in IR and the rest of IR research. Instead of adopting a reactionary strategy of trying to mitigate potential social harms from emerging technologies, the community should aim to proactively set the research agenda for the kinds of systems we should build inspired by diverse explicitly stated sociotechnical imaginaries. The sociotechnical imaginaries that underpin the design and development of information access technologies needs to be explicitly articulated, and we need to develop theories of change in context of these diverse perspectives. Our guiding future imaginaries must be informed by other academic fields, such as democratic theory and critical theory, and should be co-developed with social science scholars, legal scholars, civil rights and social justice activists, and artists, among others.
Neuro-symbolic is not enough, we need neuro-*semantic*Frank van Harmelen
Neuro-symbolic (NeSy) AI is on the rise. However, simply machine learning on just any symbolic structure is not sufficient to really harvest the gains of NeSy. These will only be gained when the symbolic structures have an actual semantics. I give an operational definition of semantics as “predictable inference”.
All of this illustrated with link prediction over knowledge graphs, but the argument is general.
Connector Corner: Automate dynamic content and events by pushing a buttonDianaGray10
Here is something new! In our next Connector Corner webinar, we will demonstrate how you can use a single workflow to:
Create a campaign using Mailchimp with merge tags/fields
Send an interactive Slack channel message (using buttons)
Have the message received by managers and peers along with a test email for review
But there’s more:
In a second workflow supporting the same use case, you’ll see:
Your campaign sent to target colleagues for approval
If the “Approve” button is clicked, a Jira/Zendesk ticket is created for the marketing design team
But—if the “Reject” button is pushed, colleagues will be alerted via Slack message
Join us to learn more about this new, human-in-the-loop capability, brought to you by Integration Service connectors.
And...
Speakers:
Akshay Agnihotri, Product Manager
Charlie Greenberg, Host
Kubernetes & AI - Beauty and the Beast !?! @KCD Istanbul 2024Tobias Schneck
As AI technology is pushing into IT I was wondering myself, as an “infrastructure container kubernetes guy”, how get this fancy AI technology get managed from an infrastructure operational view? Is it possible to apply our lovely cloud native principals as well? What benefit’s both technologies could bring to each other?
Let me take this questions and provide you a short journey through existing deployment models and use cases for AI software. On practical examples, we discuss what cloud/on-premise strategy we may need for applying it to our own infrastructure to get it to work from an enterprise perspective. I want to give an overview about infrastructure requirements and technologies, what could be beneficial or limiting your AI use cases in an enterprise environment. An interactive Demo will give you some insides, what approaches I got already working for real.
Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...Jeffrey Haguewood
Sidekick Solutions uses Bonterra Impact Management (fka Social Solutions Apricot) and automation solutions to integrate data for business workflows.
We believe integration and automation are essential to user experience and the promise of efficient work through technology. Automation is the critical ingredient to realizing that full vision. We develop integration products and services for Bonterra Case Management software to support the deployment of automations for a variety of use cases.
This video focuses on the notifications, alerts, and approval requests using Slack for Bonterra Impact Management. The solutions covered in this webinar can also be deployed for Microsoft Teams.
Interested in deploying notification automations for Bonterra Impact Management? Contact us at sales@sidekicksolutionsllc.com to discuss next steps.
JMeter webinar - integration with InfluxDB and GrafanaRTTS
Watch this recorded webinar about real-time monitoring of application performance. See how to integrate Apache JMeter, the open-source leader in performance testing, with InfluxDB, the open-source time-series database, and Grafana, the open-source analytics and visualization application.
In this webinar, we will review the benefits of leveraging InfluxDB and Grafana when executing load tests and demonstrate how these tools are used to visualize performance metrics.
Length: 30 minutes
Session Overview
-------------------------------------------
During this webinar, we will cover the following topics while demonstrating the integrations of JMeter, InfluxDB and Grafana:
- What out-of-the-box solutions are available for real-time monitoring JMeter tests?
- What are the benefits of integrating InfluxDB and Grafana into the load testing stack?
- Which features are provided by Grafana?
- Demonstration of InfluxDB and Grafana using a practice web application
To view the webinar recording, go to:
https://www.rttsweb.com/jmeter-integration-webinar
UiPath Test Automation using UiPath Test Suite series, part 3DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 3. In this session, we will cover desktop automation along with UI automation.
Topics covered:
UI automation Introduction,
UI automation Sample
Desktop automation flow
Pradeep Chinnala, Senior Consultant Automation Developer @WonderBotz and UiPath MVP
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
Software Delivery At the Speed of AI: Inflectra Invests In AI-Powered QualityInflectra
In this insightful webinar, Inflectra explores how artificial intelligence (AI) is transforming software development and testing. Discover how AI-powered tools are revolutionizing every stage of the software development lifecycle (SDLC), from design and prototyping to testing, deployment, and monitoring.
Learn about:
• The Future of Testing: How AI is shifting testing towards verification, analysis, and higher-level skills, while reducing repetitive tasks.
• Test Automation: How AI-powered test case generation, optimization, and self-healing tests are making testing more efficient and effective.
• Visual Testing: Explore the emerging capabilities of AI in visual testing and how it's set to revolutionize UI verification.
• Inflectra's AI Solutions: See demonstrations of Inflectra's cutting-edge AI tools like the ChatGPT plugin and Azure Open AI platform, designed to streamline your testing process.
Whether you're a developer, tester, or QA professional, this webinar will give you valuable insights into how AI is shaping the future of software delivery.
Epistemic Interaction - tuning interfaces to provide information for AI supportAlan Dix
Paper presented at SYNERGY workshop at AVI 2024, Genoa, Italy. 3rd June 2024
https://alandix.com/academic/papers/synergy2024-epistemic/
As machine learning integrates deeper into human-computer interactions, the concept of epistemic interaction emerges, aiming to refine these interactions to enhance system adaptability. This approach encourages minor, intentional adjustments in user behaviour to enrich the data available for system learning. This paper introduces epistemic interaction within the context of human-system communication, illustrating how deliberate interaction design can improve system understanding and adaptation. Through concrete examples, we demonstrate the potential of epistemic interaction to significantly advance human-computer interaction by leveraging intuitive human communication strategies to inform system design and functionality, offering a novel pathway for enriching user-system engagements.
PHP Frameworks: I want to break free (IPC Berlin 2024)Ralf Eggert
In this presentation, we examine the challenges and limitations of relying too heavily on PHP frameworks in web development. We discuss the history of PHP and its frameworks to understand how this dependence has evolved. The focus will be on providing concrete tips and strategies to reduce reliance on these frameworks, based on real-world examples and practical considerations. The goal is to equip developers with the skills and knowledge to create more flexible and future-proof web applications. We'll explore the importance of maintaining autonomy in a rapidly changing tech landscape and how to make informed decisions in PHP development.
This talk is aimed at encouraging a more independent approach to using PHP frameworks, moving towards a more flexible and future-proof approach to PHP development.
"Impact of front-end architecture on development cost", Viktor TurskyiFwdays
I have heard many times that architecture is not important for the front-end. Also, many times I have seen how developers implement features on the front-end just following the standard rules for a framework and think that this is enough to successfully launch the project, and then the project fails. How to prevent this and what approach to choose? I have launched dozens of complex projects and during the talk we will analyze which approaches have worked for me and which have not.
GraphRAG is All You need? LLM & Knowledge GraphGuy Korland
Guy Korland, CEO and Co-founder of FalkorDB, will review two articles on the integration of language models with knowledge graphs.
1. Unifying Large Language Models and Knowledge Graphs: A Roadmap.
https://arxiv.org/abs/2306.08302
2. Microsoft Research's GraphRAG paper and a review paper on various uses of knowledge graphs:
https://www.microsoft.com/en-us/research/blog/graphrag-unlocking-llm-discovery-on-narrative-private-data/
1. Sanders: Flows 1 Sanders: Flows
Ford Fulkerson Algorithm INFORMATIK A Bad Example for Ford Fulkerson INFORMATIK
Ô
[U. Zwick, TCS 148, p. 165–170, 1995]
½. a
Function FFMaxFlow( ´Î µ × Ø Ô: Ê) : Ê Let Ö
¾ 4 r 4
:= ¼ Consider the graph b
while path Ô ´× µ
Ø in do s 4 1 4 t
c
augment along Ô And the augmenting paths
4 1 4
return Ô¼ × Ø
d
time Ç´ÑÚ Ð ´ µµ Ô½ × Ø
Ô¾ × Ø
Ô¿ × Ø
The sequence of augmenting paths Ô¼ Ô½ Ô¾ Ô½ Ô¿ ´ µ£ is an infinite
sequence of positive flow augmentations.
The flow value does not converge to the maximum value .
Sanders: Flows 3 Sanders: Flows
Blocking Flows INFORMATIK Dinitz Algorithm INFORMATIK
is a blocking flow in À if Function DinitzMaxFlow( ´Î µ × Ø Ô: Ê) : Ê
paths Ô × Ø ¾Ô ´µ Ô´ µ := ¼
while path Ô ´×
µ do Ø in
1/1 1/0 Ö Ú Ö× Ë ´Øµ : Î Æ
s t
Ä ´Î ´Ù Úµ ¾ ´Úµ ´Ùµ ½ µ // layer graph
1/1
find a blocking flow in Ä
1/0 1/1 augment +=
return
2. Sanders: Flows 5 Sanders: Flows
Function blockingFlow(À ´Î µ) : Ê INFORMATIK Blocking Flows Analysis 1 INFORMATIK
Ô × : Path
¾ running time is ÜØ Ò × · Ö ØÖ Ø× · Ò ¡ Ö Ø ÖÓÙ ×
Ú NodeRef : Ô last ´µ
:= ¼ ¾ Ö Ø ÖÓÙ × Ñ, since at least one edge is saturated
loop // Round ¾ Ö ØÖ Ø× Ñ, since one edge is removed
if Ú Ø then // breakthrough
¾ ÜØ Ò × Ö ØÖ Ø× · Ò ¡ Ö Ø ÖÓÙ ×, since a retreat cancels
Æ := ÑÒ Ô´ µ ´ µ ¾Ô one extend and a breakthrough cancels Ò extends
foreach ¾ Ô do
´ µ+=Æ ´ · Òѵ
time is Ç Ñ ´ µ
Ç ÒÑ
if ´ µ Ô´ µ then remove from
Ô:= ×
elsif ´Ú Ûµ ¾ then Ô.pushBack Û ´ µ // extend
elsif Ú × then return // done
else delete the last edge from Ô in Ô and // retreat
Sanders: Flows 7 Sanders: Flows
Blocking Flows Analysis 2 INFORMATIK Blocking Flows Analysis 3 INFORMATIK
Unit capacities: Dynamic trees: breakthrough (!), retreat, extend in time Ç´ÐÓ Òµ
breakthroughs saturates all edges on Ô, i.e., amortized constant cost per
time Ç Ñ´´ · ÒµÐÓ Òµ
edge. Theory alert: In practice, this seems to be slower (few breakthroughs, many
time Ç Ñ ´ · Òµ retreat, extend ops.)
4. Sanders: Flows 13 Sanders: Flows
Preflow-Push Algorithms INFORMATIK Level Function INFORMATIK
Idea: make progress by pushing towards Ø
Preflow : a flow where the flow conservation constraint is relaxed to
excess Ú´ µ ¼. Maintain
Procedure push ´ ´Ú Ûµ Ƶ an approximation ´Úµ of the BFS distance from Ú to Ø in .
assert Æ ¼ invariant ´Øµ ¼
assert residual capacity of Æ invariant ´×µ Ò
assert excess Ú ´µ Æ invariant ´Ú Ûµ ¾ ´Úµ ´Ûµ · ½ // no steep edges
´ µ Æ
excess Ú
if ´ µ ¼ then ´ µ· Æ Edge directions of ´Ú Ûµ
else ´reverse´ µµ Æ steep: ´Û µ ´Úµ ½
downward: ´Û µ ´Úµ
horizontal: ´Û µ ´Úµ
upward: ´Û µ ´Úµ
Sanders: Flows 15 Sanders: Flows
INFORMATIK Lemma 3. INFORMATIK
Procedure genericPreflowPush(G=(V,E), var f)
forall ´× Úµ ¾ do push ´ Ô´ µµ // saturate
active nodes Ú Ü ×× ´Ú µ ¼µ path Ú × ¾
´×µ:= Ò Intuition: what got there can always go back.
´Úµ:= ¼ for all other nodes
while Ú ¾Î Ò × Ø Ü ×× ´Ú µ
¼ do // select active node Proof. Ë Ù ¾Î path Ú Ù ¾ ,Ì Î Ò Ë . Then
if ´Ú Ûµ ¾ ´Ûµ ´Úµ then // select eligible edge
choose some Æ Ñ Ò Ü ×× ´Úµ Ö × Ô ´ µ Ü ×× ´Ùµ ´ µ ´µ
push´ Æ µ // no new steep edges since reverse edge goes upward Ù¾Ë ¾ ´Ì ¢Ë µ ¾ ´Ë ¢Ì µ
else ´Ú µ·· // relabel. Cannot introduce steep edges !
´Ú Ûµ ¾ ¾Ë Û¾Ë
Ú by Def. of ,Ë
Obvious choice for Æ Æ Ñ Ò Ü ×× ´Úµ Ö × Ô ´ µ Thus ´Ù Ûµ ¾ ´Ì ¢ Ë µ ´ µµ ¼ Otherwise Û Ù ´ µ¾
Ö × Ô´ µ
È
Saturating push: Æ Hence, Ü ×× ´Ùµ ¼
Ù¾Ë
Ö × Ô´ µ
nonsaturating push: Æ
One the negative excess of × can outweigh excess Ú ´ µ ¼.
To be filled in: Hence × ¾ Ë.
How to select active nodes and eligible edges?
5. Sanders: Flows 17 Sanders: Flows
Lemma 4. INFORMATIK Partial Correctness INFORMATIK
Ú ¾Î ´Úµ ¾Ò
Lemma 5. When Ò Ö ÈÖ ÓÛÈÙ× terminates is a maximal flow.
Proof. Suppose Ú is lifted to ´Úµ ¾Ò.
By Lemma 3, there is a (simple) path Ô to × in . Proof.
Ô has at most Ò ½ nodes is a flow since Ú ¾Î Ò × Ø Ü ×× ´Ú µ ¼.
´×µ Ò.
Hence ´Úµ ¾Ò. Contradiction. To show that is maximal, it suffices to show that
path Ô × Ø ¾ (Max-Flow Min-Cut Theorem):
Since ´×µ Ò, ´Øµ ¼, Ô would have to contain steep edges.
That would be a contradiction.
Sanders: Flows 19 Sanders: Flows
Lemma 6. # Relabels ¾Ò ¾ INFORMATIK Lemma 7. # saturating pushes ÒÑ INFORMATIK
Proof. ´Úµ ¾Ò, i.e., Ú is relabeled at most ¾Ò time. Proof.
Hence, at most Î ¡ ¾Ò ¾Ò relabels.
¾ We show that there are at most Ò sat. pushes over any edge ´Ú Ûµ.
´ Ƶ removes from
A saturating push .
Only a push on ´Û Ú µ can reinsert into .
For this to happen, Û must be lifted at least two levels.
Hence, at most Ò ¾ ¾ Ò saturating pushes over Ú Û´ µ
6. Sanders: Flows 21 Sanders: Flows
¡
Lemma 8. # nonsaturating pushes Ç Ò¾ Ñ INFORMATIK Searching for Eligible Edges INFORMATIK
if Æ ÑÒ Ü ×× ´Ú µ Ö × Ô´ µ
for arbitrary node and edge selection rules. (arbitrary-preflow-push)
Every node Ú maintains a ÙÖÖ ÒØ pointer to its sequence of outgoing
edges in .
Proof. ¨ ´Úµ. (Potential)
¨ ¼ initially
Ú Ú is active
invariant no edge ´Ú Ûµ to the left of ÙÖÖ ÒØ is eligible
relabel increases ¨ by one. ( ¾Ò ¢)
¾
Reset ÙÖÖ ÒØ at a relabel ( ¾Ò¢)
saturating push increases ¨ by at most ¾Ò ( ÒÑ ) ¢ Invariant cannot be violated by a push over a reverse edge ¼ ´Û Úµ since
µ total increase at most ¾Ò · ¾Ò Ñ ¾ ¾
this only happens when ¼ is downward,
nonsaturating push decreases ¨ by at least one i.e., is upward and hence not eligible.
¨ ¼ always.
Lemma 9.
Total cost for searching ¾Ò ¡ Ö ´Úµ ÒÑ Ç´Òѵ
Ú ¾Î
Sanders: Flows 23 Sanders: Flows
INFORMATIK Highest Level Preflow Push INFORMATIK
¡
Ç Ò¾ Ñ .
Theorem 10. Arbitrary Preflow Push finds a maximum flow in time
Always select active nodes that maximize ´Úµ
Proof. Use bucket priority queue (insert, increaseKey, deleteMax)
Lemma 5: partial correcntess not monotone (!) but relabels “pay” for scan operations
Initialization in time Ç´Ò · ѵ. ÔÑ nonsaturating pushes.
Maintain set (e.g., stack, FIFO) of active nodes. Lemma 11. At most Ò¾
Use reverse edge pointers to implement push.
¾
Lemma 6: Ò¾ relabels
Proof. later
Lemma 7: ÒÑ saturating pushes
Ç Ò ÔÑ
Theorem 12. Highest Level Preflow Push finds a maximum flow in time
¡ ¡
Lemma 8: Ç ¾
Ò Ñ nonsaturating pushes ¾
Lemma 9: Ç ´Òѵ search time for eligible edges
———————————————————————–
¡
Total time Ç Ò¾ Ñ
7. Sanders: Flows 25 Sanders: Flows
Proof of Lemma 11 INFORMATIK Claims: INFORMATIK
Ã
ÔÑ tuning parameter 1. Ò¾ Ã nonsaturating pushes in all cheap phases together
¼ ´Ú µ Û ´Ûµ ´Úµ scaled number of dominated nodes 2. ¨ ¼ always, ¨ Ò¾ Ã initially (obvious)
Ã
¨ ´µ
¼Ú. (Potential) ¨ by at most Ò Ã .
3. a relabel or saturating push increases
Ú Ú is active
£ Ñ Ü ´Úµ Ú is active (highest level) 4. a nonsaturating push does not increase ¨.
phase:= all pushes between two consecutive changes of £ 5. an expensive phase with É Ã nonsaturating pushes decreases ¨ by
expensive phase: more than à pushes at least É.
cheap phase: otherwise
· · · · µ total decrease ´¾Ò · Òѵ à · Ò¾
Lemma 6 Lemma 7 2. 3. 4.: Ò
Ã
¾
· ´¾Ò · Ò · ÑÒ µ Ã nonsat. pushes in expensive phases
¿ ¾ ¾
´¾Ò · Ò · ÑÒ µ Ã · Ò Ã Ç Ò ÔÑ¡
This
This ·½ ¿ ¾ ¾ ¾ ¾
ÔÑ
nonsaturating pushes overall for
Ã
Sanders: Flows 27 Sanders: Flows
¾ INFORMATIK INFORMATIK
Claim 1: Ò Ã nonsat. pushes in cheap phases
Claim 3: A relabel or saturating push increases ¨ by at most Ò Ã
¾
We first show that there are at most Ò phases
£ Ñ Ü Ú Ú is active Let Ú denote the relabeled or activated node.
´Ûµ ´Úµ
(changes of ).
£ ¼ initially, £ ¼ always. ¼ ´Ú µ Û Ò
£ , i.e., Ã Ã
A relabel of Ú can increas only the ¼ -value of Ú .
Only relabels increase
¾Ò ¾
increases by Lemma 6 and hence
A saturating push on ´Ù Û µ only changes the ¼ -value of Û .
¾Ò ¾
decreases
——————————————————
Ò¾ changes overall
Claim 4: a nonsaturating push across ´Ú Û µ does not increase ¨
By Definition of a cheap phase, it has at most à pushes.
Ú is deactivated
Û may be activated
but ¼ ´Ûµ ¼ ´Ú µ
8. Sanders: Flows 29 Sanders: Flows
Claim 5: an expensive phase INFORMATIK Heuristic Improvements INFORMATIK
¨ by at least
ª Ò ¡. Why?
with É Ã nonsaturating pushes decreases É.
¾
Naive algorithm has best case
During a phase £ remains constant We can do better.
£
Each nonsat. push decreases the number of nodes at level aggressive local relabeling: ´Úµ:= ½ · Ñ Ò ´Ûµ ´Ú Ûµ ¾
Hence, Û ´Ûµ £ Ã during an expensive phase (like a sequence of relabels)
Each nonsat. push across Ú Û decreases´ µ ¨ by
¼ ´Ú µ ¼ ´Ûµ Û ´Ûµ £ à à à ½ global relabeling: (initially and every Ǵѵ edge inspections):
´Úµ Ö Ú Ö× Ë ´Øµ for nodes that can reach Ø in .
Special treatment of nodes with ´Úµ Ò. (Returning flow is easy)
Gap Heuristics. Nobody can reach Ø across an empty level:
if Ú ´Úµ then foreach Ú with ´Úµ do ´Úµ:= Ò
Sanders: Flows 31 Sanders: Flows
Timings: Random Graphs INFORMATIK Timings: CG1 INFORMATIK
Gen Rule BASIC HL LRH GRH GAP LEDA Gen Rule BASIC HL LRH GRH GAP LEDA
rand FF 5.84 6.02 4.75 0.07 0.07 — CG1 FF 3.46 3.62 2.87 0.9 1.01 —
33.32 33.88 26.63 0.16 0.17 — 15.44 16.08 12.63 3.64 4.07 —
HL 6.12 6.3 4.97 0.41 0.11 0.07 HL 20.43 20.61 20.51 1.19 1.33 0.8
27.03 27.61 22.22 1.14 0.22 0.16 192.8 191.5 193.7 4.87 5.34 3.28
MF 5.36 5.51 4.57 0.06 0.07 — MF 3.01 3.16 2.3 0.89 1.01 —
26.35 27.16 23.65 0.19 0.16 — 12.22 12.91 9.52 3.65 4.12 —
Ò ¾ ½¼¼¼ ¾¼¼¼ Ñ ¿Ò Ò ¾ ½¼¼¼ ¾¼¼¼ Ñ ¿Ò
FF FIFO node selection, HL hightest level, MF modified FIFO FF FIFO node selection, HL hightest level, MF modified FIFO
HL ´Úµ Ò is special, HL ´Úµ Ò is special,
LRH local relabeling heuristic, LRH local relabeling heuristic,
GRH global relabeling heuristics GRH global relabeling heuristics
9. Sanders: Flows 33 Sanders: Flows
Timings: CG2 INFORMATIK Timings: AMO INFORMATIK
Gen Rule BASIC HL LRH GRH GAP LEDA Gen Rule BASIC HL LRH GRH GAP LEDA
CG2 FF 50.06 47.12 37.58 1.76 1.96 — AMO FF 12.61 13.25 1.17 0.06 0.06 —
239 222.4 177.1 7.18 8 — 55.74 58.31 5.01 0.1399 0.1301 —
HL 42.95 41.5 30.1 0.17 0.14 0.08002 HL 15.14 15.8 1.49 0.13 0.13 0.07001
173.9 167.9 120.5 0.3599 0.28 0.1802 62.15 65.3 6.99 0.26 0.26 0.1399
MF 45.34 42.73 37.6 0.94 1.07 — MF 10.97 11.65 0.04999 0.06 0.06 —
198.2 186.8 165.7 4.11 4.55 — 46.74 49.48 0.1099 0.1301 0.1399 —
Ò ¾ ½¼¼¼ ¾¼¼¼ Ñ ¿Ò Ò ¾ ½¼¼¼ ¾¼¼¼ Ñ ¿Ò
FF FIFO node selection, HL hightest level, MF modified FIFO FF FIFO node selection, HL hightest level, MF modified FIFO
HL ´Úµ Ò is special, HL ´Úµ Ò is special,
LRH local relabeling heuristic, LRH local relabeling heuristic,
GRH global relabeling heuristics GRH global relabeling heuristics
Sanders: Flows 35 Sanders: Flows
Asymptotics, Ò ¾ ¼¼¼ ½¼¼¼¼ ¾¼¼¼¼ INFORMATIK Research Problem INFORMATIK
Gen Rule GRH GAP LEDA
Define a family of flow networks such that highest level preflow push with all
rand FF 0.16 0.41 1.16 0.15 0.42 1.05 — — —
the heuristics is forced into its worst case even if ties are broken randomly.
HL 1.47 4.67 18.81 0.23 0.57 1.38 0.16 0.45 1.09
MF 0.17 0.36 1.06 0.14 0.37 0.92 — — —
CG1 FF 3.6 16.06 69.3 3.62 16.97 71.29 — — —
HL 4.27 20.4 77.5 4.6 20.54 80.99 2.64 12.13 48.52
MF 3.55 15.97 68.45 3.66 16.5 70.23 — — —
CG2 FF 6.8 29.12 125.3 7.04 29.5 127.6 — — —
HL 0.33 0.65 1.36 0.26 0.52 1.05 0.15 0.3 0.63
MF 3.86 15.96 68.42 3.9 16.14 70.07 — — —
AMO FF 0.12 0.22 0.48 0.11 0.24 0.49 — — —
HL 0.25 0.48 0.99 0.24 0.48 0.99 0.12 0.24 0.52
MF 0.11 0.24 0.5 0.11 0.24 0.48 — — —
10. Sanders: Flows 37 Sanders: Flows
Minimum Cost Flows INFORMATIK The Cycle Canceling Algorithm for Min-Cost Flow INFORMATIK
Define ´Î µ, , Ü ×× , and Ô as for maximum flows. Residual cost: Let ´Ú Ûµ ¾ , ¼ ´Û Úµ.
Let Ê denote the edge costs.
È
´ µ ´ ¼µ if ¼ ¾ , ´ ¼µ ¼, ´ µ ´ µ otherwise.
Consider ×ÙÔÔÐÝ Î Ê with ھΠ×ÙÔÔÐÝ Ú ´ µ ¼. A negative supply Lemma 13. A feasible flow is optimal iff cycle ¾ ´ µ ¼
is called a demand.
Objective: minimize ´µ ´µ´µ Proof. not here
¾ A pseudopolynomial Algorithm:
subject to
Ú ¾Î Ü ×× ´Ú µ ×ÙÔÔÐÝ ´Úµ flow conservation constraints := any feasible flow // Exercise: solve this problem using maximum flows
¾ ´µ Ô´ µ capacity constraints invariant is feasible
while cycle ´ µ ¼ do augment flow around
Corollary 14 (Integrality Property:). If all edge capacities are integral then
there exists an integral minimum cost flow.
Sanders: Flows 39 Sanders: Flows
Finding a Feasible Flow INFORMATIK Better Algorithms INFORMATIK
set up a maximum flow network £ starting with the min cost flow problem : Theorem 15. The min-cost flow problem can be solved in time
¾ Add a vertex × Ç ÑÒ ÐÓ Ò · Ñ ÐÓ Ñ Ü ¾
¾
Ô´ µ¡ .
¾ Ú ¾ Î with ×ÙÔÔÐÝ ´Úµ ¼, add edge ´× Úµ with cap. ×ÙÔÔÐÝ ´Úµ For details take the courses in optimization or network flows.
¾ Add a vertex Ø
¾ Ú ¾ Î with ×ÙÔÔÐÝ ´Úµ ¼, add edge ´Ú ص with cap. ×ÙÔÔÐÝ ´Úµ
¾ find a maximum flow in £
saturates the edges leaving × µ is feasible for
otherwise there cannot be a feasible flow ¼ because ¼ could easily be
converted into a flow in £ with larger value.
11. Sanders: Flows 41 Sanders: Flows
Special Cases of Min Cost Flows INFORMATIK Maximum Weight Matching INFORMATIK
Transportation Problem: ¾ Ô´ µ ½ Generalization of maximum cardinality matching. Find a matching Å £
È
Minimum Cost Bipartite Perfect Matching:
such that Û Å £´ µ ¾Å £ Û´ µ is maximized
A transportation problem in a bipartite graph ´ ¢ µ Applications: Graph partitioning, selecting communication partners
with Theorem 16. A maximum weighted matching can be found in time
×ÙÔÔÐÝ ´Ú µ ½ for Ú ¾ , ¡
Ç ÒÑ · Ò ÐÓ
¾
Ò . [Gabow 1992]
×ÙÔÔÐÝ ´Ú µ ½ for Ú ¾ .
An integral flow defines a matching
Approximate Weighted Matching
Reminder: Å ´ µ
is a matching if Î Å has maximum degree one.
Theorem 17. There is an Ǵѵ time algorithm that finds a matching of
weight at leastÑ Ü Å Û´Å µ ¾. [Drake Hougardy 2002]
matching
The algorithm is a ½ ¾-approximation algorithm.
A rule of Thumb: If you have a combinatorial optimization problem. Try to
formulate it as a shortest path, flow, or matching problem. If this fails its likely
to be NP-hard.
Sanders: Flows 43 Sanders: Flows
Approximate Weighted Matching Algorithm INFORMATIK Proof of Approximation Ratio INFORMATIK
Å ¼ :=
invariant Å ¼ is a set of simple paths Let Å £ denote a maximum weight matching.
while do // find heavy simple paths ´ µ
It suffices to show that Û Å ¼ ´ µ
Û Å£ .
select any Ú ¾ Î with degree´Úµ ¼ // select a starting node Assign each edge to that incident node that is deleted first.
while degree Ú ´ µ ¼ do // extend path greedily £ ¾ Å £ are assigned to different nodes.
´Ú Ûµ:= heaviest edge leaving Ú
All
Consider any edge £ ¾ Å £ and assume it is assigned to node Ú .
// (*)
Å ¼ := Å ¼ ´Ú Ûµ Since £ is assigned to Ú , it was available in line (*).
remove Ú from the graph
Hence, there is an edge ¾Å ¼½ assigned to Ú with Û ´µ Û ´ £µ.
Ú := Û
return any matching Å ´ µ
Å ¼ with Û Å ´ µ¾
Û Å¼
// one path at a time, e.g., look at the two ways to take every other edge.