FPT CHALLENGE

The first FPT implementation challenge PACE: Parameterized Algorithms and Computational Experiments Challenge is respectfully dedicated to David Johnson, creator of the DIMACS algorithms challenges and a leader and advocate for algorithms and theoretical computer science.

Website https://pacechallenge.wordpress.com for details.

ENTER YOUR TEAM NOW.

Track A: Tree Decompositions: optimal solutions, heuristics, generating hard instances, and collecting real-world instances. The tree decomposition validator is available at

https://github.com/holgerdell/td-validate/ Track B: Feedback Vertex Set: fixed-parameter algorithms. IMPORTANT DATES * Benchmark instances available NOW. * 1 June 2016: Register participation. Track A for TreeWidth send email to Holger Dell at

pace16@holgerdell.com and for Track B Feedback Vertex Set send email to Christian.Komusiewicz@uni-jena.de * 1 August 2016: DEADLINE TO SUBMIT Implementations * 22–26 August 2016: Results announced at the International Symposium on Parameterized and Exact Computation (IPEC 2016).

A Kid Krypto System based on DIRECTED CYCLE COVER

Frances Rosamond Department of Informatics

University of Bergen, Norway

Scottish Combinatorics Meeting 26—27 April 2016

•  Perfect Code Kid Crypto Computer Science Unplugged

www.csunplugged.org

•  Directed Disjoint-Cycle Packing Crypto

•  Polly Cracker

•  Creative Mathematical Sciences Communication www.tcs.uni-luebeck.de/cmsc/ 4—7 October Rudiger Reischuk

Neal Koblitz, University of Washington An inventor of elliptic curve cryptography Cryptography as a Teaching Tool. https://www.math.washington.edu/~koblitz/

Neal and Ann Hibner Koblitz, author of A Convergence of Lives. Sofia Kovalevskaia: Scientist, Writer, Revolutionary.

Founders of the Kovalevskaia Prize

Michael Fellows, Univ Bergen

Parameterized Complexity

This is MEGA-Mathematics http://www.c3.lanl.gov/ captors/mega-math, (Los Alamos Natl Labs) 1992, with Nancy Casey.

Neal and Mike created a kid crypto system based on a special kind of dominating set in a graph called a Perfect Code. Def: A set of vertices V’ ⊆ V in a graph G = (V, E) is said to be a perfect code if for every vertex u ∈ V the neighborhood N[u] contains exactly one vertex of V’ . Perfect Code is an NP-hard problem.

Computer Science Unplugged!

•  http://csunplugged.com/ book, teacher guides and support

•  http://video.google.com videos

COMPUTER SCIENCE Unplugged! Michael Fellows Michael.Fellows@cdu.edu.au Frances Rosamond Frances.Rosamond@cdu.edu.au Charles Darwin University, Parameterized Complexity Research Unit, Faculty of Engineering and IT, Northern Territory, 0909 Australia REFERENCES:  More  information  and  buy  the  book:  “Computer  Science  Unplugged!”  by Tim Bell, Michael Fellows and Ian Witten, available at http://www.csunplugged.org and http://www.cosc.canterbury.ac.nz/tim.belltour2006. THEMES of the DEMONSTRATIONS: ALGORITHMS and COMPLEXITY THEME ACTIVITIES CONNECTIONS

1) P vs NP How difficult is it to solve a problem? A million-dollar prize Unsolved problems

2-coloring versus 3-coloring

Concept  of  an  “algorithm”   Time complexity table Number sense Modeling Computational thinking Concept of  “minimum”  

2) Examples of polynomial time sorting and bad sorting (parallel is good, logn).

Sorting Networks

Parallel versus serial Permutations Combinatorial objects Universal quantification Factorial Cooperative learning

3) More P vs NP

Muddy City (Minimum Spanning Tree) versus Ice Cream Stands (Steiner)

Arithmetic in action Weighted paths “Greedy”  method   Careful checking Scale and layout

4) Public Key Cryptography

Kid Krypto Coin Flip over the Phone

Perfect codes One-way functions Linear algebra Public key/private key Proofs

Color the graph with as few colors as possible. Two vertices connected by an edge must get different colors.

3-coloring

Minimum Weight Spanning Tree

6

Discrete Steiner

Tourist Town village map

Place ice cream stands so that no matter which corner you might be standing on, you need walk at most one block to get an ice-cream.

How do we know we can do it with six? Do you want to create a graph where you know the solution but it will be really hard for mom or dad to solve? The idea of a one-way function.

Create a graph with a Perfect Code. Take care that no two stars share a common vertex. Add extra edges to confuse the Adversary. Add additional disguising edges only between vertices not in the dominating set.

Create a graph with a Perfect Code Add extra edges to confuse the Adversary A Perfect Code may not be unique.

Create a graph with a Perfect Code Add extra edges to confuse the Adversary The Perfect Code is not unique.

Public-Key Cryptography (Asymmetric encryption)

Three players Alice – publishes her public key in “phonebook”, a

trusted, neutral source. She has a private key to decode messages sent to her using her public key.

Bob – has an “encryption method” for using

Alice’s public key to send her a message. Adversary – tries to crack their communication

system, knowing how it works (in general).

Alice wants to be able to receive an encrypted bit from Bob. She constructs a graph G(V, E) with a perfect code. The public key is the graph G. Alice’s private key is the perfect code.

3

5 -5

4 6

-4 2 The Encryption Method

(2 steps) Privately and secretly

Step 1. Bob puts numbers on vertices that sum to the Message. The Message is 11.

Step 2.

3 10

5 -5

4

6 8

-4 2 7 The Encryption Method

(2 steps) Privately and secretly

Step 1. Bob puts numbers on vertices that sum to the Message. The Message is 11.

Step 2. Sum the solid neighborhood of each vertex (the numbers in red).

3 10

5 3 -5 4

4 1

6 8

-4 8 2 7 The Encryption Method

(2 steps) Privately and secretly

Step 1. Bob puts numbers on vertices that sum to the Message. The Message is 11.

Step 2. Sum the solid neighborhood of each vertex (the numbers in red).

Bob erases all traces of his calculations. Bob returns the graph to Alice annotated only with the red numbers.

10

3 4

1 8

8 7

To decipher the message, Alice takes the sum over the perfect code. 10

3 4

1 8

8 7

To decipher the message, Alice takes the sum over the perfect code. 10

3 4

1 8

8 7

Sharing secrets is very exciting for kids. Research in cryptography has been awarded the Turing Award three times. Whitfield Diffie and Martin Hellman were awarded the Turing Award in 2015. The 2012 Turing Award was awarded to Shafi Goldwasser and Silvio Micali. Ron Rivest, Adi Shamir and Leonard Adleman won the 2002 Turing Award.

New kid crypto system based on directed cycles Directed Disjoint Cycle Cover problem asks, for input a digraph D = {V, A} whether there exists a family F = {C1, ..., Cm} vertex-disjoint directed cycles that “spans D”, that is, for every v in V there is a unique directed cycle of F that passes through V. Directed Disjoint Cycle Cover is an NP-hard problem.

Disjoint directed cycles The cycles with disguising arcs.

Encryption: Label the edges (twice the tail minus the head).

The message is 11. Labels the vertices to add to 11.

Both systems are secure up to smart high school students. Gaussian elimination. To decipher the message, Alice takes the sum over the perfect code.

10

3 4

1 8

8 7

Processor for each local sum. Large graph maybe 10,000 vertices. Equations with 10,000 variables. Linear algebra sequential, O(n3). New memory heirarchies.

Graph Coloring Kid Crypto

Mathematics communication is a two-way street

Polly Cracker system

– Elementary school students deserve to experience profound and imaginative mathematical ideas.

– Open unsolved problems are the creative drivers for mathematical activity.

– Mathematics is an “interdisciplinary powerhouse.” – Mathematics popularization is a research area of

basic interest. Fellows, M.: Computer SCIENCE in the elementary schools. (1991)

Lay our best at the feet of the children, including the frontiers of what we know

3rd CREATIVE MATHEMATICAL SCIENCES COMMUNICATION CONFERENCE (CMSC)

The Creative Mathematical Sciences Communication conference (CMSC) explores new ways of popularizing the rich mathematics underlying computer science including outdoor activities, art, dance, drama and all forms of storytelling. Hang out with people who develop creative new ways to explain your research to your colleagues down the hall, in different disciplines, government, your kids, mom.

Date: 4-7 October 2016 Location: Lübeck, Germany Abstracts due: 10 June 2016

Submissions due: 8 July 2016 Early Registration: 15 August 2016

Website http://www.tcs.uni-luebeck.de/cmsc/

Thank you

3rd CREATIVE MATHEMATICAL SCIENCES COMMUNICATION CONFERENCE (CMSC) The Creative Mathematical Sciences Communication conference (CMSC) explores new ways of popularizing the rich mathematics underlying computer science including outdoor activities, art, dance, drama and all forms of storytelling. How do you explain your research to your colleagues down the hall, in different disciplines, government, your kids, mom. Date: 4-7 October 2016 Location: Lübeck, Germany Abstracts due: 10 June 2016 Submissions due: 8 July 2016 Early Registration: 15 August 2016 Website http://www.tcs.uni-luebeck.de/cmsc/ This is the third event in a conference series that explores new ways of helping students to achieve 21st Century competencies in mathematics and computer science. The previous conferences, held in Darwin, Australia, in 2013 and in Chennai, India, in 2014 (Videos from 2014) saw a unique interaction between computer science / mathematics researchers and educators and artists (theatre, dance, graphic arts). The CMSC has several aspects. • Involve and support researchers to share the frontiers of computer science and mathematics with children and the general public. • Research communication is a “two-way street”. Explaining your research can inspire new research questions. For example, Mike Fellows describes how “Kid Crypto” inspired the new research of Polly Cracker crypto systems. • Future directions of Computer Science Unplugged! Discuss with Tim Bell, Mike Fellows and others future directions of this grass-roots movement, which is now translated into 19 languages. • Storyfull, whole-body, kinesthetic math activities. Demonstrate and design new whole body activities that connect math with the inner self and community. Design activities that include cultural understanding and relevance. Demonstrate activities that foster curiosity, enthusiasm and perseverance. • Expand computational thinking across the curriculum, and explore how mathematical thinking strategies nurture 21st Century competencies. • Policy makers in government, business and industry. What are the issues and unanswered questions of executives and policy makers?