FUN 2014: Highlights from the 7th International Conference on Fun with Algorithms - PowerPoint Presentation

Slide1

FUN 2014:Highlights from the 7th International Conference on Fun with Algorithms

Michael Brand

July 1-3, 2014Slide2

Some words about funSlide3

Is a semiannual conference

Is a biannual conference

Occurs every two years

Approximately.

Exercise #1: Complete the sequence:1998, 2001, 2004, 2007, 2010, 2012, 2014, ?

Some words about fun(with algorithms)

Not to be confused with the functional analysis conference.Slide4

Is B-ranked (CORE 2013, ERA 2010)Submissions are from all walks of math

e.g., one paper this year was from

Prof.

David

Peleg (dean of Math&CS at the Weizmann Institute of Science).

Is traditionally hosted in Italy1998: Isola d'Elba

2001: Isola d'Elba2004: Isola

d'Elba2007: Castiglioncello (Livorno), Tuscany2010: Ischia (Napoli)

2012: San Servolo Island, Venice2014: Lipari Island, SicilyThey don't insist on continuing with Italy, but they do insist on holding it someplace fun.Some words about fun

(with algorithms)Slide5

1. When your paper gets accepted.S

everal points at which you realise that FUN is different.Slide6

2. When your read the program.

S

everal points at which you realise that FUN is different.Slide7

3. When you realise how difficult it is to get there.

S

everal points at which you realise that FUN is different.

Melbourne to Singapore

Singapore to Munich

Munich to CataniaSlide8

3. When you realise how difficult it is to get there.Recap so far:31 hours in so far

With very good connections!

Time to realise that Italy has its own power plug system.

Two of them.

And that they don't believe in grounding their power.Also, that no power converters are for sale at the Catania airport.

In fact, there's not much in Catania airport, unless you're after gelato.

Several points at which you realise that FUN is different.Slide9

3. When you realise how difficult it is to get there.

S

everal points at which you realise that FUN is different.

Next, by bus from Catania to

Milazzo

,

4 hours.

5 hours, because the bus had an accident on the way to Catania.

6 hours, because the bus broke down on the way to

Milazzo

.Slide10

But at least it broke down where we had some good view.

Several points at which you realise that FUN is different.

Mount Etna

At over

3.3km

, Europe's tallest active volcano.

(exact height changes after each eruption)

In an almost-constant state of eruption.

One of 17 "decade volcanoes" world-wide.

World heritage site.

Darn big.Slide11

3. When you realise how difficult it is to get there.

S

everal points at which you realise that FUN is different.

From

Milazzo

to Lipari via hydrofoil.

A hydrofoil

A hydrofoil in a hurry.

A hydrofoil two hours overdue, due to bus problems.

Note to self

:

Never board a hydrofoil whose crew is two hours overdue

anywhere

.

Time from

Milazzo

to Lipari:

1 hour

50 minutes when in a hurry.Slide12

3. When you realise how difficult it is to get there.

S

everal points at which you realise that FUN is different.

Total door-to-door travel time, over 40 hours.

Longer on the way back.

Where we also had a bus breakdown.

And switched to a

GiuntaBus

.

Same route on the way back,

replacing Munich for Frankfurt.

Note to self

: Frankfurt airport

prides itself on its buggy service.

Total time on the road: 85 hours.

Total time on the island: 83 hours.Slide13

3. When you realise how difficult it is to get there.

S

everal points at which you realise that FUN is different.

And if you think that's bad, consider that

this

guy only came from nearby Oman, and

still

managed to spend 35 hours on the way over.

Prof.

Rudolf Fleischer

Head of department of computer science and dean of engineering,

GUTech

, Oman.

Record holder for guy with the worst connections.Slide14

4. When you find out that while getting there is no fun at all, being

there is pretty good.

S

everal points at which you realise that FUN is different.

Lipari Island

Volcano Island:

Home of the original volcano

StromboliSlide15

Greek influences.Lovely canyons.Clear, warm water.

Abundant night-life.

Hot weather, so you are encouraged to drink lots of wine.

Ridiculously expensive food.

Some notable island features

Insalata

verde

4euro

approx.

AU$6Slide16

5. When you realise that everyone is on a first-name basis.

S

everal points at which you realise that FUN is different.

Giuseppe

Maaler

Irina

Takaaki

Rudolf

Erik

Vincenzo

Giovanni

Pawel

Florian

Alfredo

Erik

Fermi

Zsuzsanna

Paolo

MinghuiSlide17

5. When you realise that everyone is on a first-name basis.

S

everal points at which you realise that FUN is different.

Aaron

Pascal

There is actually a good reason for this.

For most participants, this isn't their first FUN.

In fact, it's almost assumed that if you came here once, you'll want to come back again every time.

Many of the participants were in all 7

FUNs

so far.Slide18

Erik

Demaine

Record holder: most FUN

Participated in all seven FUN conferences.

Co-authored 3 of the papers in this FUN

C

ited in, perhaps, most other papers, too.

Designed the FUN logo.

Was this year's invited speaker.

Organiser of next year's FUN.

Oh, and:

His PhD thesis was on mathematical origami.

My first encounter

with him

was seven

years ago

in the context of

polyomino

tiling

. He was a fun guru already back then.Slide19

But also (among his less fun achievements):

Youngest professor in the history of MIT.

MacArthur fellow (and many other awards besides).

Member of the Theory of Computation group at MIT Computer Science and Artificial Intelligence Laboratory.

Erik

Demaine

Record holder: most FUNSlide20

6. ... that activities are somewhat unusual.

S

everal points at which you realise that FUN is different.

Barbara

Fermi

ErikSlide21

6. ... that activities are somewhat unusual.7. ... that wacky props are encouraged.

S

everal points at which you realise that FUN is different.

Vincenzo

ZsuzsannaSlide22

6. ... that activities are somewhat unusual.7. ... that wacky props are encouraged.

8. ... that dressing up is allowed.

S

everal points at which you realise that FUN is different.

Maaler

IrinaSlide23

6. ... that activities are somewhat unusual.7. ... that wacky props are encouraged.

8. ... that dressing up is allowed.

9. ... as are nerdy jokes.

S

everal points at which you realise that FUN is different.

GiovanniSlide24

6. ... that activities are somewhat unusual.7. ... that wacky props are encouraged.

8. ... that dressing up is allowed.

9. ... as are nerdy jokes.

10. ... and that what you get when you register is a beach towel.

Several points at which you realise that FUN is different.

(Because, hey, you're on an island...)Slide25

Some repeating themes:

And yet, amazingly, everything here is good math.Slide26

Hardness results on gamesSlide27

Greg Aloupis, Erik Demaine

, Alan

Guo

,

Gionvanni VigliettaAbstract:

We prove NP-hardness results for five of Nintendo's largest video game franchises: Mario, Donkey Kong, Legend of Zelda

, Metroid, and Pokémon. Our results apply to generalized versions of Super Mario Bros. 1

, 3, Lost Levels, and Super Mario World; Donkey Kong Country 1-3

; all Legend of Zelda games; all Metroid games; and all Pokémon role-playing games. In addition, we prove PSPACE-completeness of the Donkey Kong Country

games and several

Legend of Zelda

games.

Classic Nintendo GamesSlide28

Rules of the game remain as they are.Maps are invented.NP reductions from 3-SAT.

PSPACE

reductions from

TQBF

.Other reductions are from 'push' game variants and from door/pressure-plate puzzles.Additional proofs include:Gadget-fixes against Super Mario glitches.

Positive PSPACE results for memory-limited game variants.

Is it possible to reach t from s?Slide29

Giovanni VigliettaOptimisation

prob

: how many can be saved?

PSPACE

-complete even for single builder/basher.In NP if there are only polynomially many builders, bashers and miners.

Finding maximum is APX-hard even when only climbers are available. (Relative error 1/8.)[Cormode 2004] In P for levels with no "deadly areas" and only climbers and floaters.

Accounts for all game glitches.LemmingsSlide30

Most proofs involve multiple lemming-killing contraptions (no fun), but not NP proof.Number of lemmings polynomial; number of player actions effectively polynomial.Terrain changers only work for poly moves.

Total terrain changes polynomial.

At all other times, poly many lemmings follow poly-length independent paths.

Exptime

waits (full cycle) can be calculated efficiently.Proof string: time stamps for player actions.

NP for poly build/bash/minersSlide31

Minghui Jiang, Pedro Tejada, Haitao Wang

Droplet slides to maximal extent (4 directions) after each move by the player. Collects pearls.

ANY-MOVES-ALL-PEARLS in P

ANY-MOVES-MAX-PEARLS & MIN-MOVES-ALL-PEARLS --

APX-hard with NPC+FPT

decision problems.ANY-MOVES-MAX-PEARLS 2-approximable.

QuellSlide32

Compact graph representation of the board and division into strongly connected components can be done in time P.After: solving ANY+ALL

is 2-

SAT

, hence in P.

k+ALL, ANY+k

in NP: path on graph can be given as proof string.Greedy algorithm for ANY+MAX can pick as many as possible graph edges that contain pearls, but each pearl may be counted on two edges, hence 2-approx.

APX result is for 22/21.Positive resultsSlide33

Guillaume Fertin, Shahrad

Jamshidi

, Christian

Komusiewicz

[Friedman 2002]: NPC

Now: FPT for #corners

Spiral Galaxies (Tentai Show)Slide34

n cells, l corners.Describe each galaxy as a tiling of O(

l

) rectangles (and symmetric rectangles).

Describe the rectangles as having relations in terms of relative position and adjacency.

Enumerate over all possible descriptions.(Exponential.)

For each description, exact dimensions can be solved by an ILP with O(l) variables.

Time: f(l) polylog(

n)Proof ideaSlide35

Takashi Horyiama et al. (7 authors)

Old Western-Japanese game.

Connect point sets to (empty) triangles. No extra turn when closing triangles (unlike dots-and-boxes [

Berlekamp

]). Player with most triangles wins.Known: if getting extra turn, 1st player wins on odd-sized point sets, tie on even.

New results:For convex sets, 1st to play wins. (Inductive proof.)NPC to determine if k triangles can be closed in the next

l turns.Sankaku-ToriSlide36

Windfall (Rudolf Fleischer, Tao Zhang)How many falling coins can Mario catch, using an online strategy with finite look-ahead?

Latin square completion (

Kazuya

Haraguchi

, Hirotaka Ono)

How many cells can a simple strategy solve in Sudoku, Futoshiki & BlockSum?

Other papersSlide37

Graph problems posing as gamesSlide38

Palash Dey,

Prachi

Goyal

, Neeldhara Misra

Decision problem: can all cards in a given hand be discarded? c colours, unlimited numbers.Known:[Demaine

(s) et al.] NPC, FPT: nO(

c^2) algorithm.New:2

O(c^2 log c) nO

(1)

algorithm.

Exponential

algo

& NPC proof for newly introduced harder variant "all or nothing UNO".

Proof technique:

Kernelisation

to reduce to O(

c

2

)

numbers,

followed by use of known dynamic programming algorithm from

Demaine

et al..

Single-player UNOSlide39

Erik Demaine, Fermi Ma, Erik Waingarten

Single player in P

Cooperative multi-player is NPC

Competitive play is

PSPACE-completeSimilar results for team play.

Trivia:Earliest known Domino set dates back to an Egyptian tomb from ~1350 BC.DominoesSlide40

Straight up graph problemsSlide41

Alam, Kobourov,

Pupyrev

,

Toeniskoetter

Given a graph with edges labelled either "near" or "far", colour the vertices such that near vertices differ by at most t and far vertices by more than

t.Studied on Archimedean & Laves lattices.Results:Some colourable with fixed number of colours.

Some require unbounded colours for specific labelings.Some are not threshold colourable.

Threshold ColouringSlide42

Borassi et al.Idea: iterative refinement of heuristic bounds.

Exploiting relation between eccentricity and farness.

Exploiting relation between farness and sampled distance from arbitrary nodes. (Consider diametric vertices.)

Worst case: O(|V||E|).

On real graphs, requires at most 10-100 BFSs

, so ~O(|E|).This was a main theme of Paolo Boldi's invited talk.

Diameter & radius computationSlide43

Kevin Bacon was never central until 2014.

It was never possible to win "6-degrees"

of anyone.

The

D&R

of the graph (and list of centrals) actually provides much insight on cinema history.

Sample resultsSlide44

Bang Ye WuTree not given; only distance Oracle is used.2n

-3

queries are necessary and sufficient to find diameter, radius & centres. (

n

=#leaves)To find median:Deterministic algorithm:

n log n.Randomized algorithm: expectation < 6n

.Finding Centres and Medians of a Tree by Distance QueriesSlide45

Shoelace TSP with very old shoes (Deineko, Woeginger

)

(But does this really count as straight-laced graph theory?)

Optimizing Airspace Closure with Respect to Politicians' Egos (

Kostitsyna, Löffler

, Polishchuk)Pareto-optimal House allocations (Asinowski, Keszegh

, Miltzow)How many houses can ever be allocated?What makes a house unavoidable?How many separate solution sets are there?

Other papersSlide46

Network problems(which is almost the same thing as graph problems, but with some subtle nuances.)Slide47

Cicalese et al.Each node in a graph becomes "influenced" once enough of its neighbours are.

The general "influencers" problem is known to be hard (even to approximate).

Solved here

polynomially

for trees, paths, cycles and complete graphs.

How to go viralSlide48

Krumke, Schwahn

,

Thielen

Similar to previous, but now the question is computing optimal price given that perceived price is affine in the purchase choices of the neighbours.

Results:Strongly polynomial if weights are nonnegative.

NP-hard otherwise.Has pseudo-polynomial-time solution.But cannot be approximated to any constant factor unless P=NP.

Influencers in sellingSlide49

Keller, Peleg,

Wattenhofer

Similar to previous, but now the question is stabilization times.

Results:

Exponential lower and upper bounds on stabilization times.Example of an asymmetric-weight network with an exponential-length cycle.

Tiny Influence - Big ImpactSlide50

Clearing Connections by Few Agents (Levcopoulos, Lingas

, Nilsson,

Żyliński

)

Swapping Labeled Tokens on Graphs (Yamanaka et al.)

Other papersSlide51

Fun with roboticsSlide52

Vincenzo Gervasi, Giuseppe Prencipe and Valerio VolpiA blend of Look-Compute-Move (LCM) robotics with Hollywood lore.Set of zombies. Set of humans. Zombie speed increases with amount of sound emitted by humans. Go for closest human.

Zombie SwarmsSlide53

Problems investigated:Can a human gather the zombies without becoming one himself?Demonstrated experiments with circular motion; showed that there is an optimal speed.

Can a human cause zombies to flock to a particular place?

Two-stage algorithm: gathering, then gathering plus linear motion.

... spread the zombies? Every pair? Some pair? Split into sub-groups?

Various strategies tried. Results by simulation.

Zombie SwarmsSlide54

Shantau Das, Paola Flocchini, Giuseppe

Prencipe

, Nicola Santoro

Another LCM robotics question

What if robots can maintain a state in the form of a colour? As a function of number of colours?

Results show that the spin invariant is the main constraint. One set of chameleons (rotationally symmetric) is used to signal by their relative distances.

Synchronized Dancing of Oblivious ChameleonsSlide55

Retro-hardwareMathematical de-

abstractisationSlide56

Takaaki Mizuki and Hiroki

Shizuya

Motivation: very,

very

shy teens.Improved protocols for securely calculating general Boolean functions using a small number of cards.

Resilience against players exploiting scuff marks and rotationally not-invariant back-sides.Dishonest players (exploitation of input format).Card-based CryptographySlide57

Jannik Dreier, Hugo Jonker, Pascal

Lafourcade

Objective: "

Woodako

"

Secure AuctionsSlide58

Woodako is a hardware implementation of Sako's secure auction.

Meant to implement

Sako

without use of cryptography

so that the non-mathematical public can be given answers to questions around auction security... that they never asked (because they're not mathematicians)

... and the answer for which, though not reliant on cryptography, still requires the ability to follow complex mathematical proofs."

Woodako"Slide59

"Inspired by real events!"Interesting models for real-world situations.Slide60

Ke Chen, Adrian DumitrescuA ruler with

n

links and maximal link-length 1 is folded into a simple case of diameter 1. What is the minimal area of a case that can carry all such rulers for all possible

n

?Previous results (mainly by the authors) reach an upper bound of 0.614 and a lower bound of 0.476 for the convex case.

Nonconvex: [0.073, 0.583]Nonconvex

Cases for Carpenter's RulersSlide61

ConstructionsUpper bound

Lower bound (simplified)Slide62

The Courteous Theatregoer's Problem (Georgiou, Kranakis,Krizanc)

Jigsaw puzzles (

MB

)

Other papersSlide63

MiscellaniaThings so far out of the box they don't know where the box is.Slide64

Burcsi, Fici, Lipták

,

Ruskey

, Sawada

Background: indexed jumbled pattern matchingA real-world problem of much interest (computational biology).

Given a binary word w, does w have a substring with s

zeroes and t ones?Can be solved in O(1) with linear-sized index.But best known index-building algorithms are O(

n2/log n).One of them by same authors from FUN 2010.

Prefix normal wordsSlide65

The way to create a linear index is to note that if w has two

k

-length prefixes with

a

1s and b 1s, respectively (w.l.o.g.

a<b), then it also contains a k-length prefix with x

1s for every a<x<b.

[Folklore]Thus, the index only needs to include the minima and the maxima.Jumbled pattern indexSlide66

There is a unique word that matches all the maxima precisely.It has the property that no substring of any length

k

of it has more 1s than the prefix of the same length. We call this property

prefix normality

(w.r.t. 1).We call this word the canonical prefix normal form representation of

w (w.r.t. 1).The unique word matching all the minima precisely is the canonical prefix normal form representation of

w w.r.t. 0.

Canonical representationsSlide67

The rest of the paper is devoted to fun things you can do with prefix normal words. These include:Canonizing a word.

Deciding if a word is canonical.

Playing prefix normal word games.

A mechanical canonization algorithm.

... and more.Results are not profound, but show that the authors are really trying to think outside the box in order to improve

IJPM bounds.Prefix normal wordsSlide68

The Harassed Waitress Problem (Harrah Essed

and Wei

Threse

; Italian House of Pancakes

*)Fun with Fonts: Algorithmic Typography (Erik

Demaine and Martin Demaine) -- 2nd invited talk.

Other papers*

Joe Sawada and Aaron Williams, following Jacob Goodman.Slide69
Slide70

?