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2 nd Parameterized Algorithms & Computational Experiments Challenge Where it came from, how it went, who won, and whats next September 6 th , IPEC 2017, Vienna, Austria Program committee track A, treewidth Holger Dell Saarland

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2nd Parameterized Algorithms & Computational Experiments Challenge

Where it came from, how it went, who won, and what’s next

September 6th, IPEC 2017, Vienna, Austria

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Program committee track A, treewidth Holger Dell

Saarland University & Cluster of Excellence

Program committee track B, minimum fill-in Christian Komusiewicz*

Friedrich-Schiller-University Jena

Nimrod Talmon

Weizmann Institute of Science

Mathias Weller

LIRMM Montpellier

Steering committee Holger Dell

Saarland University & Cluster of Excellence

Bart M. P. Jansen

Eindhoven University of Technology

Thore Husfeldt

ITU Copenhagen and Lund University

Petteri Kaski

Aalto University

Christian Komusiewicz

Friedrich-Schiller-University Jena

Frances A. Rosamond*

University of Bergen

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WHERE PACE CAME FROM

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History of PACE

  • PACE was conceived in fall 2015 when many FPT researchers

gathered at the Simons institute

  • Born from a feeling that parameterized algorithmics should

have a greater impact on practice

  • Partially inspired by the success of SAT-solving competitions

in neighboring communities

  • First iteration in 2015-2016

– Track A: Treewidth (heuristically & exact) – Track B: Feedback Vertex Set

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Goals

Investigate the applicability of algorithmic ideas from parameterized algorithmics

  • 1. provide bridge between algorithm design&analysis theory

and algorithm engineering practice

  • 2. inspire new theoretical developments
  • 3. investigate the competitiveness of analytical and design

frameworks developed in the communities

  • 4. produce universally accessible libraries of implementations

and repositories of benchmark instances

  • 5. encourage dissemination of the findings in scientific papers
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Publications following the first PACE

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Publications following the first PACE

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Publications following the first PACE

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Publications following the first PACE

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Publications following the first PACE

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Publications following the first PACE

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Publications following the first PACE

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Publications following the first PACE

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Publications following the first PACE

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Publications following the first PACE

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PACE timeline in 2016-2017

  • 1. Treewidth track
  • 2. Track for computing minimum fill-in (chordal completion)

Time schedule – November 1st 2016: Announcement of problems and inputs – March 1st 2017: Submission of prototype program – May 1st 2017: Submission of final program – June 1st 2017: Result are communicated to participants – September 6th 2017: Award ceremony at IPEC

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Sponsor for prizes & travel

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thenetworkcenter.nl

The NETWORKS project generously sponsors PACE with € 4000 1st prize (€ 500), 2nd prize (€ 300) and 3rd prize (€ 200) Three subcategories in the competition, with €1000 travel award

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PACE timeline in 2017-2018

  • PACE will focus on a single challenge problem next year

Time schedule – Today: Announcement of the problem – November 1st 2017: Detailed problem setting and inputs – March 1st 2018: Submission of prototype program – May 1st 2018: Submission of final program – June 1st 2018: Result are communicated to participants – August 20-24 2018: Award ceremony at IPEC

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The third iteration of PACE

PACE 2017-2018 program committee Édouard Bonnet

Middlesex University, London

Florian Sikora

University Paris Dauphine

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TRACK A: TREEWIDTH

How it went and who won

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PACE 2017

Track A: Treewidth

Holger Dell

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Treewidth Applications (outside of FPT)

  • Register allocation in compilers

(e.g., Thorup 1998)

  • Preprocessing for shortest path

(e.g., Chatterjee Ibsen-Jensen Pavlogiannis 2016)

  • Treewidth of specific graph families

(e.g., Kiyomia Okamotob Otachic 2015)

  • Preprocessing for probabilistic inference

(e.g., Otten Ihler Kask Dechter 2011)

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PACE: submission requirements

  • repository on github.com
  • “edge list” input format
  • Output: tree decomposition
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Heuristic treewidth competition

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100 public + 100 secret instances: 35% graphs from the UAI 2014 competition (probabilistic inference) 35% incidence graphs of SAT competition instances 16% graphs from treedecomposition.com 7% road graphs 7% transit networks

Benchmark instances

number

  • f edges

treewidth (upper bound) median 14k 93 mean 991k 13k

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Ranking by Preferential Voting

“Ballot” for instance he166.gr: submission width after 30 minutes B 672 E 957 A 994 C 33279

→ Use Schulze method to combine votes Instances=Voters

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Participants

6 submissions: 3 new teams 3 teams from last year

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Honorable mentions

Max Bannach (University of Lübeck), Sebastian Berndt (University of Lübeck), Thorsten Ehlers (University of Kiel) Philippe Jégou Hanan Kanso Cyril Terrioux Lukas Larisch (King-Abdullah University of Science and Engineering) Felix Salfelder (University of Leeds) Rank 4 Rank 5 Rank 6 (Aix-Marseille Université, LSIS)

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2nd Parameterized Algorithms and Computational Experiments Challenge

PACE

ALGO/IPEC 2017 September 4 – 8 Vienna, Austria

______________________________________________ ______________________________________________

This is to certify that the 2017 PACE Program Committee has selected

Michael Abseher, Nysret Musliu, Stefan Woltran

as the

Third Place Winners in Heuristic Treewidth Decomposition

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2nd Parameterized Algorithms and Computational Experiments Challenge

PACE

ALGO/IPEC 2017 September 4 – 8 Vienna, Austria

This is to certify that the 2017 PACE Program Committee has selected

Ben Strasser

Karlsruhe Institute of Technology

as the

Second Place Winner in the Heuristic Treewidth Decomposition Challenge

______________________________________________ ______________________________________________

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2nd Parameterized Algorithms and Computational Experiments Challenge

PACE

ALGO/IPEC 2017 September 4 – 8 Vienna, Austria

This is to certify that the 2017 PACE Program Committee has selected

Keitaro Makii, Hiromu Ohtsuka, Takuto Sato, Hisao Tamaki

Meiji University

as the

First Place Winners in Heuristic Treewidth Decomposition

______________________________________________ ______________________________________________

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Exact treewidth competition

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Benchmark instances

100 public + 100 secret instances Grow balls in graphs from heuristic challenge Use CPU months to test “instance difficulty” by running last year’s winning solver number

  • f edges

treewidth median 730 11 mean 7300 31

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Outcome

3 submissions: 1 new team 2 teams from last year Everyone was 100x faster than last year!

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2nd Parameterized Algorithms and Computational Experiments Challenge

PACE

ALGO/IPEC 2017 September 4 – 8 Vienna, Austria

This is to certify that the 2017 PACE Program Committee has selected

Max Bannach, Sebastian Berndt, Thorsten Ehlers

as the

Third Place Winners in the Optimal Treewidth Decomposition Competition

______________________________________________ ______________________________________________

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2nd Parameterized Algorithms and Computational Experiments Challenge

PACE

ALGO/IPEC 2017 September 4 – 8 Vienna, Austria

This is to certify that the 2017 PACE Program Committee has selected

and

Meiji University

as the

Second Place Winners in the Optimal Treewidth Decomposition Competition

______________________________________________ ______________________________________________

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2nd Parameterized Algorithms and Computational Experiments Challenge

PACE

ALGO/IPEC 2017 September 4 – 8 Vienna, Austria

This is to certify that the 2017 PACE Program Committee has selected

Lukas Larisch and Felix Salfelder

King-Abdullah University of Science and Engineering

University of Leeds

as the

First Place Winners in the Optimal Treewidth Decomposition Competition

______________________________________________ ______________________________________________

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Exact treewidth: Plot

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Treewidth competition future

New instance set for exact treewidth:

  • Supports 1000x speed improvements over PACE 2017
  • Persistent competition on optil.io
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tdlib – PACE 2017

Lukas Larisch, Felix Salfelder IPEC 2017

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About tdlib, goals

◮ Tree decomposition (and related) algorithms

◮ Free (libre) heuristic/exact implementations ◮ Pre/post processing ◮ As C++ library
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About tdlib, goals

◮ Tree decomposition (and related) algorithms

◮ Free (libre) heuristic/exact implementations ◮ Pre/post processing ◮ As C++ library

◮ Explore theoretic results in practice

◮ Register allocation (sdcc)
  • P. K. Krause, L. Larisch: The Treewidth of C, (SCOPES’15)
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About tdlib, goals

◮ Tree decomposition (and related) algorithms

◮ Free (libre) heuristic/exact implementations ◮ Pre/post processing ◮ As C++ library

◮ Explore theoretic results in practice

◮ Register allocation (sdcc)
  • P. K. Krause, L. Larisch: The Treewidth of C, (SCOPES’15)
◮ Treewidth bounds in large instances

(e.g. maxsat, up to 1.e7/4.e11 vertices/edges, 7% rel. err)

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About tdlib, goals

◮ Tree decomposition (and related) algorithms

◮ Free (libre) heuristic/exact implementations ◮ Pre/post processing ◮ As C++ library

◮ Explore theoretic results in practice

◮ Register allocation (sdcc)
  • P. K. Krause, L. Larisch: The Treewidth of C, (SCOPES’15)
◮ Treewidth bounds in large instances

(e.g. maxsat, up to 1.e7/4.e11 vertices/edges, 7% rel. err)

◮ Python bindings ◮ A Sagemath package
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Preprocessing

◮ Rule based complete reduction for treewidth 4

islet, twig, buddy, series, cube. c.f. tdlib documentation

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Preprocessing

◮ Rule based complete reduction for treewidth 4 ◮ (Almost) simplicial vertex elimination rules

v w

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Preprocessing

◮ Rule based complete reduction for treewidth 4 ◮ (Almost) simplicial vertex elimination rules

w

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tdlib and PACE’16

◮ refactoring: C++11, generic programming

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tdlib and PACE’16

◮ refactoring: C++11, generic programming ◮ structural/algorithmic improvements

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tdlib and PACE’16

◮ refactoring: C++11, generic programming ◮ structural/algorithmic improvements ◮ reference implementations, exact & heuristic

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tdlib and PACE’16

◮ reference implementations, exact & heuristic

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PACE’17 submission Heuristic ”anytime” algorithm

◮ Guided elimination order brute forcing ◮ interruptible exact algorithm ◮ Postprocessing

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PACE’17 submission Heuristic ”anytime” algorithm

◮ Guided elimination order brute forcing ◮ interruptible exact algorithm ◮ Postprocessing

Exact algorithm, recycling

◮ Rule based preprocessor

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PACE’17 submission Heuristic ”anytime” algorithm

◮ Guided elimination order brute forcing ◮ interruptible exact algorithm ◮ Postprocessing

Exact algorithm, recycling

◮ Rule based preprocessor ◮ Exact kernel inspired by PACE’16 (Tamaki)

◮ .. implementing Arnborg, Corneil, Proskurowski + more ideas.
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PACE’17 submission Heuristic ”anytime” algorithm

◮ Guided elimination order brute forcing ◮ interruptible exact algorithm ◮ Postprocessing

Exact algorithm, recycling

◮ Rule based preprocessor ◮ Exact kernel inspired by PACE’16 (Tamaki)

◮ .. implementing Arnborg, Corneil, Proskurowski + more ideas. ◮ Restructured, object oriented
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PACE’17 submission Heuristic ”anytime” algorithm

◮ Guided elimination order brute forcing ◮ interruptible exact algorithm ◮ Postprocessing

Exact algorithm, recycling

◮ Rule based preprocessor ◮ Exact kernel inspired by PACE’16 (Tamaki)

◮ .. implementing Arnborg, Corneil, Proskurowski + more ideas. ◮ Restructured, object oriented ◮ Ported to tdlib/gala
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PACE’17 submission Heuristic ”anytime” algorithm

◮ Guided elimination order brute forcing ◮ interruptible exact algorithm ◮ Postprocessing

Exact algorithm, recycling

◮ Rule based preprocessor ◮ Exact kernel inspired by PACE’16 (Tamaki)

◮ .. implementing Arnborg, Corneil, Proskurowski + more ideas. ◮ Restructured, object oriented ◮ Ported to tdlib/gala

◮ Optimised for speed ◮ pretty fast on small instances

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Thank You.

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TRACK B: MINIMUM FILL-IN

How it went and who won

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The 2nd Parameterized Algorithms and Computational Experiments Challenge: Track B Minimum Fill-In

Christian Komusiewicz

Friedrich-Schiller-Universit¨ at Jena

Nimrod Talmon

Weizmann Institute of Science

Mathias Weller

LIRMM, Universit´ e de Montpellier II

  • C. Komusiewicz (FSU Jena)
PACE Track B 1
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Challenge Problem

Minimum Fill-In Input: An undirected graph G = (V , E). Task: Find a minimum-size edge set F such that (V , E ∪ F) is chordal.

  • C. Komusiewicz (FSU Jena)
PACE Track B 2
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Challenge Problem

Minimum Fill-In Input: An undirected graph G = (V , E). Task: Find a minimum-size edge set F such that (V , E ∪ F) is chordal.

  • C. Komusiewicz (FSU Jena)
PACE Track B 2
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Challenge Problem

Minimum Fill-In Input: An undirected graph G = (V , E). Task: Find a minimum-size edge set F such that (V , E ∪ F) is chordal. Minimum Fill-In is fixed-parameter tractable e.g. parameterized by solution size |F|, admits subexponential-time algorithms

  • C. Komusiewicz (FSU Jena)
PACE Track B 2
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Challenge Setup

Benchmark Instances: 100 public + 100 hidden instances Instance origin: Systems of linear equations, phylogenetic networks, social networks, molecular interaction networks

  • C. Komusiewicz (FSU Jena)
PACE Track B 3
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Challenge Setup

Benchmark Instances: 100 public + 100 hidden instances Instance origin: Systems of linear equations, phylogenetic networks, social networks, molecular interaction networks

102 103 104 102 103 104 Vertices Edges

Ranking: # solved hidden instances within 30 minutes (each)

  • C. Komusiewicz (FSU Jena)
PACE Track B 3
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  • C. Komusiewicz (FSU Jena)
PACE Track B 4
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Results

10 20 30 40 50 1 2 3 4 5 6 7 8

  • C. Komusiewicz (FSU Jena)
PACE Track B 5
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Results

10 20 30 40 50 1 2 3 4 5 6 7 8

ITU Copenhagen University of Portsmouth IMS Chennai IIT Madras ITU Copenhagen II
  • C. Komusiewicz (FSU Jena)
PACE Track B 5
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Results

10 20 30 40 50 1 2 3 4 5 6 7 8

ITU Copenhagen University of Portsmouth IMS Chennai IIT Madras ITU Copenhagen II Paris-Dauphine & MTA Hungary
  • C. Komusiewicz (FSU Jena)
PACE Track B 5
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2nd Parameterized Algorithms and Computational Experiments Challenge

PACE

Unitjng FPT and practjce

______________________________________________ Holger Dell, Saarland University. Track A Chair ______________________________________________ Christjan Komusiewicz, Friedrich-Schiller-University Jena. Track B Chair 2017 PACE Programme Commitee Co-chairs This is to certify that the 2017 PACE Program Committee has selected

Édouard Bonnet, R.B. Sandeep, Florian Sikora

University Paris-Dauphine Hungarian Academy of Sciences University Paris-Dauphine as the

Third Place Winners in the Minimum Fill-In Challenge

  • C. Komusiewicz (FSU Jena)
PACE Track B 6
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Results

10 20 30 40 50 1 2 3 4 5 6 7 8

ITU Copenhagen University of Portsmouth IMS Chennai IIT Madras ITU Copenhagen II Paris-Dauphine & MTA Hungary University of Helsinki
  • C. Komusiewicz (FSU Jena)
PACE Track B 7
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2nd Parameterized Algorithms and Computational Experiments Challenge

PACE

Unitjng FPT and practjce

ALGO/IPEC 2017 September 4 – 8 Vienna, Austria ______________________________________________ Holger Dell, Saarland University. Track A Chair ______________________________________________ Christjan Komusiewicz, Friedrich-Schiller-University Jena. Track B Chair 2017 PACE Programme Commitee Co-chairs This is to certify that the 2017 PACE Program Committee has selected

Jeremias Berg, Matti Järvisalo, Tuukka Korhonen

University of Helsinki

as the

Second Place Winners in the Minimum Fill-In Challenge

  • C. Komusiewicz (FSU Jena)
PACE Track B 8
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Results

10 20 30 40 50 1 2 3 4 5 6 7 8

ITU Copenhagen University of Portsmouth IMS Chennai IIT Madras ITU Copenhagen II Paris-Dauphine & MTA Hungary University of Helsinki Kyoto University & Meiji University
  • C. Komusiewicz (FSU Jena)
PACE Track B 9
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2nd Parameterized Algorithms and Computational Experiments Challenge

PACE

Unitjng FPT and practjce

ALGO/IPEC 2017 September 4 – 8 Vienna, Austria ______________________________________________ Holger Dell, Saarland University. Track A Chair ______________________________________________ Christjan Komusiewicz, Friedrich-Schiller-University Jena. Track B Chair 2017 PACE Programme Commitee Co-chairs This is to certify that the 2017 PACE Program Committee has selected

Yasuaki Kobayashi, Hisao Tamaki

Kyoto University Meiji University as the

First Place Winners in the Minimum Fill-In Challenge

  • C. Komusiewicz (FSU Jena)
PACE Track B 10
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About our submission (Track B)

Yasuaki Kobayashi Hisao Tamaki

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Minimum Fill-In Problem

Given: undirected graph G = (V, E) Task: find a smallest F such that G’ = (V, E ∪ F) is chordal

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Techniques

  • A sufficient condition for edges that can be safely added.
  • A modified version of “Positive-instance driven dynamic programming

for treewidth”.

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Edges that can be safely added

Lemma [Bodlaender et al. 2011]: Let S be a minimal separator of G such that S ⊆ N(v) for some v ∈ V. Suppose |miss(S)| = 1, where miss(S) is the set of missing edges in G[S]. Then, there is an optimal solution that contains miss(S).

  • If G has a minimal separator S that satisfies the above condition, we

can decompose G by using S.

  • We can generalize this lemma for minimal separators that have more

than one missing edges (with some additional conditions).

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Positive-Instance Driven DP

  • The treewidth and minimum fill-in problem can be solved by DP algorithms based
  • n minimal separators and potential maximal cliques [Bouchitté & Todinca 2011].
  • Tamaki developed a positive-instance driven DP for treewidth [Tamaki 2017].
  • applicable to the min fill-in problem with some non-trivial modifications.
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Thank you! https://github.com/TCS-Meiji/PACE2017-TrackB/

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CHANGING ROLES

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https://pacechallenge.wordpress.com