From 05b0149331814d4ea4c270b734b855dd767a2ea3 Mon Sep 17 00:00:00 2001 From: Artem Demchenko Date: Fri, 20 Jun 2025 15:21:47 +0300 Subject: [PATCH 1/2] Update slides --- data/small.mtx | 334 ---------------------------------- slides/experiment_results.pdf | Bin 875724 -> 1024461 bytes 2 files changed, 334 deletions(-) delete mode 100644 data/small.mtx diff --git a/data/small.mtx b/data/small.mtx deleted file mode 100644 index 6f4e69c..0000000 --- a/data/small.mtx +++ /dev/null @@ -1,334 +0,0 @@ -%%MatrixMarket matrix coordinate integer symmetric -% NOTE: the weights were randomly generated -%------------------------------------------------------------------------------- -% UF Sparse Matrix Collection, Tim Davis -% http://www.cise.ufl.edu/research/sparse/matrices/DIMACS10/chesapeake -% name: DIMACS10/chesapeake -% [DIMACS10 set: clustering/chesapeake] -% id: 2457 -% date: 2011 -% author: unknown -% ed: H. Meyerhenke -% fields: name title A id date author ed kind notes -% kind: undirected graph -%------------------------------------------------------------------------------- -% notes: -% 10th DIMACS Implementation Challenge: -% -% http://www.cc.gatech.edu/dimacs10/index.shtml -% -% As stated on their main website ( -% http://dimacs.rutgers.edu/Challenges/ ), the "DIMACS Implementation -% Challenges address questions of determining realistic algorithm -% performance where worst case analysis is overly pessimistic and -% probabilistic models are too unrealistic: experimentation can provide -% guides to realistic algorithm performance where analysis fails." -% -% For the 10th DIMACS Implementation Challenge, the two related -% problems of graph partitioning and graph clustering were chosen. -% Graph partitioning and graph clustering are among the aforementioned -% questions or problem areas where theoretical and practical results -% deviate significantly from each other, so that experimental outcomes -% are of particular interest. -% -% Problem Motivation -% -% Graph partitioning and graph clustering are ubiquitous subtasks in -% many application areas. Generally speaking, both techniques aim at -% the identification of vertex subsets with many internal and few -% external edges. To name only a few, problems addressed by graph -% partitioning and graph clustering algorithms are: -% -% * What are the communities within an (online) social network? -% * How do I speed up a numerical simulation by mapping it -% efficiently onto a parallel computer? -% * How must components be organized on a computer chip such that -% they can communicate efficiently with each other? -% * What are the segments of a digital image? -% * Which functions are certain genes (most likely) responsible -% for? -% -% Challenge Goals -% -% * One goal of this Challenge is to create a reproducible picture -% of the state-of-the-art in the area of graph partitioning -% (GP) and graph clustering (GC) algorithms. To this end we -% are identifying a standard set of benchmark instances and -% generators. -% -% * Moreover, after initiating a discussion with the community, we -% would like to establish the most appropriate problem -% formulations and objective functions for a variety of -% applications. -% -% * Another goal is to enable current researchers to compare their -% codes with each other, in hopes of identifying the most -% effective algorithmic innovations that have been proposed. -% -% * The final goal is to publish proceedings containing results -% presented at the Challenge workshop, and a book containing -% the best of the proceedings papers. -% -% Problems Addressed -% -% The precise problem formulations need to be established in the course -% of the Challenge. The descriptions below serve as a starting point. -% -% * Graph partitioning: -% -% The most common formulation of the graph partitioning problem -% for an undirected graph G = (V,E) asks for a division of V into -% k pairwise disjoint subsets (partitions) such that all -% partitions are of approximately equal size and the edge-cut, -% i.e., the total number of edges having their incident nodes in -% different subdomains, is minimized. The problem is known to be -% NP-hard. -% -% * Graph clustering: -% -% Clustering is an important tool for investigating the -% structural properties of data. Generally speaking, clustering -% refers to the grouping of objects such that objects in the same -% cluster are more similar to each other than to objects of -% different clusters. The similarity measure depends on the -% underlying application. Clustering graphs usually refers to the -% identification of vertex subsets (clusters) that have -% significantly more internal edges (to vertices of the same -% cluster) than external ones (to vertices of another cluster). -% -% There are 10 data sets in the DIMACS10 collection: -% -% Kronecker: synthetic graphs from the Graph500 benchmark -% dyn-frames: frames from a 2D dynamic simulation -% Delaunay: Delaunay triangulations of random points in the plane -% coauthor: citation and co-author networks -% streets: real-world street networks -% Walshaw: Chris Walshaw's graph partitioning archive -% matrix: graphs from the UF collection (not added here) -% random: random geometric graphs (random points in the unit square) -% clustering: real-world graphs commonly used as benchmarks -% numerical: graphs from numerical simulation -% -% Some of the graphs already exist in the UF Collection. In some cases, -% the original graph is unsymmetric, with values, whereas the DIMACS -% graph is the symmetrized pattern of A+A'. Rather than add duplicate -% patterns to the UF Collection, a MATLAB script is provided at -% http://www.cise.ufl.edu/research/sparse/dimacs10 which downloads -% each matrix from the UF Collection via UFget, and then performs whatever -% operation is required to convert the matrix to the DIMACS graph problem. -% Also posted at that page is a MATLAB code (metis_graph) for reading the -% DIMACS *.graph files into MATLAB. -% -% -% clustering: Clustering Benchmarks -% -% These real-world graphs are often used as benchmarks in the graph -% clustering and community detection communities. All but 4 of the 27 -% graphs already appear in the UF collection in other groups. The -% DIMACS10 version is always symmetric, binary, and with zero-free -% diagonal. The version in the UF collection may not have those -% properties, but in those cases, if the pattern of the UF matrix -% is symmetrized and the diagonal removed, the result is the DIMACS10 -% graph. -% -% DIMACS10 graph: new? UF matrix: -% --------------- ---- ------------- -% clustering/adjnoun Newman/adjoun -% clustering/as-22july06 Newman/as-22july06 -% clustering/astro-ph Newman/astro-ph -% clustering/caidaRouterLevel * DIMACS10/caidaRouterLevel -% clustering/celegans_metabolic Arenas/celegans_metabolic -% clustering/celegansneural Newman/celegansneural -% clustering/chesapeake * DIMACS10/chesapeake -% clustering/cnr-2000 LAW/cnr-2000 -% clustering/cond-mat-2003 Newman/cond-mat-2003 -% clustering/cond-mat-2005 Newman/cond-mat-2005 -% clustering/cond-mat Newman/cond-mat -% clustering/dolphins Newman/dolphins -% clustering/email Arenas/email -% clustering/eu-2005 LAW/eu-2005 -% clustering/football Newman/football -% clustering/hep-th Newman/hep-th -% clustering/in-2004 LAW/in-2004 -% clustering/jazz Arenas/jazz -% clustering/karate Arenas/karate -% clustering/lesmis Newman/lesmis -% clustering/netscience Newman/netscience -% clustering/PGPgiantcompo Arenas/PGPgiantcompo -% clustering/polblogs Newman/polblogs -% clustering/polbooks Newman/polbooks -% clustering/power Newman/power -% clustering/road_central * DIMACS10/road_central -% clustering/road_usa * DIMACS10/road_usa -%------------------------------------------------------------------------------- -2000 2000 170 -7 1 18 -8 1 15 -11 1 13 -12 1 1 -13 1 2 -22 1 5 -23 1 18 -34 1 15 -35 1 8 -37 1 7 -39 1 11 -7 2 1 -8 2 4 -9 2 9 -11 2 20 -12 2 6 -13 2 19 -22 2 9 -23 2 18 -35 2 7 -36 2 11 -39 2 4 -14 3 12 -15 3 15 -16 3 2 -17 3 4 -18 3 6 -36 3 3 -39 3 11 -17 4 4 -36 4 5 -37 4 2 -39 4 4 -6 5 2 -34 5 17 -35 5 9 -39 5 16 -7 6 7 -35 6 9 -39 6 19 -8 7 5 -9 7 16 -11 7 3 -12 7 7 -13 7 2 -35 7 10 -39 7 7 -9 8 13 -10 8 13 -20 8 11 -21 8 6 -22 8 6 -23 8 2 -24 8 8 -35 8 18 -38 8 11 -39 8 6 -10 9 4 -35 9 20 -36 9 5 -39 9 5 -35 10 8 -36 10 7 -39 10 16 -19 11 1 -35 11 9 -36 11 8 -39 11 1 -19 12 20 -26 12 19 -35 12 7 -36 12 12 -38 12 16 -39 12 6 -35 13 10 -36 13 13 -38 13 14 -39 13 12 -25 14 4 -26 14 15 -27 14 9 -28 14 10 -29 14 8 -36 14 15 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Meyerhenke +% fields: name title A id date author ed kind notes +% kind: undirected graph +%------------------------------------------------------------------------------- +% notes: +% 10th DIMACS Implementation Challenge: +% +% http://www.cc.gatech.edu/dimacs10/index.shtml +% +% As stated on their main website ( +% http://dimacs.rutgers.edu/Challenges/ ), the "DIMACS Implementation +% Challenges address questions of determining realistic algorithm +% performance where worst case analysis is overly pessimistic and +% probabilistic models are too unrealistic: experimentation can provide +% guides to realistic algorithm performance where analysis fails." +% +% For the 10th DIMACS Implementation Challenge, the two related +% problems of graph partitioning and graph clustering were chosen. +% Graph partitioning and graph clustering are among the aforementioned +% questions or problem areas where theoretical and practical results +% deviate significantly from each other, so that experimental outcomes +% are of particular interest. +% +% Problem Motivation +% +% Graph partitioning and graph clustering are ubiquitous subtasks in +% many application areas. Generally speaking, both techniques aim at +% the identification of vertex subsets with many internal and few +% external edges. To name only a few, problems addressed by graph +% partitioning and graph clustering algorithms are: +% +% * What are the communities within an (online) social network? +% * How do I speed up a numerical simulation by mapping it +% efficiently onto a parallel computer? +% * How must components be organized on a computer chip such that +% they can communicate efficiently with each other? +% * What are the segments of a digital image? +% * Which functions are certain genes (most likely) responsible +% for? +% +% Challenge Goals +% +% * One goal of this Challenge is to create a reproducible picture +% of the state-of-the-art in the area of graph partitioning +% (GP) and graph clustering (GC) algorithms. To this end we +% are identifying a standard set of benchmark instances and +% generators. +% +% * Moreover, after initiating a discussion with the community, we +% would like to establish the most appropriate problem +% formulations and objective functions for a variety of +% applications. +% +% * Another goal is to enable current researchers to compare their +% codes with each other, in hopes of identifying the most +% effective algorithmic innovations that have been proposed. +% +% * The final goal is to publish proceedings containing results +% presented at the Challenge workshop, and a book containing +% the best of the proceedings papers. +% +% Problems Addressed +% +% The precise problem formulations need to be established in the course +% of the Challenge. The descriptions below serve as a starting point. +% +% * Graph partitioning: +% +% The most common formulation of the graph partitioning problem +% for an undirected graph G = (V,E) asks for a division of V into +% k pairwise disjoint subsets (partitions) such that all +% partitions are of approximately equal size and the edge-cut, +% i.e., the total number of edges having their incident nodes in +% different subdomains, is minimized. The problem is known to be +% NP-hard. +% +% * Graph clustering: +% +% Clustering is an important tool for investigating the +% structural properties of data. Generally speaking, clustering +% refers to the grouping of objects such that objects in the same +% cluster are more similar to each other than to objects of +% different clusters. The similarity measure depends on the +% underlying application. Clustering graphs usually refers to the +% identification of vertex subsets (clusters) that have +% significantly more internal edges (to vertices of the same +% cluster) than external ones (to vertices of another cluster). +% +% There are 10 data sets in the DIMACS10 collection: +% +% Kronecker: synthetic graphs from the Graph500 benchmark +% dyn-frames: frames from a 2D dynamic simulation +% Delaunay: Delaunay triangulations of random points in the plane +% coauthor: citation and co-author networks +% streets: real-world street networks +% Walshaw: Chris Walshaw's graph partitioning archive +% matrix: graphs from the UF collection (not added here) +% random: random geometric graphs (random points in the unit square) +% clustering: real-world graphs commonly used as benchmarks +% numerical: graphs from numerical simulation +% +% Some of the graphs already exist in the UF Collection. In some cases, +% the original graph is unsymmetric, with values, whereas the DIMACS +% graph is the symmetrized pattern of A+A'. Rather than add duplicate +% patterns to the UF Collection, a MATLAB script is provided at +% http://www.cise.ufl.edu/research/sparse/dimacs10 which downloads +% each matrix from the UF Collection via UFget, and then performs whatever +% operation is required to convert the matrix to the DIMACS graph problem. +% Also posted at that page is a MATLAB code (metis_graph) for reading the +% DIMACS *.graph files into MATLAB. +% +% +% clustering: Clustering Benchmarks +% +% These real-world graphs are often used as benchmarks in the graph +% clustering and community detection communities. All but 4 of the 27 +% graphs already appear in the UF collection in other groups. The +% DIMACS10 version is always symmetric, binary, and with zero-free +% diagonal. The version in the UF collection may not have those +% properties, but in those cases, if the pattern of the UF matrix +% is symmetrized and the diagonal removed, the result is the DIMACS10 +% graph. +% +% DIMACS10 graph: new? UF matrix: +% --------------- ---- ------------- +% clustering/adjnoun Newman/adjoun +% clustering/as-22july06 Newman/as-22july06 +% clustering/astro-ph Newman/astro-ph +% clustering/caidaRouterLevel * DIMACS10/caidaRouterLevel +% clustering/celegans_metabolic Arenas/celegans_metabolic +% clustering/celegansneural Newman/celegansneural +% clustering/chesapeake * DIMACS10/chesapeake +% clustering/cnr-2000 LAW/cnr-2000 +% clustering/cond-mat-2003 Newman/cond-mat-2003 +% clustering/cond-mat-2005 Newman/cond-mat-2005 +% clustering/cond-mat Newman/cond-mat +% clustering/dolphins Newman/dolphins +% clustering/email Arenas/email +% clustering/eu-2005 LAW/eu-2005 +% clustering/football Newman/football +% clustering/hep-th Newman/hep-th +% clustering/in-2004 LAW/in-2004 +% clustering/jazz Arenas/jazz +% clustering/karate Arenas/karate +% clustering/lesmis Newman/lesmis +% clustering/netscience Newman/netscience +% clustering/PGPgiantcompo Arenas/PGPgiantcompo +% clustering/polblogs Newman/polblogs +% clustering/polbooks Newman/polbooks +% clustering/power Newman/power +% clustering/road_central * DIMACS10/road_central +% clustering/road_usa * DIMACS10/road_usa +%------------------------------------------------------------------------------- +2000 2000 170 +7 1 18 +8 1 15 +11 1 13 +12 1 1 +13 1 2 +22 1 5 +23 1 18 +34 1 15 +35 1 8 +37 1 7 +39 1 11 +7 2 1 +8 2 4 +9 2 9 +11 2 20 +12 2 6 +13 2 19 +22 2 9 +23 2 18 +35 2 7 +36 2 11 +39 2 4 +14 3 12 +15 3 15 +16 3 2 +17 3 4 +18 3 6 +36 3 3 +39 3 11 +17 4 4 +36 4 5 +37 4 2 +39 4 4 +6 5 2 +34 5 17 +35 5 9 +39 5 16 +7 6 7 +35 6 9 +39 6 19 +8 7 5 +9 7 16 +11 7 3 +12 7 7 +13 7 2 +35 7 10 +39 7 7 +9 8 13 +10 8 13 +20 8 11 +21 8 6 +22 8 6 +23 8 2 +24 8 8 +35 8 18 +38 8 11 +39 8 6 +10 9 4 +35 9 20 +36 9 5 +39 9 5 +35 10 8 +36 10 7 +39 10 16 +19 11 1 +35 11 9 +36 11 8 +39 11 1 +19 12 20 +26 12 19 +35 12 7 +36 12 12 +38 12 16 +39 12 6 +35 13 10 +36 13 13 +38 13 14 +39 13 12 +25 14 4 +26 14 15 +27 14 9 +28 14 10 +29 14 8 +36 14 15 +39 14 20 +19 15 12 +25 15 11 +26 15 14 +27 15 6 +28 15 18 +29 15 18 +36 15 12 +39 15 4 +19 16 20 +27 16 3 +36 16 4 +39 16 11 +36 17 17 +39 17 7 +19 18 20 +25 18 19 +26 18 4 +27 18 7 +29 18 16 +32 18 18 +36 18 12 +39 18 2 +33 19 19 +36 19 18 +38 19 8 +39 19 20 +36 20 16 +38 20 3 +39 20 7 +33 21 3 +36 21 1 +38 21 10 +39 21 5 +27 22 10 +28 22 18 +30 22 13 +31 22 4 +32 22 19 +33 22 4 +35 22 10 +36 22 14 +38 22 1 +39 22 13 +30 23 10 +32 23 14 +33 23 14 +35 23 4 +36 23 13 +38 23 4 +39 23 18 +36 24 4 +38 24 5 +39 24 16 +36 25 2 +38 25 7 +39 25 19 +36 26 6 +38 26 20 +39 26 16 +30 27 15 +36 27 1 +38 27 9 +39 27 16 +36 28 16 +38 28 10 +39 28 7 +36 29 11 +38 29 3 +39 29 19 +36 30 1 +38 30 18 +39 30 4 +32 31 14 +36 31 13 +38 31 10 +39 31 9 +36 32 9 +38 32 9 +39 32 1 +36 33 15 +38 33 14 +39 33 12 +37 34 15 +36 35 10 +37 35 2 \ No newline at end of file