Instance - cdc7-4-3-2

cdc7-4-3-2: Instance-to-Instance Comparison Results

Type:	Instance
Submitter:	Sascha Kurz
Description:	Codes for Networkcoding A constant dimension code with parameters n, k, d and q is a collection of k-dimensional subspaces of the n-dimensional vector space \$GF(q)^n\$ over a finite field with q elements, called codewords, such that the dimension of the intersection of each pair of different k-dimensional subspaces is at most \$k-d/2\$. Let \$A_q(n,d;k)\$ denote the maximum number of codewords. For instance cdc6-4-3-2 \$A_2(6,4;3)=77\$ is known , while \$333 \\le A_2(7,4;3) \\le 381\$ for instance cdc7-4-3-2 are the tightest known bounds, see e.g. . A code of size 381 would correspond to a putative binary q-analog of the Fano plane (finite projective plane of order 2 with 7 points and lines). More bounds are available at http://subspacecodes.uni-bayreuth.de.
	MIPLIB Entry


	Raw This is the CCM image before the decomposition procedure has been applied.	Decomposed This is the CCM image after a decomposition procedure has been applied. This is the image used by the MIC's image-based comparisons for this query instance.	Composite of MIC Top 5 Composite of the five decomposed CCM images from the MIC Top 5.	Composite of MIPLIB Top 5 Composite of the five decomposed CCM images from the MIPLIB Top 5.	Model Group Composite Image Composite of the decomposed CCM images for every instance in the same model group as this query.

Decomposed These decomposed images were created by GCG.
Name	pythago7825 [MIPLIB]	reblock115 [MIPLIB]	pythago7824 [MIPLIB]	iis-hc-cov [MIPLIB]	neos-5189128-totara [MIPLIB]
Rank / ISS The image-based structural similarity (ISS) metric measures the Euclidean distance between the image-based feature vectors for the query instance and all other instances. A smaller ISS value indicates greater similarity.	1 / 1.449	2 / 1.458	3 / 1.459	4 / 1.484	5 / 1.487
Raw These images represent the CCM images in their raw forms (before any decomposition was applied) for the MIC top 5.

Decomposed These decomposed images were created by GCG.
Name	cod105 [MIPLIB]	a2864-99blp [MIPLIB]	z26 [MIPLIB]	sorrell7 [MIPLIB]	sorrell8 [MIPLIB]
Rank / ISS The image-based structural similarity (ISS) metric measures the Euclidean distance between the image-based feature vectors for the query instance and all model groups. A smaller ISS value indicates greater similarity.	78 / 1.864	145 / 2.067	146 / 2.069	270 / 2.310	430 / 2.499
Raw These images represent the CCM images in their raw forms (before any decomposition was applied) for the MIPLIB top 5.

Instance Summary

The table below contains summary information for cdc7-4-3-2, the five most similar instances to cdc7-4-3-2 according to the MIC, and the five most similar instances to cdc7-4-3-2 according to MIPLIB 2017.

	INSTANCE	SUBMITTER	DESCRIPTION	ISS	RANK
Parent Instance	cdc7-4-3-2 [MIPLIB]	Sascha Kurz	Codes for Networkcoding A constant dimension code with parameters n, k, d and q is a collection of k-dimensional subspaces of the n-dimensional vector space \$GF(q)^n\$ over a finite field with q elements, called codewords, such that the dimension of the intersection of each pair of different k-dimensional subspaces is at most \$k-d/2\$. Let \$A_q(n,d;k)\$ denote the maximum number of codewords. For instance cdc6-4-3-2 \$A_2(6,4;3)=77\$ is known , while \$333 \\le A_2(7,4;3) \\le 381\$ for instance cdc7-4-3-2 are the tightest known bounds, see e.g. . A code of size 381 would correspond to a putative binary q-analog of the Fano plane (finite projective plane of order 2 with 7 points and lines). More bounds are available at http://subspacecodes.uni-bayreuth.de.	0.000000	-
MIC Top 5	pythago7825 [MIPLIB]	Felix J. L. Willamowski	2-coloring of Pythagorean triples	1.449394	1
	reblock115 [MIPLIB]	Andreas Bley	Multi-period mine production scheduling instances	1.458029	2
	pythago7824 [MIPLIB]	Felix J. L. Willamowski	2-coloring of Pythagorean triples	1.459055	3
	iis-hc-cov [MIPLIB]	Marc Pfetsch	23 "middlehard" Set-Covering Instances for MIPLIB: they have a small number of variables compared to the number of constraints and CPLEX 12.1 needs about one hour to solve them.For more information, have a look into the readme file which explains how the instances can be created.	1.483555	4
	neos-5189128-totara [MIPLIB]	Hans Mittelmann	distribution of fruit	1.486982	5
MIPLIB Top 5	cod105 [MIPLIB]	MIPLIB submission pool	Imported from the MIPLIB2010 submissions.	1.864078	78
	a2864-99blp [MIPLIB]	Daniel Heinlein	Clique problems arising from a selection problem of subspaces in the PG(7,2) with different prescribed variables and numerically instable linear programming relaxation.	2.066876	145
	z26 [MIPLIB]	Daniel Bienstock	Set packing problem arising from the ongoing "Frequency Spectrum Auction" in the U.S. Work is collaboration with Ion Media Networks, Inc.	2.069385	146
	sorrell7 [MIPLIB]	Toni Sorrell	These instances are based on Neil Sloane's Challenge problems: Independent Sets in Graphs.	2.310253	270
	sorrell8 [MIPLIB]	Toni Sorrell	These instances are based on Neil Sloane's Challenge problems: Independent Sets in Graphs.	2.498613	430

cdc7-4-3-2: Instance-to-Model Comparison Results

Model Group Assignment from MIPLIB:	no model group assignment
Assigned Model Group Rank/ISS in the MIC:	N.A. / N.A.

These are model group composite (MGC) images for the MIC top 5 model groups.
Name	f2gap	independentset	2hopcds	neos-pseudoapplication-19	pb-
Rank / ISS The image-based structural similarity (ISS) metric measures the Euclidean distance between the image-based feature vectors for the query instance and all other instances. A smaller ISS value indicates greater similarity.	1 / 1.812	2 / 1.849	3 / 1.880	4 / 1.914	5 / 1.918

Model Group Summary

The table below contains summary information for the five most similar model groups to cdc7-4-3-2 according to the MIC.

	MODEL GROUP	SUBMITTER	DESCRIPTION	ISS	RANK
MIC Top 5	f2gap	Salim Haddadi	Restrictions of well-known hard generalized assignment problem models (D10400,D20400,D40400,D15900,D30900,D60900,D201600,D401600,D801600)	1.812152	1
	independentset	Toni Sorrell	These models are based on Neil Sloane's Challenge problems: Independent Sets in Graphs.	1.849294	2
	2hopcds	Austin Buchanan	A problem in wireless networks. The objective is to select a minimum number of relay nodes so that any two nonadjacent nodes can communicate by way of the chosen relay nodes in at most s hops, where s is a problem input. The 2-hop case of this problem can be formulated as a set cover/hitting set problem with n binary variables and n^2 constraints: _{ k N(i) N(j) } x_k 1 for nonadjacent node pairs {i,j}. Despite the formulation's simplicity, models with as few as 120 variables are left unsolved after one hour using Gurobi 7.0.2.	1.879872	3
	neos-pseudoapplication-19	Hans Mittelmann	similar to model ns5223573 submitted in January Solved with ParaSCIP in 525353 seconds with 71 solvers(72 cores).	1.914399	4
	pb-	Gleb Belov	These are the models from MiniZinc Challenges 2012-2016 (see www.minizinc.org), compiled for MIP WITH INDICATOR CONSTRAINTS using the develop branch of MiniZinc and CPLEX 12.7.1 on 30 April 2017. Thus, these models can only be handled by solvers accepting indicator constraints. For models compiled with big-M/domain decomposition only, see my previous submission to MIPLIB.To recompile, create a directory MODELS, a list lst12_16.txt of the models with full paths to mzn/dzn files of each model per line, and say$> ~/install/libmzn/tests/benchmarking/mzn-test.py -l ../lst12_16.txt -slvPrf MZN-CPLEX -debug 1 -addOption "-timeout 3 -D fIndConstr=true -D fMIPdomains=false" -useJoinedName "-writeModel MODELS_IND/%s.mps" Alternatively, you can compile individual model as follows: $> mzn-cplex -v -s -G linear -output-time ../challenge_2012_2016/mznc2016_probs/zephyrus/zephyrus.mzn ../challenge_2012_2016/mznc2016_p/zephyrus/14__8__6__3.dzn -a -timeout 3 -D fIndConstr=true -D fMIPdomains=false -writeModel MODELS_IND/challenge_2012_2016mznc2016_probszephyruszephyrusmzn-challenge_2012_2016mznc2016_probszephyrus14__8__6__3dzn.mps	1.918309	5

cdc7-4-3-2: Instance-to-Instance Comparison Results

Parent Instance (cdc7-4-3-2)

MIC Top 5 Instances

MIPLIB Top 5 Instances

Instance Summary

cdc7-4-3-2: Instance-to-Model Comparison Results

MIC Top 5 Model Groups

Model Group Summary