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I am looking for websites or articles where can I find a data with test graphs for domination set problem. In my heuristic algorithms I use undirected and unweighted graphs. So I search for some graphs which already have been tested from other people.

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    $\begingroup$ I cannot see any research level statement in the question, but on the other hand when I saw a question I did a google search to see if deserves to downvote, but I didn't find any reference as requested (in quick search), so I think while the question is not well explained, it's also not very welcome to downvote a new user without any explanation. $\endgroup$
    – Saeed
    Apr 8, 2014 at 12:38
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    $\begingroup$ You can search hard instances of problems which can be easily reduced to dominating set. For example search "DIMACS graph benchmarks vertex cover". $\endgroup$ Apr 8, 2014 at 13:59
  • $\begingroup$ @MarzioDeBiasi, That's a good idea, then may be is not bad to explain it in more details as answer (e.g by mentioning that it's approximation or heuristic preserving reduction), e.g I personally had no idea about the good search term for the case that OP looking for, but your suggestion seems to be nice. Well, as I said question is not well explained and we don't know what is the OP's algorithm (approximation, heuristic, exact), but your suggestion is nice anyway. $\endgroup$
    – Saeed
    Apr 8, 2014 at 14:07
  • $\begingroup$ @Saeed: I'll wait OP's clarifications :) $\endgroup$ Apr 8, 2014 at 14:25
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    $\begingroup$ This is a serious research question. Many query complexity problems can be formulated as DOM sets. I had to roll my own C code for MinDomSet. Any recommendation would be appreciated. $\endgroup$ Apr 8, 2014 at 14:38

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A quick google search revealed Experiments on Data Reduction for Optimal Domination in Networks. If you look at their tables they cite a number of data sets for which the actual dominating set is given. They also use a number of random graph generators and publish the average dominating set size for these.

There's another paper from 2002: Experimental Analysis of Heuristic Algorithms for the Dominating Set Problem. I couldn't find an online copy, but I'm sure this paper also documents data sets and actual DS sizes.

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