We present a polynomial time heuristic algorithm for the minimum dominating set problem. The algorithm can readily be used for solving the minimum α -all-neighbor dominating set problem and the minimum set cover problem. We apply the algorithm in heuristic solving the minimum k-center problem in polynomial time. Using a standard set of 40 test problems we experimentally show that our k-center algorithm performs much better than other well-known heuristics and is competitive with the best known (non-polynomial time) algorithms for solving the k-center problem in terms of average quality and deviation of the results as well as the execution time.

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Abstract-Motivated by improving the efficiency of pattern matching on graphs, we define a new kind of equivalence on graph vertices. Since it can be used in various graph algorithms that explore graphs, we call it exploratory equivalence. The equivalence is based on graph automorphisms. Because many similar equivalences exist (some also based on automorphisms), we argue that this one is novel. For each graph, there are many possible exploratory equivalences, but for improving the efficiency of the exploration, some are better than others. To this end, we define a goal function that models the reduction of the search space in such algorithms. We describe two greedy algorithms for the underlying optimization problem. One is based directly on the definition using a straightforward greedy criterion, whereas the second one uses several practical speedups and a different greedy criterion. Finally, we demonstrate the huge impact of exploratory equivalence on a real application, i.e., graph grammar parsing.

A modern computer system provides its support via system software that consists of applications such as an assembler, a linker, a loader and virtual machines. It is of prime importance to give students that are learning system‐software concepts a solid base of knowledge without any unnecessary details. To make the subject easy to understand we designed a simulator for a hypothetical computer that is already used in several courses on system software. In the paper, we describe the simulator's behavior as well as its design and implementation. Additionally, we present three case studies of using a simulator in teaching and describe our experience of its use in a course on system software. From the experience of using the simulator in a pedagogical process we conclude that it decreases the time invested by the students to comprehend the topic, and at the same time it enables in depth understanding. © 2013 Wiley Periodicals, Inc. Comput Appl Eng Educ 23:137–146, 2015; View this article online at http://wileyonlinelibrary.com/journal/cae; DOI

The subgraph isomorphism problem is one of the most important problems for pattern recognition in graphs. Its applications are found in many di®erent disciplines, including chemistry, medicine, and social network analysis. Because of the N P-completeness of the problem, the existing exact algorithms exhibit an exponential worst-case running time. In this paper, we propose several improvements to the well-known Ullmann's algorithm for the problem. The improvements lower the time consumption as well as the space requirements of the algorithm. We experimentally demonstrate the e±ciency of our improvement by comparing it to another set of improvements called FocusSearch, as well as other state-of-the-art algorithms, namely VF2 and LAD. 1 row = select an unmatched row; 2 for col ∈ U :M d (row, col) = 1 do 3 if d = n then 4 subgraph isomorphism found; 5 else 6 M tmp = filter(M d ); 7 M d+1 = refine(M tmp ); 8 findIso(M d+1 , d + 1);