Complexity of domination-type problems in graphs
Nordic Journal of Computing
Determinant: Old Algorithms, New Insights (Extended Abstract)
SWAT '98 Proceedings of the 6th Scandinavian Workshop on Algorithm Theory
Independent Sets with Domination Constraints
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
The intractability of computing the minimum distance of a code
IEEE Transactions on Information Theory
Parameterized complexity of weak odd domination problems
FCT'13 Proceedings of the 19th international conference on Fundamentals of Computation Theory
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We develop an O(n3) algorithm for deciding if an n-vertex digraph has a subset of vertices with the property that each vertex of the graph has an even number of arcs into the subset. This algorithm allows us to give a combinatorial interpretation of Gauss-Jordan and Gauss elimination on square boolean matrices. In addition to solving this independence-mod-2 (even) set existence problem we also give efficient algorithms for related domination-mod-2 (odd) set existence problems on digraphs. However, for each of the four combinations of these two properties we show that even though the existence problem on digraphs is tractable, the problems of deciding the existence of a set of size exactly k, larger than k, or smaller than k, for a given k, are all NP-complete for undirected graphs.