Approximation hardness of optimization problems in intersection graphs of d-dimensional boxes
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation hardness of dominating set problems in bounded degree graphs
Information and Computation
The parameterized complexity of the induced matching problem
Discrete Applied Mathematics
On Distance-3 Matchings and Induced Matchings
Graph Theory, Computational Intelligence and Thought
The parameterized complexity of the induced matching problem in planar graphs
FAW'07 Proceedings of the 1st annual international conference on Frontiers in algorithmics
On distance-3 matchings and induced matchings
Discrete Applied Mathematics
Minimizing flow time in the wireless gathering problem
ACM Transactions on Algorithms (TALG)
Approximability results for the maximum and minimum maximal induced matching problems
Discrete Optimization
New results on maximum induced matchings in bipartite graphs and beyond
Theoretical Computer Science
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Damaschke, Müller, and Kratsch [Inform. Process. Lett., 36 (1990), pp. 231--236] gave a polynomial-time algorithm to solve the minimum dominating set problem in convex bipartite graphs $B=(X \cup Y,E)$, that is, where the nodes in Y can be ordered so that each node of X is adjacent to a contiguous sequence of nodes. Gamble et al. [Graphs Combin., 11 (1995), pp. 121--129] gave an extension of their algorithm to weighted dominating sets. We formulate the dominating set problem as that of finding a minimum weight subset of elements of a graphic matroid, which covers each fundamental circuit and fundamental cut with respect to some spanning tree T. When T is a directed path, this simultaneous covering problem coincides with the dominating set problem for the previously studied class of convex bipartite graphs. We describe a polynomial-time algorithm for the more general problem of simultaneous covering in the case when T is an arborescence. We also give NP-completeness results for fairly specialized classes of the simultaneous cover problem. These are based on connections between the domination and induced matching problems.