Improved Budgeted Connected Domination and Budgeted Edge-Vertex Domination

• Improved approximation algorithm for Budgeted Connected Dominating Set. Optimal Star Edge-Vertex Domination. We consider the version of classical Set problem (BCDS). Given a graph G and budget k , we seek connected subset at most vertices maximizing number dominated in . improve over previous ( 1 − e ) / 13 state art [Khuller, Purohit, Sarpatwar, SODA 2014 ] by introducing new method performing tree decompositions analysis algorithm. This approach provides 12 guarantee. By generalizing analysis, are able to obtain further improvement 7 8 11 On other hand, prove + ϵ inapproximability bound, any > 0 holding also if is required have star as subgraph. In latter case, design another with matching Also, examine edge-vertex domination variant, where an edge dominates its endpoints all neighboring them. Domination (BEVD), (not necessarily connected) edges -approximation -inapproximability reductions to/from maximum coverage problem. Finally, study “dual” Partial (PEVD) problem, present log-approximation reduction partial cover