Maximum rooted connected expansion

Prefetching constitutes a valuable tool toward the goal of efficient Web surfing. As result, estimating amount resources that need to be preloaded during surfer's browsing becomes an important task. In this regard, prefetching can modeled as two-player combinatorial game (Fomin et al. (2014) [6] ), where surfer and marker alternately play on given graph (representing graph). During its turn, chooses set k nodes mark (prefetch), whereas surfer, represented token resting nodes, moves neighboring node (Web resource). The objective is reach unmarked before all become marked wins. Intuitively, since step-by-step traversing subset in graph, satisfactory procedure would load cache (without any delay) lying neighborhood growing subset. Motivated by above, we consider following maximization problem which refer Maximum Rooted Connected Expansion (MRCE) problem. Given G root v 0 , wish find vertices S such connected, contains ratio | N [ ] maximized, denotes closed is, with at least one neighbor . We prove NP-hard even when input restricted split graph. On positive side, demonstrate Polynomial Time Approximation Scheme (PTAS) for graphs. Furthermore, present 1 6 ( ? e ) -approximation algorithm general graphs based techniques Budgeted Domination (Khuller [20] ). Finally, provide polynomial-time special case interval Our returns optimal solution MRCE O n 3 time, number logarithmic space.