Network Design for <i>s</i> - <i>t</i> Effective Resistance

We consider a new problem of designing network with small s - t effective resistance. In this problem, we are given an undirected graph G = (V,E) , two designated vertices s,t ∈ V and budget k . The goal is to choose subgraph at most edges minimize the This interpolation between shortest path minimum cost flow has applications in electrical design. present several algorithmic hardness results for its variants. On side, show that NP-hard, weighted version hard approximate within factor smaller than assuming small-set expansion conjecture. analyze convex programming relaxation design constant approximation algorithm. key rounding algorithm randomized path-rounding procedure based on optimality conditions decomposition fractional solution. also use dynamic obtain fully polynomial time scheme when input series-parallel graph, better ratio integrality gap program these graphs.