Citation Context

...ot write those edges explicitly. Our algorithm does not need an explicit representation of edges and hence solves this version too. The most general case with factor 2 was the Steiner forest problem (=-=[3]-=-), where f(S) is 0-1 proper function. Hence our algorithm puts the generalized case at par with this special case. Our algorithm falls into the class of rounding algorithms. Rounding algorithms use an...

Citation Context

...ntralized optimum of the connection game, i.e. the network of bought edges which minimizes the sum of the players’ contributions, is the classic network design problem of the generalized Steiner tree =-=[1, 10]-=-. 1sOur Results We are most interested in deterministic Nash equilibria of the connection game, and in the optimistic price of anarchy, as the pessimistic price of anarchy in our game can be quite bad...

Citation Context

...one can obtain a 2-approximation algorithm for this problem using the primal-dual method, but one must use a different integer programming formulation of the problem. It has been shown that the integrality gap for the hitting set formulation of the problem is Ω(logn) [30]. We now turn to modifications of the basic primal-dual algorithm of Bar-Yehuda and Even. The first is a relatively simple idea: once a feasible solution A has been obtained, we should examine the elements of A and delete any that are not needed for a feasible solution. This idea was first introduced by Goemans and Williamson [41], but we will present here a refinement discovered independently by Klein and Ravi [53] and Saran, Vazirani, and Young [64]. They showed that it is useful for the analysis of the algorithm to examine the elements of A for possible deletion in a certain order; in particular, in the reverse of the order in which the elements of A were added. This part of the algorithm is sometimes called the reverse delete. We present the modified algorithm in Figure 2. To see why the reverse delete step is useful for the analysis, consider the set Til chosen in the lth iteration of the algorithm. Let Al be the ...

Citation Context

...ted to different refineries (multiple wells may be connected to the same refinery). For the special case of step function pricing, this reduces the generalized network connectivity problem, solved in =-=[9, 1]-=-. The essence of this problem is minimizing the cost of a sub-graph in which given pairs of points are connected. ffl Selective network design: some subset of k wells must be connected to the (single)...