Design Of Algorithms And Analysis Of The Call Control Problem With Penalty Costs

In this thesis,we consider the problem of embedding directed hypergraph into a path and the recoverable robust call control problem with penalty costs.(1)The problem of embedding directed hypergraph into a path is described as follows:given a bidirected path and a directed hypergraph,each arc in bidirected path has a weight,and each directed hyperedge in directed hypergraph has a demand and penalty cost.Any directed hyperedge can be accepted or rejected.A directed hyperedge is rejected with penalty cost.Otherwise,the load of each arc in the bidirected path is the total demand of the accepted directed hyperedges which contains the arc multiplied by the weight of the arc.The objective is to find an accepted subset of directed hyperedges to minimize the maximum load in bidirected path plus the penalty costs of the rejected hyperedges.(2)The recoverable robust call control problem with penalty costs is described as follows:given a line and a set of request calls,each edge in line has a weight,each request call has a demand and penalty cost,but the exact value is uncertain.Any request call can be accepted or rejected.A request call is rejected with penalty cost.Otherwise,the load of each edge in line is the total demand of the accepted request calls which contains the edge multiplied by the weight of the edge.The objective is to find an accepted subset of request calls to minimize the maximum load in line plus the penalty costs of the rejected request calls.In this thesis,we first prove that the problem of embedding directed hypergraph into a path is a NP-hard problem,we then design a 1.58-approximation algorithm to solve the problem.For the recoverable robust call control problem with penalty costs,we present a randomized rounding 1.58-approximation algorithm.In particular,when there are two edges in a line and two scenarios,an accurate dynamic programming algorithm is designed.Based on the dynamic programming algorithm,we also design a fully polynomial-time approximation scheme to solve the recoverable robust call control problem with penalty costs in the special case.