Graph algorithms for planning and partitioning

In this thesis, we present new approximation algorithms as well as hardness of approximation results for several planning and partitioning problems. In planning problems, one is typically given a set of locations to visit, along with timing constraints, such as deadlines for visiting them; The goal is to visit a large number of locations as efficiently as possible. We give the first approximation algorithms for problems such as ORIENTEERING, DEADLINES-TSP, and TIME-WINDOWS-TSP, as well as results for planning in stochastic graphs (Markov decision processes). The goal in partitioning problems is to partition a set of objects into clusters while satisfying "split" or "combine" constraints on pairs of objects. We consider three kinds of partitioning problems, viz. CORRELATION-C LUSTERING, SPARSEST-CUT, and M ULTICUT. We give approximation algorithms for the first two, and improved hardness of approximation results for SPARSEST-C UT and MULTICUT.

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