Kernekoncepter
This paper introduces two novel graph partitioning problems motivated by optimizing big data computing applications: (1) workload-driven balanced graph partitioning to optimize the performance of specific workloads, and (2) motif-driven balanced graph partitioning to optimize the computation of graph motifs. The paper provides formal problem definitions, complexity analyses, and bi-criteria approximation algorithms with performance guarantees for these problems.
Resumé
The paper introduces two novel graph partitioning problems motivated by optimizing big data computing applications:
Workload-Driven Balanced Graph Partitioning (WkBGP):
- Aims to partition the graph to optimize the performance of specific workloads, rather than just minimizing the cut edges.
- Formally defines the WkBGP problem and shows it is NP-complete.
- Proposes a bi-criteria O(√log n log k)-approximation algorithm using semidefinite programming and rounding techniques.
Motif-Driven Balanced Graph Partitioning (MkBGP):
- Aims to partition the graph to optimize the computation of graph motifs, rather than just minimizing the cut edges.
- Formally defines the MkBGP problem and shows it is NP-complete even for the special case of k=2 and the motif being a triangle.
- Proves the inapproximability of MkBGP, showing there are no efficient algorithms with finite approximation ratio.
- Proposes a bi-criteria O(√log n log k)-approximation algorithm for the special case where the motif is a triangle, using semidefinite programming.
The paper provides a comprehensive theoretical analysis of the complexities and approximability of these two novel graph partitioning problems, and designs efficient approximation algorithms with performance guarantees.