Approximation algorithms for Min-k-overlap problems using the principal lattice of partitions approach

Greedy splitting algorithms for approximating multiway partition problems

“…We first show a simple lemma (Lemma 1) that holds for all submodular systems, then derive guarantees for various MPPs by easy calculations. In particular, the same or improved results compared to [13,23,27,26] can be obtained in a much simpler way. The next table shows the main approximation results (due to the greedy algorithm).…”

“…Queyranne [26] claimed that the greedy algorithm in [13,27] can be extended to approximate k-PPSSS, enjoying the same performance guarantee of 2 − 2 k . Narayanan, Roy and Patkar [23] showed (without showing the running time) that, k-PPH-T1 and k-PPH-T3 can be approximated within factors d max (1 − 1 n ) and 2 − 2 n respectively, where d max is the maximum degree of hyperedges.…”

“…We note that, all the proofs in [23,26,27] use specific structures (cut tree or the so-called principal partition), which are rather complicated and cannot be applied to general submodular systems (see [1]). In this paper, we consider the greedy algorithm.…”