Improved approximation algorithms for weighted 2-path partitions

Amotz Bar-Noy, David Peleg, George Rabanca, Ivo Vigan

Research output: Contribution to journalArticlepeer-review


We investigate two NP-complete vertex partition problems on edge-weighted complete graphs with 3k vertices. The first problem asks to partition the graph into k vertex disjoint paths of length 2 (referred to as 2-paths) such that the total weight of the paths is maximized. We present a cubic time approximation algorithm that computes a 2-path partition whose total weight is at least.5833 of the weight of an optimal partition, improving upon the (.5265−ϵ)-approximation algorithm of Tanahashi and Chen (2010). Restricting the input to graphs with edge weights in {0,1}, we present a.75 approximation algorithm improving upon the.55-approximation algorithm of Hassin and Schneider (2013). Combining this algorithm with a previously known approximation algorithm for the 3-SET PACKING problem, we obtain a.6-approximation algorithm for the problem of partitioning a {0,1}-edge-weighted graph into k vertex disjoint triangles of maximum total weight. The best known approximation algorithm for general weights is due to Chen and Tanahashi (2009) and achieves an approximation ratio of.5257.

Original languageEnglish
Pages (from-to)15-37
Number of pages23
JournalDiscrete Applied Mathematics
StatePublished - 20 Apr 2018


  • Approximation algorithms
  • Graph factor
  • Graph packing
  • Graph partitioning

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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