Erratum to “An approximation algorithm for maximum triangle packing”

An Approximation Algorithm for Maximum Triangle Packing

We present a randomized ( 89 169 − )-approximation algorithm for the weighted maximum triangle packing problem, for any given > 0. This is the first algorithm for this problem whose performance guarantee is better than 1 2 . The algorithm also improves the best-known approximation bound for the maximum 2-edge path packing problem. © 2005 Elsevier B.V. All rights reserved.

An Improved Randomized Approximation Algorithm for Maximum Triangle Packing

This paper deals with the maximum triangle packing problem. For this problem, Hassin and Rubinstein gave a randomized polynomial-time approximation algorithm that achieves an expected ratio of 43 83 (1− ) (≈ 0.518(1− )) for any constant > 0. By modifying their algorithm, we obtain a new randomized polynomial-time approximation algorithm for the problem which achieves an expected ratio of 0.5257...

An Approximation Algorithm for Maximum Packing of 3-Edge Paths

A Deterministic Approximation Algorithm for Maximum 2-Path Packing

This paper deals with the maximum-weight 2-path packing problem (M2PP), which is the problem of computing a set of vertex-disjoint paths of length 2 in a given edge-weighted complete graph so that the total weight of edges in the paths is maximized. Previously, Hassin and Rubinstein gave a randomized cubic-time approximation algorithm for M2PP which achieves an expected ratio of 35 67 − ≈ 0.522...

An approximation algorithm for square packing

We consider the problem of packing squares into bins which are unit squares, where the goal is to minimize the number of bins used. We present an algorithm for this problem with an absolute worst-case ratio of 2, which is optimal provided P 6= NP.