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An instance of Hypergraph Max k-Cut with given sizes of parts (or Hyp Max k-Cut with gsp) consists of a hypergraph H = (V, E), nonnegative weights ws defined on its edges S ∈ E, and k positive integers p1,..., pk such that $$ \Sigma _{i = 1}^k pi = {\mathbf{ }}|V| $$ . It is required to partition the vertex set V into k parts X1,..., Xk, with each part X ...
We study the two-machine flow shop problem with minimum delays. The problem is known to be strongly NP-hard even in the case of unit processing times and to be approximable within a factor of 2 of the length of an optimal schedule in the general case. The question whether there exists a polynomial-time algorithm with a better approximation ratio has been posed by several researchers but still remains...
We give first constant-factor approximations for various cases of the coupled-task single machine and two-machine flow shop scheduling problems with exact delays and makespan as the objective function. In particular, we design 3.5- and 3-approximation algorithms for the general cases of the single-machine and the two-machine problems, respectively. We also prove that the existence of a (2−ε)-approximation...
In this paper the process of data transmission in optical communication networks is modeled as a shop-type scheduling problem, where channels (wavelengths) are treated as machines. We formulate an Open Block problem with the minimum makespan objective (an problem) in which a relation of a new type between the operations of each job is introduced: any two operations of a job...
In the m-peripatetic traveling salesman problem (m-PSP), given an n-vertex complete undirected edge-weighted graph, it is required to find m edge disjoint Hamiltonian cycles of minimum total weight. The problem was introduced by Krarup (1974) and has network design and scheduling applications. It is known that 2-PSP is NP-hard even in the metric case and does not admit any constant-factor approximation...
In the CUT PACKING problem, given an undirected connected graph G, it is required to find the maximum number of pairwise edge disjoint cuts in G. It is an open question if CUT PACKING is NP-hard on general graphs. In this paper we prove that the problem is polynomially solvable on Seymour graphs which include both all bipartite and all series-parallel graphs. We also consider the weighted version...
In this paper we demonstrate a general method of designing constant-factor approximation algorithms for some discrete optimization problems with cardinality constraints. The core of the method is a simple deterministic (“pipage”) procedure of rounding of linear relaxations. By using the method we design a (1 − (1 − 1/k)k)-approximation algorithm for the maximum coverage problem where k is the maximum...
In this paper we consider coupled-task single-machine and two-machine flow shop scheduling problems with exact delays, unit processing times, and the makespan as an objective function. The main results of the paper are fast 7/4- and 3/2-approximation algorithms for solving the single- and two-machine problems, respectively.
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