Scheduling with Communication Delays

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Inapproximability and Polynomial-Time Approximation Algorithm for UET Tasks on Structured Processor Networks

We investigate complexity and approximation results on a processor networks where the communication delay depends on the distance between the processors performing tasks. We then prove that there is no heuristic with a performance guarantee smaller than 4/3 for makespan minimization for precedence graph on a large class of processor networks like hypercube, grid, torus, and so forth, with a fixed diameter ∈ℕ. We extend complexity results when the precedence graph is a bipartite graph. We also design an efficient polynomial-time (2)-approximation algorithm for the makespan minimization on processor networks with diameter

The k-Sparsest Subgraph Problem

Given a simple undirected graph G = (V, E) and an integer k ≤ |V |, the k-sparsest subgraph problem asks for a set of k vertices that induce the minimum number of edges. As a generalization of the classical independent set problem, k-sparsest subgraph cannot admit (unless P = N P) neither an approximation nor an FPT algorithm (parameterized by the number of edges in the solution) in all graph classes where independent set is N P-hard. Thus, it appears natural to investigate the approximability and fixed parameterized tractability of k-sparsest subgraph in graph classes where independent set is polynomial, such as subclasses of perfect graphs. In this paper, we first present a simple greedy tight 2-approximation algorithm in proper interval graphs, and then we use dynamic programming to design a PTAS in proper interval graph and an FPT algorithm in interval graphs (parameterized by the number of edges in the solution)

On the hardness of approximating the UET-UCT scheduling problem with hierarchical communications

We consider the unit execution time unit communication time (UET-UCT) scheduling model with hierarchical communica tions [CITE], and we study the impact of the hierarchical communications hypothesis on the hardness of approximation. We prove that there is no polynomial time approximation algorithm with performance guarantee smaller than 5/4 (unless P = NP). This result is an extension of the result of Hoogeveen et al. [CITE] who proved that there is no polynomial time ρ-approximation algorithm with p < 7/6 for the classical UET-UCT scheduling problem with homogeneous communication delays and an unrestricted number of identical machines