SIAM Journal on Discrete Mathematics
Analysis of disk arm movement for large sequential reads
PODS '92 Proceedings of the eleventh ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
The primal-dual method for approximation algorithms and its application to network design problems
Approximation algorithms for NP-hard problems
Nonoverlapping local alignments (weighted independent sets of axis-parallel rectangles)
Discrete Applied Mathematics - Special volume on computational molecular biology
A 2-Approximation Algorithm for the Undirected Feedback Vertex Set Problem
SIAM Journal on Discrete Mathematics
A unified approach to approximating resource allocation and scheduling
Journal of the ACM (JACM)
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
On the Approximation Properties of Independent Set Problem in Degree 3 Graphs
WADS '95 Proceedings of the 4th International Workshop on Algorithms and Data Structures
Greedy Approximations of Independent Sets in Low Degree Graphs
ISAAC '95 Proceedings of the 6th International Symposium on Algorithms and Computation
On the Equivalence between the Primal-Dual Schema and the Local Ratio Technique
SIAM Journal on Discrete Mathematics
Optimization problems in multiple-interval graphs
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
On the parameterized complexity of multiple-interval graph problems
Theoretical Computer Science
Optimization problems in multiple-interval graphs
ACM Transactions on Algorithms (TALG)
Theoretical Computer Science
Scheduling jobs with multiple non-uniform tasks
Euro-Par'13 Proceedings of the 19th international conference on Parallel Processing
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We consider the problem of scheduling jobs that are given as groups of non-intersecting intervals on the real line. Each job j is associated with a t-interval, which consists of up to t segments, for some t ≥ 1, a demand, dj∈[0,1], and a weight, w(j). A schedule is a collection of jobs, such that, for every $s \in {\mathbb R}$, the total demand of the jobs in the schedule whose t-interval contains s does not exceed 1. Our goal is to find a schedule that maximizes the total weight of scheduled jobs. We present a 6t-approximation algorithm that uses a novel extension of the primal-dual schema called fractional primal-dual. The first step in a fractional primal-dual r-approximation algorithm is to compute an optimal solution, x*, of an LP relaxation of the problem. Next, the algorithm produces an integral primal solution x, and a new LP, denoted by P′, that has the same objective function as the original problem, but contains inequalities that may not be valid with respect to the original problem. Moreover, x* is a feasible solution of P′. The algorithm also computes a solution y to the dual of P′. x is r-approximate, since its weight is bounded by the value of y divided by r. We present a fractional local ratio interpretation of our 6t-approximation algorithm. We also discuss the connection between fractional primal-dual and the fractional local ratio technique. Specifically, we show that the former is the primal-dual manifestation of the latter.