Parallel circle-cover algorithms
Information Processing Letters
An optimal parallel algorithm for the minimum circle-cover problem
Information Processing Letters
Linear time algorithms on circular-arc graphs
Information Processing Letters
Improved performance of the greedy algorithm for partial cover
Information Processing Letters
Using homogeneous weights for approximating the partial cover problem
Journal of Algorithms
Scheduling Algorithms
Computational Complexity of Machine Learning
Computational Complexity of Machine Learning
Dependent Rounding in Bipartite Graphs
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Covering Problems with Hard Capacities
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
Improved Approximation Algorithms for the Partial Vertex Cover Problem
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Distributions on Level-Sets with Applications to Approximation Algorithms
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Journal of Algorithms - Special issue: Twelfth annual ACM-SIAM symposium on discrete algorithms
Approximation algorithms for partial covering problems
Journal of Algorithms
Local ratio: A unified framework for approximation algorithms. In Memoriam: Shimon Even 1935-2004
ACM Computing Surveys (CSUR)
Optimizing over Consecutive 1's and Circular 1's Constraints
SIAM Journal on Optimization
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Algorithms for capacitated rectangle stabbing and lot sizing with joint set-up costs
ACM Transactions on Algorithms (TALG)
A Primal-Dual Bicriteria Distributed Algorithm for Capacitated Vertex Cover
SIAM Journal on Computing
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Multi-item lot-sizing with joint set-up costs
Mathematical Programming: Series A and B
An improved approximation algorithm for vertex cover with hard capacities
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Approximation of partial capacitated vertex cover
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Approximation algorithms for capacitated rectangle stabbing
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
Improved complexity bounds for location problems on the real line
Operations Research Letters
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In the Capacitated Arc Stabbing problem (CAS) we are given a set of arcs and a set of points on a circle. We say that a point p covers, or stabs, an arc A if p is contained in A. Each point has a weight and a capacity that determines the number of arcs it may cover. The goal is to find a minimum weight set of points that stabs all the arcs. CAS models a periodic multi-item lot sizing problem in which we are given a set of production requests each with its own periodic release time and deadline. Production takes place in batches of bounded capacity: each time unit t is associated with a capacity c(t) and weight w(t), where c(t) bounds the number of requests that can be manufactured at time t, and w(t) is a fixed cost for manufacturing any positive number of requests up to c(t) at time t. The goal is to find a minimum weight periodic schedule. We present a polynomial time algorithm for CAS that is based on a non-trivial reduction to Capacitated Interval Stabbing. Our approach applies to both hard and soft capacities. We also consider two variants of CAS in which some arcs may remain uncovered: in the partial variant there is a covering requirement g, and the goal is to find a minimum weight set of points that covers at least g arcs; and in the prize collecting variant each arc has a penalty that must be paid if this arc is not covered.