The maximum k-colorable subgraph problem for chordal graphs
Information Processing Letters
Approximation algorithms for fixed job schedule problems
Operations Research - Supplement
Trans-dichotomous algorithms for minimum spanning trees and shortest paths
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
On-line scheduling of jobs with fixed start and end times
Theoretical Computer Science - Special issue on dynamic and on-line algorithms
Randomized algorithms
On the k-coloring of intervals
Discrete Applied Mathematics
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Bounding the Power of Preemption in Randomized Scheduling
SIAM Journal on Computing
Online computation and competitive analysis
Online computation and competitive analysis
Computationally Manageable Combinational Auctions
Management Science
Patience is a virtue: the effect of slack on competitiveness for admission control
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Undirected single-source shortest paths with positive integer weights in linear time
Journal of the ACM (JACM)
Online scheduling with hard deadlines
Journal of Algorithms
A unified approach to approximating resource allocation and scheduling
Journal of the ACM (JACM)
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Approximating the Throughput of Multiple Machines in Real-Time Scheduling
SIAM Journal on Computing
Priority Queues: Small, Monotone and Trans-dichotomous
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
Aligning two fragmented sequences
Discrete Applied Mathematics - Special issue: Computational molecular biology series issue IV
Approximation Algorithms for the Job Interval Selection Problem and Related Scheduling Problems
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
New hardness results for congestion minimization and machine scheduling
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
New hardness results for congestion minimization and machine scheduling
Journal of the ACM (JACM)
Randomized priority algorithms
Theoretical Computer Science
How well can primal-dual and local-ratio algorithms perform?
ACM Transactions on Algorithms (TALG)
Online interval coloring and variants
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
WAOA'04 Proceedings of the Second international conference on Approximation and Online Algorithms
Scheduling with a minimum number of machines
Operations Research Letters
Priority algorithms for the subset-sum problem
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Interval selection with machine-dependent intervals
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
Online selection of intervals and t-intervals
Information and Computation
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Given a set of jobs, each consisting of a number of weighted intervals on the real line, and a positive integer m, we study the problem of selecting a maximum weight subset of the intervals such that at most one interval is selected from each job and, for any point p on the real line, at most m intervals containing p are selected. We give a parameterized algorithm GREEDYα that belongs to the class of "myopic" algorithms, which are deterministic algorithms that process the given intervals in order of non-decreasing right endpoint and can either reject or select each interval (rejections are irrevocable). We show that there are values of the parameter α so that GREEDYα produces a 2-approximation in the case of unit weights, an 8-approximation in the case of arbitrary weights, and a (3 + 2√2)- approximation in the case where the weights of all intervals corresponding to the same job are equal. We also show that no deterministic myopic algorithm can achieve ratio better than 2 in the case of unit weights, better than ≈ 7.103 in the case of arbitrary weights, and better than 3 + 2√2 in the case where the weights of all intervals corresponding to the same job are equal. Furthermore, we give additional results for the case where all intervals have the same length as well as a lower bound of e/e-1≈ 1.582 on the approximation ratio of randomized myopic algorithms in the case of unit weights.