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
Improved Approximation Algorithms for Shop Scheduling Problems
SIAM Journal on Computing
Chernoff-Hoeffding Bounds for Applications with Limited Independence
SIAM Journal on Discrete Mathematics
An introduction to the analysis of algorithms
An introduction to the analysis of algorithms
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Nonoverlapping local alignments (weighted independent sets of axis-parallel rectangles)
Discrete Applied Mathematics - Special volume on computational molecular biology
On the complexity of coupled-task scheduling
Discrete Applied Mathematics - Special issue on models and algorithms for planning and scheduling problems
Makespan minimization in job shops: a polynomial time approximation scheme
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Competitive non-preemptive call control
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Patience is a virtue: the effect of slack on competitiveness for admission control
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the third international conference on Graphs and optimization
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
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Non-approximability results for optimization problems on bounded degree instances
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A d/2 approximation for maximum weight independent set in d-claw free graphs
Nordic Journal of Computing
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
On-line Scheduling with Hard Deadlines (Extended Abstract)
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
ESA '95 Proceedings of the Third Annual European Symposium on Algorithms
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Approximation schemes for constrained scheduling problems
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Routing and Admission Control in Networks with Advance Reservations
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
On the computational complexity of 2-interval pattern matching problems
Theoretical Computer Science
Hardness of approximation for non-overlapping local alignments
Discrete Applied Mathematics
Local ratio: A unified framework for approximation algorithms. In Memoriam: Shimon Even 1935-2004
ACM Computing Surveys (CSUR)
Approximation hardness of optimization problems in intersection graphs of d-dimensional boxes
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Dotted interval graphs and high throughput genotyping
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Designing optimally multiplexed SNP genotyping assays
Journal of Computer and System Sciences - Special issue on bioinformatics II
Theoretical Computer Science - Parameterized and exact computation
An efficient approximation for the generalized assignment problem
Information Processing Letters
Admission control with advance reservations in simple networks
Journal of Discrete Algorithms
Optimization problems in multiple-interval graphs
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Extracting constrained 2-interval subsets in 2-interval sets
Theoretical Computer Science
Approximating the 2-interval pattern problem
Theoretical Computer Science
Spectrum Bidding in Wireless Networks and Related
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
On the parameterized complexity of multiple-interval graph problems
Theoretical Computer Science
Complexity issues in color-preserving graph embeddings
Theoretical Computer Science
Optimization problems in multiple-interval graphs
ACM Transactions on Algorithms (TALG)
A PTAS for the weighted 2-interval pattern problem over the preceding-and-crossing model
COCOA'07 Proceedings of the 1st international conference on Combinatorial optimization and applications
Optimization problems in multiple subtree graphs
Discrete Applied Mathematics
How well can primal-dual and local-ratio algorithms perform?
ACM Transactions on Algorithms (TALG)
Matching and P2-packing: weighted versions
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
How well can primal-dual and local-ratio algorithms perform?
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Approximating the 2-interval pattern problem
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Using fractional primal-dual to schedule split intervals with demands
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Improved algorithms for largest cardinality 2-interval pattern problem
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
ACM Transactions on Algorithms (TALG)
Online selection of intervals and t-intervals
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Optimization problems in multiple subtree graphs
WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
Theoretical Computer Science
Using fractional primal-dual to schedule split intervals with demands
Discrete Optimization
Combination of parallel machine scheduling and vertex cover
Theoretical Computer Science
Topology independent protein structural alignment
WABI'07 Proceedings of the 7th international conference on Algorithms in Bioinformatics
Matching and Weighted P2-Packing: Algorithms and Kernels
Theoretical Computer Science
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We consider the problem of scheduling jobs that are given as groups of non-intersecting segments on the real line. Each job Jj is associated with an interval, Ij, which consists of up to t segments, for some t ≥ 1, a positive weight, wj, and two jobs are in conflict if any of their segments intersect. Such jobs show up in a wide range of applications, including the transmission of continuous-media data, allocation of linear resources (e.g. bandwidth in linear processor arrays), and in computational biology/geometry. The objective is to schedule a subset of non-conflicting jobs of maximum total weight.In a single machine environment, our problem can be formulated as the problem of finding a maximum weight independent set in a t-interval graph (the special case of t = 1 is an ordinary interval graph). We show that, for t ≥ 2, this problem is APX-hard, even for highly restricted instances. Our main result is a 2t-approximation algorithm for general instances, based on a novel fractional version of the Local Ratio technique. Previously, the problem was considered only for proper union graphs, a restricted subclass of t-interval graphs, and the approximation factor achieved was (2t - 1 + 1/2t). A bi-criteria polynomial time approximation scheme (PTAS) is developed for the subclass of t-union graphs.In the online case, we consider uniform weight jobs that consist of at most two segments. We show that when the resulting 2-interval graph is proper, a simple greedy algorithm is 3-competitive, while any randomized algorithm has competitive ratio at least 2.5. For general instances, we give a randomized O(log2 R)-competitive (or O((log R)2+ε)-competitive) algorithm, where R is the known (unknown) ratio between the longest and the shortest segment in the input sequence.