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Scheduling Split Intervals
, 2002
"... We consider the problem of scheduling jobs that are given as groups of nonintersecting 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 of their segments intersect. Such jobs show up in a I.I Problem Statement and Mo ..."
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Cited by 63 (5 self)
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We consider the problem of scheduling jobs that are given as groups of nonintersecting 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 of their segments intersect. Such jobs show up in a I.I Problem Statement and Motivation. We wide range of applications, including the transmission consider the problem of scheduling jobs that are given of continuousmedia data, allocation of linear resources as groups of nonintersecting segments on the real line. (e.g. bandwidth in linear processor arrays), and in Each job Jj is associated with a tinterval, Ij, which
Sequential Elimination Graphs
"... A graph is chordal if it does not contain any induced cycle of size greater than three. An alternative characterization of chordal graphs is via a perfect elimination ordering, which is an ordering of the vertices such that, for each vertex v, the neighbors of v that occur later than v in the order ..."
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Cited by 13 (2 self)
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A graph is chordal if it does not contain any induced cycle of size greater than three. An alternative characterization of chordal graphs is via a perfect elimination ordering, which is an ordering of the vertices such that, for each vertex v, the neighbors of v that occur later than v in the ordering form a clique. Akcoglu et al [2] define an extension of chordal graphs whereby the neighbors of v that occur later than v in the elimination order have at most k independent vertices. We refer to such graphs as sequentially kindependent graphs. Clearly this extension of chordal graphs also extends the class of (k+1)clawfree graphs. We study properties of such families of graphs, and we show that several natural classes of graphs are sequentially kindependent for small k. In particular, any intersection graph of translates of a convex object in a two dimensional plane is a sequentially 3independent graph; furthermore, any planar graph is a sequentially 3independent graph. For any fixed constant k, we develop simple, polynomial time approximation algorithms for sequentially kindependent graphs with respect to several wellstudied NPcomplete problems based on this ksequentially independent ordering. Our generalized formulation unifies and extends several previously known results. We also consider other classes of sequential elimination graphs.
Approximation Hardness of Optimization Problems in Intersection Graphs of ddimensional Boxes
 proceedings of the 16th Annual ACMSIAM Symposium on Discrete Algorithms
, 2005
"... Abstract The Maximum Independent Set problem in dbox graphs, i.e., in the intersection graphs of axisparallel rectangles in R d , is a challenge open problem. For any fixed d ≥ 2 the problem is NPhard and no approximation algorithm with ratio o(log d−1 n) is known. In some restricted cases, e.g. ..."
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Cited by 8 (0 self)
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Abstract The Maximum Independent Set problem in dbox graphs, i.e., in the intersection graphs of axisparallel rectangles in R d , is a challenge open problem. For any fixed d ≥ 2 the problem is NPhard and no approximation algorithm with ratio o(log d−1 n) is known. In some restricted cases, e.g., for dboxes with bounded aspect ratio, a PTAS exists Introduction The intersection graph of a family of sets S v , v ∈ V , is a graph with vertex set V such that u is adjacent to v if and only if S u ∩ S v = ∅. The family {S v , v ∈ V } is an intersection representation of this graph. Geometrical models of intersection graphs deal with families of subsets of R d with some geometric properties. In this paper we are mainly interested in families of axis For convenience, terms an interval and a rectangle are used for 1box and 2box, respectively. In this paper we describe a generic approach to approximation hardness results for many graph optimization problems as, e.g., Minimum Vertex Cover,
Algorithms and Complexities of a few Sequence Comparison Problems
, 2005
"... The modern era of molecular biology began with the discovery of the double helical structure of DNA. Today, sequencing nucleic acids, the determination of genetic information at the most fundamental level, is a major tool of biological research [30]. This revolution in biology has created a huge amo ..."
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The modern era of molecular biology began with the discovery of the double helical structure of DNA. Today, sequencing nucleic acids, the determination of genetic information at the most fundamental level, is a major tool of biological research [30]. This revolution in biology has created a huge amount of data at great speed by directly reading DNA sequences. The growth rate of data volume is exponential. For instance,