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68
Complexity and Algorithms for Reasoning About Time: A GraphTheoretic Approach
, 1992
"... Temporal events are regarded here as intervals on a time line. This paper deals with problems in reasoning about such intervals when the precise topological relationship between them is unknown or only partially specified. This work unifies notions of interval algebras in artificial intelligence ..."
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Cited by 86 (11 self)
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Temporal events are regarded here as intervals on a time line. This paper deals with problems in reasoning about such intervals when the precise topological relationship between them is unknown or only partially specified. This work unifies notions of interval algebras in artificial intelligence with those of interval orders and interval graphs in combinatorics. The satisfiability, minimal labeling, all solutions and all realizations problems are considered for temporal (interval) data. Several versions are investigated by restricting the possible interval relationships yielding different complexity results. We show that even when the temporal data comprises of subsets of relations based on intersection and precedence only, the satisfiability question is NPcomplete. On the positive side, we give efficient algorithms for several restrictions of the problem. In the process, the interval graph sandwich problem is introduced, and is shown to be NPcomplete. This problem is als...
Interval Routing Schemes
, 1998
"... Interval routing was introduced to reduce the size of routing tables: a router finds the direction where to forward a message by determining which interval contains the destination address of the message, each interval being associated to one particular direction. This way of implementing a routin ..."
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Cited by 30 (7 self)
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Interval routing was introduced to reduce the size of routing tables: a router finds the direction where to forward a message by determining which interval contains the destination address of the message, each interval being associated to one particular direction. This way of implementing a routing function is quite attractive but very little is known about the topological properties that must satisfy a network to support an interval routing function with particular constraints (shortest paths, limited number of intervals associated to each direction, etc.). In this paper we investigate the study of the interval routing functions. In particular, we characterize the set of networks which support a linear or a linear strict interval routing function with only one interval per direction. We also derive practical tools to measure the efficiency of an interval routing function (number of intervals, length of the paths, etc.), and we describe large classes of networks which support optimal (linear) interval routing functions. Finally, we derive the main properties satisfied by the popular networks used to interconnect processors in a distributed memory parallel computer.
Efficient parallel algorithms for chordal graphs
"... We give the first efficient parallel algorithms for recognizing chordal graphs, finding a maximum clique and a maximum independent set in a chordal graph, finding an optimal coloring of a chordal graph, finding a breadthfirst search tree and a depthfirst search tree of a chordal graph, recognizing ..."
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Cited by 26 (0 self)
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We give the first efficient parallel algorithms for recognizing chordal graphs, finding a maximum clique and a maximum independent set in a chordal graph, finding an optimal coloring of a chordal graph, finding a breadthfirst search tree and a depthfirst search tree of a chordal graph, recognizing interval graphs, and testing interval graphs for isomorphism. The key to our results is an efficient parallel algorithm for finding a perfect elimination ordering.
Optimization of Dynamic Hardware Reconfigurations
, 2001
"... Recent generations of Field Programmable Gate Arrays (FPGA) allow the dynamic reconfiguration of cells on the chip during runtime. For a given problem consisting of a set of tasks with computation requirements modeled by rectangles of cells, several optimization problems such as finding the array o ..."
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Cited by 23 (3 self)
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Recent generations of Field Programmable Gate Arrays (FPGA) allow the dynamic reconfiguration of cells on the chip during runtime. For a given problem consisting of a set of tasks with computation requirements modeled by rectangles of cells, several optimization problems such as finding the array of minimal size to accomplish the tasks within a given time limit are considered. Existing approaches based on ILP formulations to solve these problems as multidimensional packing problems turn out not to be applicable for problem sizes of interest. Here, a breakthrough is achieved in solving these problems to optimality by using the new notion of packing classes. It allows a significant reduction of the search space such that problems of the above type may be solved exactly using a special branchandbound technique. We validate the usefulness of our method by providing computational results.
An Exact Algorithm for HigherDimensional Orthogonal Packing
 Operations Research
, 2006
"... Higherdimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Combining the use of our data structure for characterizing feasible packings with our new classes of lower bounds, and other heuristics, we develop a twolevel tr ..."
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Cited by 21 (3 self)
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Higherdimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Combining the use of our data structure for characterizing feasible packings with our new classes of lower bounds, and other heuristics, we develop a twolevel tree search algorithm for solving higherdimensional packing problems to optimality. Computational results are reported, including optimal solutions for all twodimensional test problems from recent literature.
On moredimensional packing III: Exact Algorithms
, 2000
"... Moredimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Combining the use of our data structure for characterizing feasible packings with our new classes of lower bounds, and other heuristics, we develop a twolevel tree s ..."
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Cited by 16 (6 self)
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Moredimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Combining the use of our data structure for characterizing feasible packings with our new classes of lower bounds, and other heuristics, we develop a twolevel tree search algorithm for solving moredimensional packing problems to optimality. Computational results are reported, including optimal solutions for all twodimensional test problems from recent literature. This is the third in a series of three articles describing new approaches to moredimensional packing.
Fast and simple algorithms for recognizing chordal comparability graphs and interval graphs
 SIAM Journal on Computing
, 1999
"... Abstract. In this paper, we present a lineartime algorithm for substitution decomposition on chordal graphs. Based on this result, we develop a lineartime algorithm for transitive orientation on chordal comparability graphs, which reduces the complexity of chordal comparability recognition from O( ..."
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Cited by 16 (3 self)
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Abstract. In this paper, we present a lineartime algorithm for substitution decomposition on chordal graphs. Based on this result, we develop a lineartime algorithm for transitive orientation on chordal comparability graphs, which reduces the complexity of chordal comparability recognition from O(n 2)toO(n+m). We also devise a simple lineartime algorithm for interval graph recognition where no complicated data structure is involved. Key words. chordal graph, triangulated graph, interval graph, analysis of algorithms, graph theory, substitution decomposition, modular decomposition, cyclefree poset, transitive orientation, graph partitioning, cardinality lexicographic ordering, graph recognition
Finding Minimum Height Elimination Trees For Interval Graphs In Polynomial Time
 BIT
, 1994
"... . The elimination tree plays an important role in many aspects of sparse matrix factorization. The height of the elimination tree presents a rough, but usually effective, measure of the time needed to perform parallel elimination. Finding orderings that produce low elimination trees is therefore im ..."
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Cited by 13 (2 self)
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. The elimination tree plays an important role in many aspects of sparse matrix factorization. The height of the elimination tree presents a rough, but usually effective, measure of the time needed to perform parallel elimination. Finding orderings that produce low elimination trees is therefore important. As the problem of finding minimum height elimination tree orderings is NPhard, it is interesting to concentrate on limited classes of graphs and find minimum height elimination trees for these efficiently. In this paper, we use clique trees to find an efficient algorithm for interval graphs which make an important subclass of chordal graphs. We first illustrate this method through an algorithm that finds minimum height elimination trees for chordal graphs. This algorithm, although of exponential time complexity, is conceptionally simple and leads to a polynomialtime algorithm for finding minimum height elimination trees for interval graphs. AMS subject classifications: 05C50, 65F...
A Compendium of Problems Complete for Symmetric Logarithmic Space
 Computational Complexity
, 1996
"... . The paper's main contributions are a compendium of problems that are complete for symmetric logarithmic space (SL), a collection of material relating to SL, a list of open problems, and an extension to the number of problems known to be SLcomplete. Complete problems are one method of studying SL, ..."
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Cited by 13 (0 self)
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. The paper's main contributions are a compendium of problems that are complete for symmetric logarithmic space (SL), a collection of material relating to SL, a list of open problems, and an extension to the number of problems known to be SLcomplete. Complete problems are one method of studying SL, a class for which programming is nonintuitive. Our exposition helps make the class SL less mysterious and more accessible to other researchers. Key words. Completeness, SL, space complexity, symmetric logarithmic space. Subject classifications. 68Q17. 1. Introduction In this paper we describe problems that are logarithmic space manyone complete for symmetric logarithmic space (SL). Our hope in collecting these problems and extending this list is that more insight can be gained about the relationships between the complexity classes deterministic logarithmic space (DL), SL, and nondeterministic logarithmic space (NL). The symmetric Turing machine model introduced by Lewis & Papadimitriou ...
A Characterization of Networks Supporting Linear Interval Routing
 In 13 th Annual ACM Symposium on Principles of Distributed Computing (PODC
, 1994
"... Compact routing tables are useful to implement routing algorithms on a distributed memory parallel computer. Interval routing is a popular way of building such compact tables. It was already known that any network can support an interval routing function with only one interval per output port as soo ..."
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Cited by 12 (5 self)
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Compact routing tables are useful to implement routing algorithms on a distributed memory parallel computer. Interval routing is a popular way of building such compact tables. It was already known that any network can support an interval routing function with only one interval per output port as soon as one allows intervals to be "cyclic" [13]. However, it might be interesting for practical reasons to allow only the use of "linear" intervals (see [2]). This notion is particularly useful to derive results on networks built by cartesian products (as hypercubes and torus) [4]. In this paper, we characterize the networks that admit a linear interval routing function with at most one interval per output port. We also characterize the networks that admit a strict linear interval routing function with at most one interval per output port.