We show an algorithm for bound consistency of global cardinality constraints, which runs in time O(n + n') plus the time required to sort the assignment variables by range endpoints, where n is the number of assig...
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We show an algorithm for bound consistency of global cardinality constraints, which runs in time O(n + n') plus the time required to sort the assignment variables by range endpoints, where n is the number of assignment variables and n' is the number of values in the union of their domains. It is the first efficient algorithm that achieves bound consistency for all variables, and not only the assignment variables.
We present an O(n(3))-time randomized approximation algorithm for the maximum traveling salesman problem whose expected approximation ratio is asymptotically 251/331, where it is the number of vertices in the input (u...
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We present an O(n(3))-time randomized approximation algorithm for the maximum traveling salesman problem whose expected approximation ratio is asymptotically 251/331, where it is the number of vertices in the input (undirected) graph. This improves the previous best.
A graph G is 1-planar if it can be embedded in the plane in such a way that each edge crosses at most one other edge. Borodin showed that 1-planar graphs are 6-colorable, but his proof does not lead to a linear-time a...
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A graph G is 1-planar if it can be embedded in the plane in such a way that each edge crosses at most one other edge. Borodin showed that 1-planar graphs are 6-colorable, but his proof does not lead to a linear-time algorithm. This paper presents a linear-time algorithm for 7-coloring 1-plane graphs (which are 1-planar graphs already embedded in the plane). The main difficulty in the design of our algorithm comes from the fact that the class of 1-planar graphs is not closed under the operation of edge contraction. This difficulty is overcome by a structural lemma that may be useful in other problems on 1-planar graphs. This paper also shows that it is NP-complete to decide whether a given 1-planar graph is 4-colorable. The complexity of the problem of deciding whether a given 1-planar graph is 5-colorable is still unknown.
Public transportation networks provide time saving routes with discrete entryand exit points. The network, described as an undirected graph with positive edge weightsproportional to travel time, induces a metric on th...
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Public transportation networks provide time saving routes with discrete entryand exit points. The network, described as an undirected graph with positive edge weightsproportional to travel time, induces a metric on the plane. In this paper we describe the propertiesof this metric, give the first optimal time algorithm for the construction of shortest path mapsand Voronoi diagrams in this metric, and discuss practical issues in its implementation.
The k-MST is a well known NP-hard problem and several approximation algorithms exist to solve this problem with a guaranteed performance bound. A closely related problem, called the bottleneck k-MST (BMST(k)) can howe...
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The k-MST is a well known NP-hard problem and several approximation algorithms exist to solve this problem with a guaranteed performance bound. A closely related problem, called the bottleneck k-MST (BMST(k)) can however be solved in O(m log n) time on graph with n nodes and m edges. We propose two algorithms to solve BMST(k), one of complexity O(m + n log n) and the other of O(m) time. We also consider a generalization of BMST(k) which subsumes many bottleneck problems studied in the literature and show that this generalized problem can also be solved in 0(in) time. (c) 2005 Elsevier B.V. All rights reserved.
In a visibility representation (VR for short) of a plane graph G, each vertex of G is represented by a horizontal line segment such that the line segments representing any two adjacent vertices of G are joined by a ve...
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In a visibility representation (VR for short) of a plane graph G, each vertex of G is represented by a horizontal line segment such that the line segments representing any two adjacent vertices of G are joined by a vertical line segment. Rosenstiehl and Tarjan [Rectilinear planar layouts and bipolar orientations of planar graphs, Discrete Comput. Geom. 1 (1986) 343], Tamassia and Tollis [An unified approach to visibility representations of planar graphs, Discrete Comput. Geom. 1 (1986) 321] independently gave linear time VR algorithms for 2-connected plane graph. Afterwards, one of the main concerns for VR is the size of the representation. In this paper, we prove that any plane graph G has a VR with height bounded by [5n/6]. This improves the previously known bound [-15n/16]. We also construct a plane graph G with n vertices where any VR of G requires a size of ([2n/3]) x ([4n/3] - 3). Our result provides an answer to Kant's open question about whether there exists a plane graph G such that all of its VR require width greater that cn, where c > 1 [G. Kant, A more compact visibility representation, Internal. J. Comput. Geom. Appl. 7 (1997) 197]. (c) 2005 Elsevier B.V. All rights reserved.
In this paper. we propose an external memory depth first search algorithm for solid grid graphs, a subclass of grid graphs. The I/O-complexity of the algorithm, is O(sort(N)), where N = \V\ + \E\, sort(N) = Theta(N/B ...
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In this paper. we propose an external memory depth first search algorithm for solid grid graphs, a subclass of grid graphs. The I/O-complexity of the algorithm, is O(sort(N)), where N = \V\ + \E\, sort(N) = Theta(N/B log (M/B) N/B) is the sorting I/O-complexity. M is the memory size, and B is the block size. Since grid graphs might be nonplanar (if diagonal edges intersect), they are beyond the reach of existing planar depth first search algorithms. The best known algorithm for this class of graph is the standard (internal memory) DFS algorithm with appropriate block (sub-grid) I/O-access. Its I/O-complexity is O(N/rootB). (C) 2004 Elsevier B.V. All rights reserved.
Let G = (V, E) be a graph with vertex set V of size n and edge set E of size m. A vertex v G V is called a hinge vertex if there exist two vertices in V \ {v} such that their distance becomes longer when v is removed....
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Let G = (V, E) be a graph with vertex set V of size n and edge set E of size m. A vertex v G V is called a hinge vertex if there exist two vertices in V \ {v} such that their distance becomes longer when v is removed. In this paper, we present a distributed algorithm that finds all hinge vertices on an arbitrary graph. The proposed algorithm works for named static asynchronous networks and achieves O(n(2)) time complexity and O(m) message complexity. In particular, the total messages exchanged during the algorithm are at most 2m(log n + n log n + 1) bits.
One of the most crucial steps in the design of embedded systems is hardware/software partitioning, is, deciding which components of the system should be implemented in hardware and which ones in software. Most formula...
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One of the most crucial steps in the design of embedded systems is hardware/software partitioning, is, deciding which components of the system should be implemented in hardware and which ones in software. Most formulations of the hardware/software partitioning problem are MP-hard, so the majority-of research efforts on hardware/software partitioning has focused on developing efficient heuristics. This article considers the combinatorial structure behind hardware/software partitioning. Two similar versions of the partitioning problem are defined, one of which turns out to be NP-hard, whereas the other one can be solved in polynomial time. This helps in understanding the real cause of complexity in hardware/software partitioning. Moreover, the polynomial-time algorithm serves as the basis for a highly efficient novel heuristic for the NP-hard version of the problem. Unlike general-purpose heuristics such as genetic algorithms or simulated annealing, this heuristic makes use of problem-specific knowledge, and can thus find high-quality solutions rapidly. Moreover, it has the unique characteristic that it also calculates lower bounds on the optimum solution. It is demonstrated on several benchmarks and also large random examples that the new algorithm clearly outperforms other heuristics that are generally applied to hardware/software partitioning.
Over the past few years, the analysis of alternative splicing using bioinformatics has emerged as an important new field, and has significantly changed our view of genome function. One exciting front has been the anal...
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Over the past few years, the analysis of alternative splicing using bioinformatics has emerged as an important new field, and has significantly changed our view of genome function. One exciting front has been the analysis of microarray data to measure alternative splicing genome-wide. Pioneering studies of both human and mouse data have produced algorithms for discerning evidence of alternative splicing and clustering genes and samples by their alternative splicing patterns. Moreover, these data indicate the presence of alternative splice forms in up to 80 per cent of human genes. Comparative genomics studies in both mammals and insects have demonstrated that alternative splicing can in some cases be predicted directly from comparisons of genome sequences, based on heightened sequence conservation and exon length. Such studies have also provided new insights into the connection between alternative splicing and a variety of evolutionary processes such as Alu-based exonisation, exon creation and loss. A number of groups have used a combination of bioinformatics, comparative genomics and experimental validation to identify new motifs for splice regulatory factors, analyse the balance of factors that regulate alternative splicing, and propose a new mechanism for regulation based on the interaction of alternative splicing and nonsense-mediated decay. Bioinformatics studies of the functional impact of alternative splicing have revealed a wide range of regulatory mechanisms, from NAGNAG sites that add a single amino acid;to short peptide segments that can play surprisingly complex roles in switching protein conformation and function (as in the Piccolo C2A domain);to events that entirely remove a specific protein interaction domain or membrane anchoring domain. Common to many bioinformatics studies is a new emphasis on graph representations of alternative splicing structures, which have many advantages for analysis.
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