Objective: Protein structure prediction (PSP) aims to reconstruct the 3D structure of a given protein starting from its primary structure (chain of amino acidic residues). It is a well-known fact that the 3D structure...
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Objective: Protein structure prediction (PSP) aims to reconstruct the 3D structure of a given protein starting from its primary structure (chain of amino acidic residues). It is a well-known fact that the 3D structure of a protein only depends on its primary structure. PSP is one of the most important and still unsolved problems in computational biology. Protein structure selection (PSS), instead of reconstructing a 3D model for the given chain, aims to select among a given, possibly large, number of 3D structures (called decoys) those that are closer (according to a given notion of distance) to the original (unknown) one. In this paper we address PSS problem using graph theoretic techniques. Methods and materials: Existing methods for solving PSS make use of suitably defined energy functions which heavily rely on the primary structure of the protein and on protein chemistry. In this paper we present a new approach to PSS which does not take advantage of the knowledge of the primary structure of the protein but only depends on the graph theoretic properties of the decoys graphs (vertices represent residues and edges represent pairs of residues whose Euclidean distance is less than or equal to a fixed threshold). Results: Even if our methods only rely on approximate geometric information, experimental results show that some of the adopted graph properties score similarly to energy-based filtering functions in selecting the best decoys. Conclusion: Our results highlight the principal role of geometric information in PSS, setting a new starting point and filtering method for existing energy function-based techniques. (c) 2008 Elsevier B.V. All rights reserved.
Pressure dipoles are important long distance climate phenomena (teleconnection) characterized by pressure anomalies of the opposite polarity appearing at two different locations at the same time. Such dipoles have bee...
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Pressure dipoles are important long distance climate phenomena (teleconnection) characterized by pressure anomalies of the opposite polarity appearing at two different locations at the same time. Such dipoles have been proven important for understanding and explaining the variability in climate in many regions of the world, e.g. the El Nino Southern Oscillation (ENSO) climate phenomenon, which is described by opposite pressure anomalies between the west and east Pacific and is known to be responsible for precipitation and temperature anomalies worldwide. This paper presents a graph-based approach called shared reciprocal nearest neighbor approach that considers only reciprocal positive and negative edges in the shared nearest neighbor graph to find the dipoles. One crucial aspect of our approach to the analysis of such networks is a careful treatment of negative correlations, whose proper consideration is critical for finding the dipoles. Further, our work shows the importance of modeling the time-dependent patterns of the dipoles in a changing climate in order to better capture the impact of important climate phenomena on the globe. To show the utility of finding dipoles using our approach, we show that the data driven dynamic climate indices generated from our algorithm generally perform better than static indices formed from the fixed locations used by climate scientists in terms of capturing impact on global temperature and precipitation. Our approach can generate a single snapshot picture of all the dipole interconnections on the globe in a given dataset and thus makes it possible to study the changes in dipole interactions and movements. As teleconnections are crucial in the understanding of the global climate system, there is a pressing need to better understand the behavior and interactions of these atmospheric processes as well as to capture them precisely. Our systematic graph-based approach to find the teleconnections in climate data is an attempt in that
An i-triangulated graph is a graph in which every odd cycle has two non-crossing chords;i-triangulated graphs form a subfamily of perfect graphs. A slightly more general family of perfect graphs are clique-separable g...
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An i-triangulated graph is a graph in which every odd cycle has two non-crossing chords;i-triangulated graphs form a subfamily of perfect graphs. A slightly more general family of perfect graphs are clique-separable graphs. A graph is clique-separable precisely if every induced subgraph either has a clique cutset, or is a complete multipartite graph or a clique joined to an arbitrary bipartite graph. We exhibit a polynomial time algorithm for finding a maximum-weight induced k-partite subgraph of an i-triangulated graph, and show that the problem of finding a maximum-size bipartite induced subgraph in a clique-separable graph is NP-complete. (c) 2008 Elsevier B.V. All rights reserved.
Suppose that each edge e of an undirected graph G is associated with three nonnegative integers , and , called the cost, vulnerability and capacity of e, respectively. Then, we consider the problem of finding paths in...
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Suppose that each edge e of an undirected graph G is associated with three nonnegative integers , and , called the cost, vulnerability and capacity of e, respectively. Then, we consider the problem of finding paths in G between two prescribed vertices with the minimum total cost;each edge e can be shared without any cost by at most paths, and can be shared by more than paths if we pay , but cannot be shared by more than paths even if we pay the cost for e. This problem generalizes the disjoint path problem, the minimum shared edges problem and the minimum edge cost flow problem for undirected graphs, and it is known to be NP-hard. In this paper, we study the problem from the viewpoint of specific graph classes, and give three results. We first show that the problem is NP-hard even for bipartite outerplanar graphs, 2-trees, graphs with pathwidth two, complete bipartite graphs, and complete graphs. We then give a pseudo-polynomial-time algorithm for bounded treewidth graphs. Finally, we give a fixed-parameter algorithm for chordal graphs when parameterized by the number of required paths.
We study reconfiguration problems for cliques in a graph, which determine whether there exists a sequence of cliques that transforms a given clique into another one in a step-by-step fashion. As one step of a transfor...
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We study reconfiguration problems for cliques in a graph, which determine whether there exists a sequence of cliques that transforms a given clique into another one in a step-by-step fashion. As one step of a transformation, we consider three different types of rules, which are defined and studied in reconfiguration problems for independent sets. We first prove that all the three rules are equivalent in cliques from the viewpoint of polynomial-time solvability. We then show that the problems are PSPACE-complete for perfect graphs, while we give polynomial-time algorithms for several classes of graphs, such as even-hole-free graphs and cographs. Furthermore, we show that the shortest variant, which computes the shortest length of a desired sequence, can be solved in polynomial time for chordal graphs, bipartite graphs, planar graphs, and bounded treewidth graphs. (c) 2023 Elsevier B.V. All rights reserved.
A dynamic connectivity problem consists of an initial graph, and a sequence of operations consisting of graph modifications and graph connectivity tests. The size n of the problem is the sum of the maximum number of v...
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A dynamic connectivity problem consists of an initial graph, and a sequence of operations consisting of graph modifications and graph connectivity tests. The size n of the problem is the sum of the maximum number of vertices and edges of the derived graph, plus the number of operations to be executed. Each graph modification is a deletion of either an edge or an isolated vertex. Each graph connectivity test is to determine if there exists a path in the current graph between two given vertices (the vertices can vary for distinct tests). The best previously known time for this dynamic connectivity problem was Ω(n 2 ). Our main result is an O(ng+n log n) time algorithm for the dynamic connectivity problem in the case of the maximum genus of the derived graph being g.
We investigate the computational complexity of the following restricted variant of SUBgraph ISOMORPHISM: given a pair of connected graphs G = (V-G, E-G) and H = (V-H, E-H), determine if H is isomorphic to a spanning s...
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We investigate the computational complexity of the following restricted variant of SUBgraph ISOMORPHISM: given a pair of connected graphs G = (V-G, E-G) and H = (V-H, E-H), determine if H is isomorphic to a spanning subgraph of G. The problem is NP-complete in general, and thus we consider cases where G and H belong to the same graph class such as the class of proper interval graphs, of trivially perfect graphs, and of bipartite permutation graphs. For these graph classes, several restricted versions of SUBgraph ISOMORPHISM such as HAMILTONIAN PATH, CLIQUE, BANDWIDTH, and graph ISOMORPHISM can be solved in polynomial time, while these problems are hard in general. (c) 2012 Elsevier B.V. All rights reserved.
Two vertices of an undirected graph are called k-edge-connected if there exist k edge-disjoint paths between them (equivalently, they cannot be disconnected by the removal of less than k edges from the graph). Equival...
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Two vertices of an undirected graph are called k-edge-connected if there exist k edge-disjoint paths between them (equivalently, they cannot be disconnected by the removal of less than k edges from the graph). Equivalence classes of this relation are called classes of k-edge-connectivity or k-edge-connected components. This paper describes graph structures relevant to classes of 4-edge-connectivity and traces their transformations as new edges are inserted into the graph. Data structures and an algorithm to maintain these classes incrementally are given. Starting with the empty graph, any sequence of q Same-4-Class? queries and it Insert-Vertex and lit Insert-Edge updates can be performed in O(q + m + ii log n total time. Each individual query requires O(1) time in the worst-case. In addition, an algorithm for maintaining the classes of k-edge-connectivity (k arbitrary) in a (k-1)-edge-connected graph is presented. Its complexity is O(q + m + n). with O(M + k(2)n log(n/k)) preprocessing, where M is the number of edges initially in the graph and n is the number of its vertices.
The model-checking problem for monadic second-order logic on graphs is fixed-parameter tractable with respect to tree-width and clique-width. The proof constructs finite automata from monadic second-order sentences. T...
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The model-checking problem for monadic second-order logic on graphs is fixed-parameter tractable with respect to tree-width and clique-width. The proof constructs finite automata from monadic second-order sentences. These automata recognize the terms over fixed finite signatures that define graphs satisfying the given sentences. However, this construction produces automata of hyper-exponential sizes, and is thus impossible to use in practice in many cases. To overcome this difficulty, we propose to specify the transitions of automata by programs instead of tables. Such automata are called fly-automata. By using them, we can check certain monadic second-order graph properties with limited quantifier alternation depth, that are nevertheless interesting for graph Theory. We give explicit constructions of automata relative to graphs of bounded clique-width, and we report on experiments. (C) 2012 Elsevier B.V. All rights reserved.
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