Given a family F of subsets of a ground set V, its orthogonal is defined to be the family of subsets that do not overlap any element of F. Using this tool we revisit the problem of designing a simple linear time algor...
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Given a family F of subsets of a ground set V, its orthogonal is defined to be the family of subsets that do not overlap any element of F. Using this tool we revisit the problem of designing a simple linear time algorithm for undirected graph split (also known as 1-join) decomposition.
"Signal" alignments play critical roles in many clinical setting. This is the case of mass spectrometry (MS) data, an important component of many types of proteomic analysis. A central problem occurs when on...
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"Signal" alignments play critical roles in many clinical setting. This is the case of mass spectrometry (MS) data, an important component of many types of proteomic analysis. A central problem occurs when one needs to integrate (MS) data produced by different sources, e. g., different equipment and/or laboratories. In these cases, some form of "data integration" or "data fusion" may be necessary in order to discard some source-specific aspects and improve the ability to perform a classification task such as inferring the "disease classes" of patients. The need for new high-performance data alignments methods is therefore particularly important in these contexts. In this paper, we propose an approach based both on an information theory perspective, generally used in a feature construction problem, and the application of a mathematical programming task (i.e., the weighted bipartite matching problem). We present the results of a competitive analysis of our method against other approaches. The analysis was conducted on data from plasma/ethylenediaminetetraacetic acid of "control" and Alzheimer patients collected from three different hospitals. The results point to a significant performance advantage of our method with respect to the competing ones tested.
The graph MOTIF problem asks whether a given multiset of colors appears on a connected subgraph of a vertex-colored graph. The fastest known parameterized algorithm for this problem is based on a reduction to the k-Mu...
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The graph MOTIF problem asks whether a given multiset of colors appears on a connected subgraph of a vertex-colored graph. The fastest known parameterized algorithm for this problem is based on a reduction to the k-Multilinear Detection (k-MLD) problem: the detection of multilinear terms of total degree k in polynomials presented as circuits. We revisit k-MLD and define k-CMLD, a constrained version of it which reflects graph MOTIF more faithfully. We then give a fast algorithm for k-CMLD. As a result we obtain faster parameterized algorithms for graph MOTIF and variants of it. (C) 2012 Elsevier B.V. All rights reserved.
Let D be an oriented graph with n >= 9 vertices and minimum degree at least n - 2. such that, for any two vertices x and y, either x dominates y or d(D)(+)(x) + d(D)(-)(y) >= n - 3. Song (1994) [5] proved that D...
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Let D be an oriented graph with n >= 9 vertices and minimum degree at least n - 2. such that, for any two vertices x and y, either x dominates y or d(D)(+)(x) + d(D)(-)(y) >= n - 3. Song (1994) [5] proved that D is pancyclic. Bang-Jensen and Guo (1999) [2] proved, based on Song's result, that D is vertex pancyclic. In this article, we give a sufficient condition for D to contain a vertex whose out-arcs are pancyclic in D, when n >= 14. (c) 2012 Elsevier B.V. All rights reserved.
For r >= 3, we study the H-coloring problem on r-uniform hypergraphs with large vertex degrees. Under certain restrictions on the structure of H, it is proved that for every c > 0 the problem of deciding whether...
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For r >= 3, we study the H-coloring problem on r-uniform hypergraphs with large vertex degrees. Under certain restrictions on the structure of H, it is proved that for every c > 0 the problem of deciding whether an n-vertex r-uniform hypergraph G of minimum vertex degree delta(G) >= C((n-1)(r-1)) is H-colorable is in P. Our results seem to be the first complexity theoretic results for the H-coloring problem on dense hypergraphs. (C) 2012 Elsevier B.V. All rights reserved.
Given a graph G, a function f: V (G) -> {1, 2, ..., k} is a k-ranking of G if f (u) = f (v) implies that every u - v path contains a vertex w such that f (w) > f (u). A k-ranking is minimal if the reduction of a...
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Given a graph G, a function f: V (G) -> {1, 2, ..., k} is a k-ranking of G if f (u) = f (v) implies that every u - v path contains a vertex w such that f (w) > f (u). A k-ranking is minimal if the reduction of any label greater than 1 violates the described ranking property. We consider two norms for minimal rankings. The max-optimal norm parallel to f(G)parallel to(infinity) is the smallest k for which G has a minimal k-ranking. This value is also referred to as the rank number chi(r)(G). In this paper we introduce the sum-optimal norm parallel to f(G)parallel to(1) which is the minimum sum of all labels over all minimal rankings. We investigate similarities and differences between the two norms. In particular we show rankings for paths and cycles that are sum-optimal are also max-optimal. (C) 2011 Elsevier B.V. All rights reserved.
Let MCM(m, n) and MWM(m. n. N) be the complexities of computing a maximum cardinality matching and a maximum weight matching, and let MCMbi, MWMbi be their counterparts for bipartite graphs, where m, n, and N are the ...
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Let MCM(m, n) and MWM(m. n. N) be the complexities of computing a maximum cardinality matching and a maximum weight matching, and let MCMbi, MWMbi be their counterparts for bipartite graphs, where m, n, and N are the edge count, vertex count, and maximum integer edge weight. Kao, Lam, Sung, and Ting (2001) [1] gave a general reduction showing MWMbi(m, n, N) = 0(N . MCMbi(m, n)) and Huang and Kavitha (2012) [2] recently proved the analogous result for general graphs, that MWM(m. n, N) = 0(N . MCM(m,n)). We show that Gabow's MWMbi and MWM algorithms from 1983 [3] and 1985 [4] can be modified to replicate the results of Kao et al. and Huang and Kavitha, but with dramatically simpler proofs. We also show that our reduction leads to new bounds on the complexity of MWM on sparse graph classes, e.g., (bipartite) planar graphs, bounded genus graphs, and H-minor-free graphs. (C) 2012 Elsevier B.V. All rights reserved.
A graph is triconnected if it is connected, has at least 4 vertices and the removal of any two vertices does not disconnect the graph. We give a certifying algorithm deciding triconnectivity of Hamiltonian graphs with...
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A graph is triconnected if it is connected, has at least 4 vertices and the removal of any two vertices does not disconnect the graph. We give a certifying algorithm deciding triconnectivity of Hamiltonian graphs with linear running time (this assumes that the cycle is given as part of the input). If the input graph is triconnected, the algorithm constructs an easily checkable proof for this fact. If the input graph is not triconnected, the algorithm returns a separation pair.
The increasing availability of 3D facial data offers the potential to overcome the intrinsic difficulties faced by conventional face recognition using 2D images. Instead of extending 2D recognition algorithms for 3D p...
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The increasing availability of 3D facial data offers the potential to overcome the intrinsic difficulties faced by conventional face recognition using 2D images. Instead of extending 2D recognition algorithms for 3D purpose, this letter proposes a novel strategy for 3D face recognition from the perspective of representing each 3D facial surface with a 2D attribute image and taking the advantage of the advances in 2D face recognition. In our approach, each 3D facial surface is mapped homeomorphically onto a 2D lattice, where the value at each site is an attribute that represents the local 3D geometrical or textural properties on the surface, therefore invariant to pose changes. This lattice is then interpolated to generate a 2D attribute image. 3D face recognition can be achieved by applying the traditional 2D face recognition techniques to obtained attribute images. In this study, we chose the pose invariant local mean curvature calculated at each vertex on the 3D facial surface to construct the 2D attribute image and adopted the eigenface algorithm for attribute image recognition. We compared our approach to state-of-the-art 3D face recognition algorithms in the FRGC (Version 2.0), GavabDB and NPU3D database. Our results show that the proposed approach has improved the robustness to head pose variation and can produce more accurate 3D multi-pose face recognition. (C) 2011 Elsevier B.V. All rights reserved.
A graph G is perfect if for every induced subgraph H of G, the chromatic number of H equals the size of the largest complete subgraph of H. A bull is a graph on five vertices consisting of a triangle and two vertex-di...
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A graph G is perfect if for every induced subgraph H of G, the chromatic number of H equals the size of the largest complete subgraph of H. A bull is a graph on five vertices consisting of a triangle and two vertex-disjoint pendant edges. A graph is said to be bull-free if none of its induced subgraphs is a bull. In [SIAM J. Discrete Math., 18 (2004), pp. 226-240], de Figueiredo and Maffray gave polynomial time combinatorial algorithms that solve the following four optimization problems for weighted bull-free perfect graphs with integer weights: the maximum weighted clique problem;the maximum weighted stable set problem;the minimum weighted coloring problem;and the minimum weighted clique covering problem. In this paper, we give faster combinatorial algorithms that solve the same four problems. The running time of our algorithms for finding a maximum weighted clique and a maximum weighted stable set in a weighted bull-free perfect graph with integer weights is O(n(6)), and the running time of our algorithms for finding a minimum weighted coloring and a minimum weighted clique covering in such a graph is O(n(8)), where n is the number of vertices of the input graph.
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