In a finite undirected graph G = (V, E), a vertex v is an element of V dominates itself and its neighbors in G. A vertex set D subset of V is an efficient dominating set (e.d.s. for short) of G if every v 2 V is domin...
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In a finite undirected graph G = (V, E), a vertex v is an element of V dominates itself and its neighbors in G. A vertex set D subset of V is an efficient dominating set (e.d.s. for short) of G if every v 2 V is dominated in G by exactly one vertex of D. The Efficient Domination (ED) problem, which asks for the existence of an e.d.s. in G, is known to be NP-complete for P-7-free graphs and solvable in polynomial time for P-5-free graphs. The P-6-free case was the last open question for the complexity of ED on F-free graphs. Recently, Lokshtanov, Pilipczuk, and van Leeuwen showed that weighted ED is solvable in polynomial time for P-6-free graphs, based on their quasi-polynomial algorithm for the Maximum Weight Independent Set problem for P-6-free graphs. Independently, by a direct approach which is simpler and faster, we found an O(n(5)m) time solution for weighted ED on P-6-free graphs. Moreover, we show that weighted ED is solvable in lineartime for P-5-free graphs which solves another open question for the complexity of (weighted) ED. The result for P-5-free graphs is based on modular decomposition.
In the single-image dehazing problem, it is critical that the transmission is accurately estimated. However, the extracted transmission in the dark channel model cannot effectively deal with the edge and the sky area ...
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In the single-image dehazing problem, it is critical that the transmission is accurately estimated. However, the extracted transmission in the dark channel model cannot effectively deal with the edge and the sky area because of the poor applicability of the dark channel prior to these areas. This study aims to solve that problem by proposing a novel variational model (VM) to optimise the transmission. This VM introduces a smoothness term and a gradient-preserving term to mitigate the false edge and the distorted sky area in the recovered image. Further, a fast algorithm to solve the VM is proposed on the basis of the additional operator splitting algorithm. This algorithm is an effective linear time algorithm and has excellent performance on optimising the transmission. The average running time of the algorithm shows an improvement of over 20 times that of the guided image filtering in these experiments. Experimental results also show that the proposed algorithm is both effective and efficient for optimising the transmission.
A total dominating set in a graph is a subset of vertices such that every vertex in the graph has a neighbor in it. A graph is said to be total domishold if it admits a total domishold structure, that is, a hyperplane...
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A total dominating set in a graph is a subset of vertices such that every vertex in the graph has a neighbor in it. A graph is said to be total domishold if it admits a total domishold structure, that is, a hyperplane with non-negative coefficients that separates the characteristic vectors of its total dominating sets from the characteristic vectors of other vertex subsets. Hereditary total domishold graphs, that is, graphs every induced subgraph of which is total domishold, were recently characterized in terms of forbidden induced subgraphs;this characterization leads to an O(vertical bar V(G)vertical bar(6)) recognition algorithm of hereditary total domishold graphs. In this paper, we study a subclass g of the hereditary total domishold graphs obtained by replacing two of the forbidden induced subgraphs of order 6 with two of their proper induced subgraphs of order 5. We show that every connected graph in 9, is a leaf extension of a threshold graph, that is, it can be obtained from some threshold graph G by attaching some pendant vertices to each vertex of G. Using this property, we develop a structural characterization of graphs in g, which implies a lineartime recognition algorithm for graphs in this class. We also give a linear time algorithm for computing a total domishold structure of a graph in g. In contrast to the algorithm for the general case of (hereditary) total domishold graphs, which relies on solving a linear program, our algorithm is purely combinatorial and works directly with the graph. (C) 2014 Elsevier B.V. All rights reserved.
A path pi = (v(1), v(2), ... , v(k+1)) in a graph G = (V, E) is a downhill path if for every i, 1 = deg(v(i+1)), where deg(v(i)) denotes the degree of vertex v(i) is an element of V. A downhill dominating set DDS is a...
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A path pi = (v(1), v(2), ... , v(k+1)) in a graph G = (V, E) is a downhill path if for every i, 1 <= i <= k, deg(v(i)) >= deg(v(i+1)), where deg(v(i)) denotes the degree of vertex v(i) is an element of V. A downhill dominating set DDS is a set S subset of V having the property that every vertex v is an element of V lies on a downhill path originating from some vertex in S. The downhill domination number gamma(dn)(G) equals the minimum cardinality of a DDS of G. A DDS having minimum cardinality is called a gamma(dn)-set of G. In this note, we give an enumeration of all the distinct gamma(dn)-sets of G, and we show that there is a linear time algorithm to determine the downhill domination number of a graph. (c) 2015 Elsevier B.V. All rights reserved.
Let G be a finite undirected graph with edge set E. An edge set E'aS dagger E is an induced matching in G if the pairwise distance of the edges of E' in G is at least two;E' is dominating in G if every edg...
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Let G be a finite undirected graph with edge set E. An edge set E'aS dagger E is an induced matching in G if the pairwise distance of the edges of E' in G is at least two;E' is dominating in G if every edge eaEa-E' intersects some edge in E'. The Dominating Induced Matching Problem (DIM, for short) asks for the existence of an induced matching E' which is also dominating in G;this problem is also known as the Efficient Edge Domination Problem. The DIM problem is related to parallel resource allocation problems, encoding theory and network routing. It is -complete even for very restricted graph classes such as planar bipartite graphs with maximum degree three. However, its complexity was open for P (k) -free graphs for any ka parts per thousand yen5;P (k) denotes a chordless path with k vertices and k-1 edges. We show in this paper that the weighted DIM problem is solvable in lineartime for P (7)-free graphs in a robust way.
The square of a graph G, denoted by G(2), is the graph obtained from G by putting an edge between two distinct vertices whenever their distance in G is at most 2. Motwani and Sudan proved that it is NP-complete to dec...
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The square of a graph G, denoted by G(2), is the graph obtained from G by putting an edge between two distinct vertices whenever their distance in G is at most 2. Motwani and Sudan proved that it is NP-complete to decide whether a given graph is the square of some graph. In this paper we give a characterization of line graphs that are squares of graphs, and show that if a line graph is a square, then it is a square of a bipartite graph. As a consequence, we obtain a linear time algorithm for deciding whether a given line graph is the square of some graph. (C) 2014 Elsevier B.V. All rights reserved.
A graph H is a square root of a graph G if two vertices are adjacent in G if and only if they are at distance one or two in H. Computing a square root of a given graph is NP-hard, even when the input graph is restrict...
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A graph H is a square root of a graph G if two vertices are adjacent in G if and only if they are at distance one or two in H. Computing a square root of a given graph is NP-hard, even when the input graph is restricted to be chordal. In this paper, we show that computing a square root can be done in lineartime for a well-known subclass of chordal graphs, the class of trivially perfect graphs. This result is obtained by developing a structural characterization of graphs that have a split square root. We also develop linear time algorithms for determining whether a threshold graph given either by a degree sequence or by a separating structure has a square root. (C) 2013 Elsevier B.V. All rights reserved.
作者：
Wang, JunTan, YingPeking Univ
Sch Elect Engn & Comp Sci Dept Machine Intelligence Beijing 100871 Peoples R China Peking Univ
Key Lab Machine Percept MOE Beijing 100871 Peoples R China State Adm Taxat
Shandong Prov Off Jinan Peoples R China
In this paper, we propose an efficient algorithm, i.e., PBEDT, for short, to compute the exact Euclidean distance transform (EDT) of a binary image in arbitrary dimensions. The PBEDT is based on independent scan and i...
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In this paper, we propose an efficient algorithm, i.e., PBEDT, for short, to compute the exact Euclidean distance transform (EDT) of a binary image in arbitrary dimensions. The PBEDT is based on independent scan and implemented in a recursive way, i.e., the EDT of a d-dimensional image is able to be computed from the EDTs of its (d-1)-dimensional sub-images. In each recursion, all of the rows in the current dimensional direction are processed one by one. The points in the current processing row and their closest feature points in (d-1)-dimensional sub-images can be shown in a Euclidean plane. By using the geometric properties of the perpendicular bisector, the closest feature points of (d-1)-dimensional subimages are easily verified so as to lead to the EDT of a d-dimensional image after eliminating the invalid points. The time complexity of the PBEDT algorithm is linear in the amount of both image points and dimensions with a small coefficient. Compared with the state-of-the-art EDT algorithms, the PBEDT algorithm is much faster and more stable in most cases. (C) 2012 Elsevier Ltd. All rights reserved.
For every fixed surface S, orientable or non-orientable, and a given graph G, Mohar (STOC'96 and Siam J. Discrete Math. (1999)) described a linear time algorithm which yields either an embedding of G in S or a min...
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ISBN:
(纸本)9780769534367
For every fixed surface S, orientable or non-orientable, and a given graph G, Mohar (STOC'96 and Siam J. Discrete Math. (1999)) described a linear time algorithm which yields either an embedding of G in S or a minor of G which is not embeddable in S and is minimal with this property. That algorithm, however, needs a lot of lemmas which spanned six additional papers. In this paper, we give a new linear time algorithm for the same problem. The advantages of our algorithm are the following: 1. The proof is considerably simpler: it needs only about 10 pages, and some results (with rather accessible proofs)from graph minors theory, while Mohar's original algorithm and its proof occupy more than 100 pages in total. 2. The hidden constant (depending on the genus g of the surface S) is much smaller It is singly exponential in g, while it is doubly exponential in Mohar's algorithm. As a spinoff of our main result, we give another linear time algorithm, which is of independent interest. This algorithm computes the genus and constructs minimum genus embed dings of graphs of bounded tree-width. This resolves a conjecture by Neil Robertson and solves one of the most annoying long standing open question about complexity of algorithms on graphs of bounded tree-width.
There is a growing demand for fault diagnosis to increase the reliability of systems. Diagnosis by comparison is a realistic approach to the fault diagnosis of multiprocessor systems. In this paper, we consider n-dime...
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There is a growing demand for fault diagnosis to increase the reliability of systems. Diagnosis by comparison is a realistic approach to the fault diagnosis of multiprocessor systems. In this paper, we consider n-dimensional hypercube-like networks for n >= 5 We propose an efficient fault diagnosis algorithm for n-dimensional hypercube-like networks under the MM comparison model by exploiting the Hamiltonian and extended-star properties. Applying our algorithm, the faulty processors in n-dimensional hypercubes, n-dimensional crossed cubes, n-dimensional twisted cubes, and n-dimensional Mobius cubes can all be diagnosed in lineartime provided the number of faulty processors is not more than the dimension n.
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