We define strong lambda-extendibility as a variant of the notion of lambda-extendible properties of graphs (Poljak and Turzik, Discrete Mathematics, 1986). We show that the parameterized APT(Pi) problem - given a conn...
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We define strong lambda-extendibility as a variant of the notion of lambda-extendible properties of graphs (Poljak and Turzik, Discrete Mathematics, 1986). We show that the parameterized APT(Pi) problem - given a connected graph G on n vertices and m edges and an integer parameter k, does there exist a spanning subgraph H of G such that H is an element of Pi and H has at least [GRAPHICS] edges - is fixed-parameter tractable (FPT) for all 0 < lambda < 1, for all strongly lambda-extendible graph properties Pi for which the APT(Pi) problem is FPT on graphs which are 0(k) vertices away from being a graph in which each block is a clique. Our results hold for properties of oriented graphs and graphs with edge labels, generalize the recent result of Crowston et al. (ICALP 2012) on MAX-CUT parameterized above the Edwards-Erdos bound, and yield FPT algorithms for several graph problems parameterized above lower bounds. (C) 2014 Elsevier Inc. All rights reserved.
The Induced Graph Matching problem asks to find disjoint induced subgraphs isomorphic to a given graph in a given graph such that there are no edges between vertices of different subgraphs. This problem generalizes th...
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The Induced Graph Matching problem asks to find disjoint induced subgraphs isomorphic to a given graph in a given graph such that there are no edges between vertices of different subgraphs. This problem generalizes the classical Independent Set and Induced Matching problems, among several other problems. We show that Induced Graph Matching is fixed-parameter tractable in on claw-free graphs when is a fixed connected graph, and even admits a polynomial kernel when is a complete graph. Both results rely on a new, strong, and generic algorithmic structure theorem for claw-free graphs. Complementing the above positive results, we prove -hardness of Induced Graph Matching on graphs excluding as an induced subgraph, for any fixed complete graph . In particular, we show that Independent Set is -hard on -free graphs. Finally, we consider the complexity of Induced Graph Matching on a large subclass of claw-free graphs, namely on proper circular-arc graphs. We show that the problem is either polynomial-time solvable or -complete, depending on the connectivity of and the structure of G.
The Induced Graph Matching problem asks to find disjoint induced subgraphs isomorphic to a given graph in a given graph such that there are no edges between vertices of different subgraphs. This problem generalizes th...
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The Induced Graph Matching problem asks to find disjoint induced subgraphs isomorphic to a given graph in a given graph such that there are no edges between vertices of different subgraphs. This problem generalizes the classical Independent Set and Induced Matching problems, among several other problems. We show that Induced Graph Matching is fixed-parameter tractable in on claw-free graphs when is a fixed connected graph, and even admits a polynomial kernel when is a complete graph. Both results rely on a new, strong, and generic algorithmic structure theorem for claw-free graphs. Complementing the above positive results, we prove -hardness of Induced Graph Matching on graphs excluding as an induced subgraph, for any fixed complete graph . In particular, we show that Independent Set is -hard on -free graphs. Finally, we consider the complexity of Induced Graph Matching on a large subclass of claw-free graphs, namely on proper circular-arc graphs. We show that the problem is either polynomial-time solvable or -complete, depending on the connectivity of and the structure of G.
In the aerospace sciences, computational intelligence techniques are now key tools in addressing many problems. Such techniques have progressed along with increases in computing power, allowing numerical simulation to...
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ISBN:
(数字)9781624102714
ISBN:
(纸本)9781624102608
In the aerospace sciences, computational intelligence techniques are now key tools in addressing many problems. Such techniques have progressed along with increases in computing power, allowing numerical simulation to gradually replace experimental testing in many areas of engineering, and leading to an increasing use of nature-inspired numerical optimization methods to handle complex real world multidisciplinary design *** Intelligence in Aerospace Sciences introduces the fundamental concepts and methods used in single and multiobjective optimization, game theory, and uncertainty quantification before detailing techniques across four main areas: It provides practitioners with an overview of different computational intelligence techniques with aerospace applications, and aids newcomers to this field of research who are looking for fundamental information with advanced examples.
We revisit the polytope method for factoring sparse bivariate polynomials over finite fields, and address the bottleneck arising from solving the Hensel lifting equations using the sparse distributed polynomial repres...
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ISBN:
(纸本)9783319105154
We revisit the polytope method for factoring sparse bivariate polynomials over finite fields, and address the bottleneck arising from solving the Hensel lifting equations using the sparse distributed polynomial representation. We revise the analysis when polynomials are represented as such, which reveals how performing the polynomial multiplications and ensuing additions in separate (serialised) phases causes the Hensel lifting phase to suffer from poor work, space, and I/O complexity, and hinges on the size of the intermediary output, as size is defined in the sparse distributed representation. We propose to overlap all polynomial arithmetic in one Hensel lifting step using a MAX priority queue. The overlapping approach adapts not only to the growth in the degree of the input polynomial but also to irregularities in the sparsity of intermediary output. It also results in evading expression swell and reducing the overall work and space complexity by an order of magnitude. When the priority queue is implemented as a cache-oblivious data structure, the overlapping approach achieves an order of magnitude improvement in I/O over the serialised approach, even when the latter is using cache efficient structures to assist in polynomial multiplications and additions. We present empirical results for the polytope method using a max-heap implementation of the global priority queue, which demonstrate extremely superior performance, and specifically against Magma, for sufficiently sparse input polynomials of very high degrees.
The eviction problem for memory hierarchies is studied for the Hidden Markov Reference Model (HMRM) of the memory trace, showing how miss minimization can be naturally formulated in the optimal control setting. In add...
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The eviction problem for memory hierarchies is studied for the Hidden Markov Reference Model (HMRM) of the memory trace, showing how miss minimization can be naturally formulated in the optimal control setting. In addition to the traditional version assuming a buffer of fixed capacity, a relaxed version is also considered, in which buffer occupancy can vary and its average is constrained. Resorting to multiobjective optimization, viewing occupancy as a cost rather than as a constraint, the optimal eviction policy is obtained by composing solutions for the individual addressable items. This approach is then specialized to the Least Recently Used Stack Model (LRUSM), a type of HMRM often considered for traces, which includes V - 1 parameters, where V is the size of the virtual space. A gain optimal policy for any target average occupancy is obtained which (i) is computable in time O(V) from the model parameters, (ii) is optimal also for the Fixed capacity case, and (iii) is characterized in terms of priorities, with the name of Least Profit Rate (LPR) policy. An O(log C) upper bound (being C the buffer capacity) is derived for the ratio between the expected miss rate of LPR and that of OPT, the optimal off-line policy;the upper bound is tightened to O(1), under reasonable constraints on the LRUSM parameters. Using the stack-distance framework, an algorithm is developed to compute the number of misses incurred by LPR on a given input trace, simultaneously for all buffer capacities, in time O(log V) per access. Finally, some results are provided for miss minimization over a finite horizon and over an infinite horizon under bias optimality, a criterion more stringent than gain optimality. (C) 2013 Elsevier B.V. All rights reserved.
Let G be a graph with n vertices and m edges. A sparsifier of G is a sparse graph on the same vertex set approximating G in some natural way. It allows us to say useful things about G while considering much fewer than...
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Let G be a graph with n vertices and m edges. A sparsifier of G is a sparse graph on the same vertex set approximating G in some natural way. It allows us to say useful things about G while considering much fewer than m edges. The strongest commonly-used notion of sparsification is spectral sparsification;H is a spectral sparsifier of G if the quadratic forms induced by the Laplacians of G and H approximate one another well. This notion is strictly stronger than the earlier concept of combinatorial sparsification. In this paper, we consider a semi-streaming setting, where we have only storage space, and we thus cannot keep all of G. In this case, maintaining a sparsifier instead gives us a useful approximation to G, allowing us to answer certain questions about the original graph without storing all of it. We introduce an algorithm for constructing a spectral sparsifier of G with O(nlogn/I mu (2)) edges (where I mu is a parameter measuring the quality of the sparsifier), taking time and requiring only one pass over G. In addition, our algorithm has the property that it maintains at all times a valid sparsifier for the subgraph of G that we have received. Our algorithm is natural and conceptually simple. As we read edges of G, we add them to the sparsifier H. Whenever H gets too big, we resparsify it in time. Adding edges to a graph changes the structure of its sparsifier's restriction to the already existing edges. It would thus seem that the above procedure would cause errors to compound each time that we resparsify, and that we should need to either retain significantly more information or reexamine previously discarded edges in order to construct the new sparsifier. However, we show how to use the information contained in H to perform this resparsification using only the edges retained by earlier steps in nearly linear time.
Within a mathematically rigorous model, we analyse the curse of dimensionality for deterministic exact similarity search in the context of popular indexing schemes: metric trees. The datasets X are sampled randomly fr...
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Within a mathematically rigorous model, we analyse the curse of dimensionality for deterministic exact similarity search in the context of popular indexing schemes: metric trees. The datasets X are sampled randomly from a domain Omega, equipped with a distance, rho, and an underlying probability distribution, mu. While performing an asymptotic analysis, we send the intrinsic dimension d of Omega to infinity, and assume that the size of a dataset, n, grows superpolynomially yet subexponentially in d. Exact similarity search refers to finding the nearest neighbour in the dataset X to a query point omega a Omega, where the query points are subject to the same probability distribution mu as datapoints. Let denote a class of all 1-Lipschitz functions on Omega that can be used as decision functions in constructing a hierarchical metric tree indexing scheme. Suppose the VC dimension of the class of all sets {omega:f(omega)a parts per thousand yena}, aaa"e is o(n (1/4)/log(2) n). (In view of a 1995 result of Goldberg and Jerrum, even a stronger complexity assumption d (O(1)) is reasonable.) We deduce the Omega(n (1/4)) lower bound on the expected average case performance of hierarchical metric-tree based indexing schemes for exact similarity search in (Omega,X). In paricular, this bound is superpolynomial in d.
We study combinatorial and algorithmic questions around minimal feedback vertex sets (FVS) in tournament graphs. On the combinatorial side, we derive upper and lower bounds on the maximum number of minimal FVSs in an ...
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We study combinatorial and algorithmic questions around minimal feedback vertex sets (FVS) in tournament graphs. On the combinatorial side, we derive upper and lower bounds on the maximum number of minimal FVSs in an n-vertex tournament. We prove that every tournament on n vertices has at most 1.6740n minimal FVSs, and that there is an infinite family of tournaments, all having at least 1.5448n minimal FVSs. This improves and extends the bounds of Moon (1971). On the algorithmic side, we design the first polynomial space algorithm that enumerates the minimal FVSs of a tournament with polynomial delay. The combination of our results yields the fastest known algorithm for finding a minimum-sized FVS in a tournament.
Tutte proved that every 3-vertex-connected graph G on more than 4 vertices has a contractible edge. Barnette and Grunbaum proved the existence of a removable edge in the same setting. We show that the sequence of cont...
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Tutte proved that every 3-vertex-connected graph G on more than 4 vertices has a contractible edge. Barnette and Grunbaum proved the existence of a removable edge in the same setting. We show that the sequence of contractions and the sequence of removals from G to K (4) can be computed in O(|V|(2)) time by extending Barnette's and Grunbaum's theorem. As an application, we derive a certificate for the 3-vertex-connectivity of graphs that can be easily computed and verified.
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