A 2-walk of a graph is a walk visiting every vertex at least once and at most twice. By generalizing decompositions of Tutte and Thomassen, Gao, Richter, and Yu proved that every 3-connected planar graph contains a cl...
详细信息
A 2-walk of a graph is a walk visiting every vertex at least once and at most twice. By generalizing decompositions of Tutte and Thomassen, Gao, Richter, and Yu proved that every 3-connected planar graph contains a closed 2-walk such that all vertices visited twice are contained in 3-separators. This seminal result generalizes Tutte's theorem that every 4-connected planar graph is Hamiltonian, as well as Barnette's theorem that every 3-connected planar graph has a spanning tree with maximum degree at most 3. The algorithmic challenge of finding such a closed 2-walk is to overcome big overlapping subgraphs in the decomposition, which are also inherent in Tutte's and Thomassen's decompositions. We solve this problem by extending the decomposition of Gao, Richter, and Yu in such a way that all pieces into which the graph is decomposed are edge-disjoint. This implies the first polynomial-time algorithm that computes the closed 2-walk just mentioned. Its running time is O(n(3)).
We address the problem of how to cover a set of required points by a small number of axis-parallel ellipses that avoid a second set of forbidden points. We study geometric properties of such covers and present an effi...
详细信息
We address the problem of how to cover a set of required points by a small number of axis-parallel ellipses that avoid a second set of forbidden points. We study geometric properties of such covers and present an efficient randomized approximation algorithm for the cover construction. This question is motivated by a special pattern recognition task where one has to identify ellipse-shaped protein spots in two-dimensional electrophoresis;images.
In this paper we present new space efficient dynamic datastructures for orthogonal range reporting. The described datastructures support planar range reporting queries in time O(log n+k log log (4n/(k+1))) and space...
详细信息
In this paper we present new space efficient dynamic datastructures for orthogonal range reporting. The described datastructures support planar range reporting queries in time O(log n+k log log (4n/(k+1))) and space O(n log log n), or in time O(log n+k) and space O(nlog(epsilon) n) for any epsilon > 0. Both datastructures can be constructed in O(n log n) time and support insert and delete operations in amortized time O(log(2)n) and O(log n log log n) respectively. These results match the corresponding upper space bounds of Chazelle (SIAM J. Comput. 17, 427-462, 1988) for the static case. We also present a dynamic data structure for d-dimensional range reporting with search time O(log(d-1) n+k), update time O(log(d) n), and space O(n log(d-2+epsilon) n) for any epsilon > 0. The model of computation used in our paper is a unit cost RAM with word size log n.
For the decades that followed the publication of the Cooper-Harper report that formalized a standard and universally recognized handling qualities pilot rating scale, researchers have sought to correlate pilot compens...
详细信息
For the decades that followed the publication of the Cooper-Harper report that formalized a standard and universally recognized handling qualities pilot rating scale, researchers have sought to correlate pilot compensation-as well as physical and mental workload-with the assigned rating. A quantitative correlation remains elusive. In recent years, new physiological measurement devices have been developed that, together with software processing tools, can provide accurate measures of psychophysiological measures, including cognitive workload, distraction, and high/low engagement, based on electroencephalogram and electrocardiogram measures (i.e., brain waves and heart rate variability). The pilot compensation referred to in the Cooper-Harper scale is also a function of task performance measures that reflect aircraft characteristics and inceptor activity that reflects upon physical workload. Using a new piloted simulation test database generated in Manned Flight Simulator's containerized rotary-wing simulator with 10 experienced test pilots, a machine-learning-based software algorithm that integrates a disparate mix of pilot-vehicle system, physiological, and task performance measures was used to further develop an approach to predict handling qualities levels and ratings.
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...
详细信息
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.
The path length of a tree, that is, the sum of the lengths of all root-leaf paths, is an important measure of efficiency of the tree. The fringe of a tree is the difference between the lengths of the longest path and ...
详细信息
The path length of a tree, that is, the sum of the lengths of all root-leaf paths, is an important measure of efficiency of the tree. The fringe of a tree is the difference between the lengths of the longest path and the shortest path in the tree. The minimal and the maximal path length of trees with N leaves and given fringe have been well studied. In this paper, we initiate the study of the expected path length of the class of trees with N leaves and fringe Delta by giving a closed expression for the expected path length when Delta = 2.
In the classic Integer Programming Feasibility (IPF) problem, the objective is to decide whether, for a given m x n matrix A and an m-vector b = (b(1) ..... b(m) ), there is a non-negative integer n-vector x such that...
详细信息
In the classic Integer Programming Feasibility (IPF) problem, the objective is to decide whether, for a given m x n matrix A and an m-vector b = (b(1) ..... b(m) ), there is a non-negative integer n-vector x such that Ax = b. Solving (IPF) is an important step in numerous algorithms and it is important to obtain an understanding of the precise complexity of this problem as a function of natural parameters of the input. The classic pseudo-polynomial time algorithm of Papadimitriou [J. ACM 1981] for instances of (IPF) with a constant number of constraints was only recently improved upon by Eisenbrand and Weismantel [SODA 2018] and Jansen and Rohwedder [ITCS 2019]. Jansen and Rohwedder designed an algorithm for (IPF) with running time O(m Delta)(m) log(Delta) log (Delta + parallel to b parallel to(infinity)) + O(mn). Here, Delta is an upper bound on the absolute values of the entries of A. We continue this line of work and show that under the Exponential Time Hypothesis (ETH), the algorithm of Jansen and Rohwedder is nearly optimal, by proving a lower bound of n(O(m/log m)) . parallel to b parallel to(O(m))(infinity). We also prove that assuming ETH, (IPF) cannot be solved in time f (m) . (n . parallel to b parallel to(infinity))(O(m/log m)) for any computable function f. This motivates us to pick up the line of research initiated by Cunningham and Geelen [IPCO 2007] who studied the complexity of solving (IPF) with non-negative matrices in which the number of constraints may be unbounded, but the branch-width of the column-matroid corresponding to the constraint matrix is a constant. We prove a lower bound on the complexity of solving (IPF) for such instances and obtain optimal results with respect to a closely related parameter, path-width. Specifically, we prove matching upper and lower bounds for (IPF) when the path-width of the corresponding column-matroid is a constant.
We compute the average behaviour of additive weights over the family F-t(n) of unlabelled rooted planar t-ary trees with n nodes under the so-called Balanced Probability Model, introduced by R. Casas, J. Diaz and C. M...
详细信息
We compute the average behaviour of additive weights over the family F-t(n) of unlabelled rooted planar t-ary trees with n nodes under the so-called Balanced Probability Model, introduced by R. Casas, J. Diaz and C. Martinet. The generating function related to a particular additive weight with polynomial weight functions always satisfies an ordinary inhomogeneous differential equation, which can be solved explicitly by the variation of constant - method. These coefficients are estimated using singularity analysis. The so-called occupancy, a parameter which is analyzed in the paper of Casas et al., turns out to be additive, hence, the methods presented here are applicable to it.
The notion of resolving sets in a graph was introduced by Slater [Proceedings of the Sixth Southeastern Conference on Combinatorics, Graph Theory, and Computing, Util. Math., Winnipeg, 1975, pp. 549-559] and Harary an...
详细信息
The notion of resolving sets in a graph was introduced by Slater [Proceedings of the Sixth Southeastern Conference on Combinatorics, Graph Theory, and Computing, Util. Math., Winnipeg, 1975, pp. 549-559] and Harary and Melter [Ars Combin., 2 (1976), pp. 191-195] as a way of uniquely identifying every vertex in a graph. A set of vertices in a graph is a resolving set if for any pair of vertices x and y there is a vertex in the set which has distinct distances to x and y. A smallest resolving set in a graph is called a metric basis and its size, the metric dimension of the graph. The problem of computing the metric dimension of a graph is a well-known NP-hard problem and while it was known to be polynomial time solvable on trees, it is only recently that efforts have been made to understand its computational complexity on various restricted graph classes. In recent work, Foucaud [Algorithmica, 2016, pp. 1-31] showed that this problem is NP-complete even on interval graphs. They complemented this result by also showing that it is fixed-parameter tractable (FPT) parameterized by the metric dimension of the graph. In this work, we show that this FPT result can in fact be extended to all graphs of bounded tree-length. This includes well-known classes like chordal graphs, AT-free graphs, and permutation graphs. We also show that this problem is FPT parameterized by the modular-width of the input graph.
The fluid-structure interactions of a blunt fin mounted over a compliant panel in Mach 2 flow were investigated. The test geometry consisted of a thin, flexible panel fixed on all edges with a blunt fin with a hemisph...
详细信息
The fluid-structure interactions of a blunt fin mounted over a compliant panel in Mach 2 flow were investigated. The test geometry consisted of a thin, flexible panel fixed on all edges with a blunt fin with a hemispherically rounded leading edge mounted in a manner that the leading edge of the fin overhung the panel. The blunt fin was also pivoted to several angles of attack with respect to the oncoming flow. This allowed for the study of the dynamic system created by the interactions between the compliant panel and the blunt fin geometries. Both rigid and compliant panel models were used in order to provide a comparison between the flow with and without the dynamics of the compliant panel. High-speed schlieren and surface oil flow visualizations showed that the time-averaged flow remained almost entirely unchanged between the rigid and compliant panels. The instantaneous flow fields, however, showed a highly dynamic system where the compliant panel induced oscillatory shock waves that were both stationary and freely moving. Simultaneous high-speed schlieren visualization and stereo digital-image correlation showed a strong linkage between the motion of the shock waves and the deformation of the panel. This was demonstrated through frequency analysis and modal decomposition of the panel deformation and shock motions.
暂无评论