Oct 7, 2012 - Existing integer programming based crossing-number formulations ... This non-negative function goes to zero if no edge crossings occur. ...... margin separation can enforce maximum spacing between graph components.
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2912) ... We present an extensive experimental study of heuristics for crossing ...
Layer-Free Upward Crossing Minimization. Markus Chimani ... Crossing Reduction: Reorder the nodes on each layer with the objective to reduce the ..... directing the edges according to the node order given in the input filesâfor showing the ...
(b) it does not involve cuts of the feasible region; ... partial list of extreme points of C, and edges emanat- ..... Now a pivot in column j (i.e., making sjN basic) will.
Email [email protected], [email protected]. Telephone (518) ..... the mathematical programming methods to a Database Marketing data set. This data set. 17 ...
Abstract: Most of nonsmooth optimization methods can be divided into two ...... r-algorithm in their web-page as well as Professors L. Lukšan and J. Vlcek for pro-.
We compare different nonsmooth optimization (NSO) methods for solving uncon- strained ..... and the new subgradient ξk+1 â âf(yk+1) will force a remarkable modification of the ..... Next we briefly describe the quasi-secant method (QSM).
Jul 14, 2015 - Comparing regret minimization and utility maximization for route choice using the recursive logit model. Tien Mai. â. Fabian Bastin. â.
Dec 14, 2018 - incision, intra-operative blood loss, and post-operative length of stay in the ... tion costs among patients with pelvic fractures vary greatly. On the one .... were any differences in the cost effectiveness of pelvic fracture treatmen
Jul 9, 2008 - |A| ⤠n/2, we have |δHâ² (A)| ⥠c5|A|, and so w(δHâ² (A) ⥠c5|A|pn ⥠c5p|A|(n â |A|) ⥠c5 ... [10] M. Jerrum, A. Sinclair, and E. Vigoda.
Aug 15, 2002 - Note that we do not claim any relationship between N and L, and in particular, N may be larger than L, implying that the proposed ...
Feb 23, 2011 ... bear this notice and the full citation on the first page. .... wise methods is that they
are much more complete than the ... Fullmetal Alchemist.
Oct 23, 2015 - cantly outperforms ALM for (33) with convex rank surrogate. This is because the nonconvex surrogates approximate the rank function much ...
Aug 15, 2002 - sparse representation signals from the same dictionary using the .... Theorem 5 - Lower-Bound on the Spark: Given the dictionary D and its ...
A tree without any double claws is a set of caterpillars. Caterpillars can be embedded on 2-levels without any crossings (see Figure 4(c)). On the other hand, a ...
Oct 6, 2008 - Despite that, we prove that empirical minimization in the convex hull ... empirical risk minimization over the convex hull of an empirically chosen ...
Jul 7, 2016 - The management of an insurance portfolio's risk is one of the core challenges in actuarial ...... Norberg, R. A Theory of Bonus in Life Insurance.
that is based on a reduction to the maximum cut problem (MAXCUT). The same reduction yields a simple test for fixed linear planarity. Computational results.
Industry 4.0 is focused on smart production in smart factories where there is direct communication between humans, machine, and resources. Smart products ...
We call this the metro-line crossing minimization prob- lem (MLCM). As a first step towards solving MLCM in arbitrary graphs, we study path and tree networks.
management [24], supply chain planning [12], maintenance, and sales [8, 9]. Among these .... based implementation in of data analysis tools, like MATLAB.
Effective methods are needed to capture the nonlinear behaviour into a model. Regression trees and neural net- works are considered as candidates for the task ...
c Springer-Verlag Berlin Heidelberg 2005 ... ing minimization is that for a known species tree different gene trees should ... depend on the parent's position, let us fix the following convention: We .... In any optimum solution, there is no crossing between edges adjacent to ..... In: Proc. of 11th ACM-SIAM Symposium on.
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Comparing Trees Via Crossing Minimization Henning Fernau1,2 , Michael Kaufmann1 , and Mathias Poths1 1
2
Univ. T¨ ubingen, WSI f¨ ur Informatik, Sand 13, 72076 T¨ ubingen, Germany {fernau/mk/poths}@informatik.uni-tuebingen.de Univ. Hertfordshire, Comp. Sci., College Lane, Hatfield, Herts AL10 9AB, UK
Abstract. Two trees with the same number of leaves have to be embedded in two layers in the plane such that the leaves are aligned in two adjacent layers. Additional matching edges between the leaves give a one-to-one correspondence between pairs of leaves of the different trees. Do there exist two planar embeddings of the two trees that minimize the crossings of the matching edges ? This problem has important applications in the construction and evaluation of phylogenetic trees.
1
Introduction
The comparison of trees has applications in various areas like text data bases, bioinformatics, compiler construction etc. Various algorithms for different models for comparisons have been proposed. Keywords are tree matching, tree alignment, tree editing [12,13,14,15,16], a nice overview being [3]. Motivated by discussions with researchers from bioinformatics like D. Huson and D. Bryant, we propose to compare two tree structures by finding two most similar left-to-right orderings of their leaves. The ordering of the leaves can be made best visible by drawing one tree downward from the root and aligning all the leaves on a horizontal line. The leaves of the other tree are also aligned parallel to the first line and the corresponding tree structure is drawn from the leaves upside downward to the root. Corresponding leaves from the two trees are connected by matching edges. Let L(T ) denote the leaves of a tree T . A linear order < on L(T ) is called suitable if T can be embedded into the plane such that L(T ) is mapped onto a straight line (layer ) in the order given by
