A Kleene Theorem for Weighted Tree Automata

In this paper we prove Kleenes result for formal tree series over a commutative semiring A (which is not necessarily complete or continuous or idempotent), i.e., the class of formal tree series over A which are accepted by weighted tree automata, and the class of rational tree series over A are equal. We show the result by direct automata-theoretic constructions and prove their correctness.     

A Kleene Theorem for Weighted Tree Automata over Distributive Multioperator Monoids

Kleene’s theorem on the equivalence of recognizability and rationality for formal tree series over distributive multioperator monoids is proved. As a consequence of this, Kleene’s theorem for weighted tree automata over arbitrary, i.e., not necessarily commutative, semirings is derived.     

A Completeness Theorem for Kleene Algebras and the Algebra of Regular Events

We give a finitary axiomatization of the algebra of regular events involving only equations and equational implications. Unlike Salomaa′s axiomatizations, the axiomatization given here is sound for all interpretations over Kleene algebras.     

一种改进的有向无环图支持向量机

构造合理的有向无环图是有向无环图支持向量机亟需解决的一个关键问题。本文提出一种改进的有向无环图支持向量机,根据超球支持向量机获得类的最小包围球,根据该最小包围球计算类与类之间的最短距离,根据该最短距离形成最短距离矩阵,根据该最短距离矩阵来构造有向无环图。实验结果表明,该改进算法较传统有向无环图支持向量机分类精度有明显提高。     

Sparse Covers for Planar Graphs and Graphs that Exclude a Fixed Minor

We consider the construction of sparse covers for planar graphs and other graphs that exclude a fixed minor. We present an algorithm that gives a cover for the γ-neighborhood of each node. For planar graphs, the cover has radius less than 16γ and degree no more than 18. For every n node graph that excludes a minor of a fixed size, we present an algorithm that yields a cover with radius no more than 4γ and degree O(logn). This is a significant improvement over previous results for planar graphs and for graphs excluding a fixed minor; in order to obtain clusters with radius O(γ), it was required to have the degree polynomial in n. Our algorithms are based on a recursive application of a basic routine called shortest-path clustering, which seems to be a novel approach to the construction of sparse covers. Since sparse covers have many applications in distributed computing, including compact routing, distributed directories, synchronizers, and Universal TSP, our improved cover construction results in improved algorithms for all these problems, for the class of graphs that exclude a fixed minor.     

A Characterization of Planar Graphs by Pseudo-Line Arrangements

Let ?? be an arrangement of pseudo-lines, i.e., a collection of unbounded x -monotone curves in which each curve crosses each of the others exactly once. A pseudo-line graph (??, E) is a graph for which the vertices are the pseudo-lines of ?? and the edges are some unordered pairs of pseudo-lines of ??. A diamond of a pseudo-line graph (??, E) is a pair of edges {p,q} , {p',q'}∈ E , {p,q} ∩ {p',q'}= Ø, such that the crossing point of the pseudo-lines p and q lies vertically between p' and q' and the crossing point of p' and q' lies vertically between p and q . We show that a graph is planar if and only if it is isomorphic to a diamond-free pseudo-line graph. An immediate consequence of this theorem is that the O(k1/3n) upper bound on the k -level complexity of an arrangement of straight lines, which was very recently discovered by Dey, holds for an arrangement of pseudo-lines as well.     

A Characterization of Planar Graphs by Pseudo-Line Arrangements

Let Γ be an arrangement of pseudo-lines, i.e., a collection of unbounded x -monotone curves in which each curve crosses each of the others exactly once. A pseudo-line graph (Γ, E) is a graph for which the vertices are the pseudo-lines of Γ and the edges are some unordered pairs of pseudo-lines of Γ . A diamond of a pseudo-line graph (Γ, E) is a pair of edges {p,q} , {p',q'}∈ E , {p,q} ∩ {p',q'}= , such that the crossing point of the pseudo-lines p and q lies vertically between p' and q' and the crossing point of p' and q' lies vertically between p and q . We show that a graph is planar if and only if it is isomorphic to a diamond-free pseudo-line graph. An immediate consequence of this theorem is that the O(k ^1/3 n) upper bound on the k -level complexity of an arrangement of straight lines, which was very recently discovered by Dey, holds for an arrangement of pseudo-lines as well.     

New Linear-Time Algorithms for Edge-Coloring Planar Graphs

We show efficient algorithms for edge-coloring planar graphs. Our main result is a linear-time algorithm for coloring planar graphs with maximum degree Δ with max {Δ,9} colors. Thus the coloring is optimal for graphs with maximum degree Δ≥9. Moreover for Δ=4,5,6 we give linear-time algorithms that use Δ+2 colors. These results improve over the algorithms of Chrobak and Yung (J. Algorithms 10:35–51, 1989) and of Chrobak and Nishizeki (J. Algorithms 11:102–116, 1990) which color planar graphs using max {Δ,19} colors in linear time or using max {Δ,9} colors in time. R. Cole supported in part by NSF grants CCR0105678 and CCF0515127 and IDM0414763. Ł. Kowalik supported in part by KBN grant 4T11C04425. Part of this work was done while Ł. Kowalik was staying at the Max Planck Institute in Saarbruecken, Germany.     

Disk Embeddings of Planar Graphs

Given a planar graph $G=(V,E)$ and a rooted forest ${\FF}=(V_{\FF}, A_{\FF})$ with leaf set $V$, we wish to decide whether $G$ has a plane embedding $\GG$ satisfying the following condition: There are $|V_{\FF}|-|V|$ pairwise noncrossing Jordan curves in the plane one-to-one corresponding to the nonleaf vertices of ${\FF}$ such that for every nonleaf vertex $f$ of ${\FF}$, the interior of the curve $\JJ_f$ corresponding to $f$ contains all the leaf descendants of $f$ in ${\FF}$ but contains no other leaves of ${\FF}$. This problem arises from theoretical studies in geographic database systems. It is unknown whether this problem can be solved in polynomial time. This paper presents an almost linear-time algorithm for a nontrivial special case where the set of leaf descendants of each nonleaf vertex $f$ in ${\FF}$ induces a connected subgraph of $G$.     

An Algorithm for Straight-Line Drawing of Planar Graphs

We present a new algorithm for drawing planar graphs on the plane. It can be viewed as a generalization of the algorithm of Chrobak and Payne, which, in turn, is based on an algorithm by de Fraysseix, Pach, and Pollack. Our algorithm improves the previous ones in that it does not require a preliminary triangulation step; triangulation proves problematic in drawing graphs ``nicely,' as it has the tendency to ruin the structure of the input graph. The new algorithm retains the positive features of the previous algorithms: it embeds a biconnected graph of n vertices on a grid of size (2n-4) x (n-2) in linear time. We have implemented the algorithm as part of a software system for drawing graphs nicely. Received September 21, 1995; revised March 15, 1996.     

A Kleene theorem for splitable signals

In this paper, we consider timed automata for piecewise constant signals and prove that they recognize exactly the languages denoted by signal regular expressions with intersection and renaming. The main differences from the usual timed automata are: time elapses on transitions (passing through a state is instantaneous), signals may be split on a run on an automaton and constraints on transitions correspond to unions of open intervals but should be satisfied on closed intervals. This makes exact rendez-vous impossible. The paper stresses on the similarities and differences from the usual model.     

A Fully Dynamic Approximation Scheme for Shortest Paths in Planar Graphs

In this paper we give a fully dynamic approximation scheme for maintaining all-pairs shortest paths in planar networks. Given an error parameter such that , our algorithm maintains approximate all-pairs shortest paths in an undirected planar graph G with nonnegative edge lengths. The approximate paths are guaranteed to be accurate to within a 1+ factor. The time bounds for both query and update for our algorithm is O( ^-1 n ^2/3 log ² n log D) , where n is the number of nodes in G and D is the sum of its edge lengths. The time bound for the queries is worst case, while that for the additions is amortized. Our approximation algorithm is based upon a novel technique for approximately representing all-pairs shortest paths among a selected subset of the nodes by a sparse substitute graph. Received January 1995; revised February 1997.     

Acyclic Directed Graphs for Automatic Image Analysis of Lung Parenchymal Geometry

We have developed a simple method for encoding pulmonary alveolar geometry suitable for morphometric analysis and modeling. The approach involves the use of 8-bit video microscopic images of lung which are thresholded to produce binary images. Each alveolar wall was thinned to its midline to produce a skeletonized image, We present an algorithm for converting such an image to an acyclic directed graph. Such a representation is quite suitable for mathematical treatment, lending itself to problems involving simulation or modeling. We present as an example application, the measurement of dihedral angles in rat lung using conventional histological sections.     

Optimal Polygonal Representation of Planar Graphs

In this paper, we consider the problem of representing planar graphs by polygons whose sides touch. We show that at least six sides per polygon are necessary by constructing a class of planar graphs that cannot be represented by pentagons. We also show that the lower bound of six sides is matched by an upper bound of six sides with a linear-time algorithm for representing any planar graph by touching hexagons. Moreover, our algorithm produces convex polygons with edges having at most three slopes and with all vertices lying on an O(n)×O(n) grid.     

无圈与或图搜索的符号OBDD算法研究

与或图搜索是人工智能领域一项重要的问题求解技术.基于传统数据结构的与或图表示技术极大地限制了与或图搜索算法可求解问题的规模.在无圈与或图符号OBDD表示的基础上,给出了一种求解无圈与或图最小代价解图的符号搜索算法.实验结果表明,与 AO*算法相比,该算法可处理问题的规模有较大的提高.     

一类可修非周期Fork-Join排队网络分析

研究一类排队空间有限且服务台可修的非周期Fork-Join排队网络,给出求解稳态概率的直接法和等效法,并计算一些排队指标和可修指标(如稳态队长、服务台的可用度和服务台的失效概率),最后通过仿真验证其正确性.     

Subgraphs of 4-Regular Planar Graphs

We shall present an algorithm for determining whether or not a given planar graph H can ever be a subgraph of a 4-regular planar graph. The algorithm has running time O(|H|^2.5) and can be used to find an explicit 4-regular planar graph G⊃H if such a graph exists. It shall not matter whether we specify that H and G must be simple graphs or allow them to be multigraphs.