Keywords: Indexing structure; Factor recognition; Suffix recognition 相似文献
In this paper, we propose a simple method to compress suffix trees by merging couples of nodes. This idea was already used in the literature in a context different from ours. The originality of our approach is that the nodes we merge are not chosen with respect to their subtrees (which is difficult to test algorithmically), nor with respect to the words spelled along branches (which usually requires testing several branches before finding the good one) but with respect to their position in the tree (which is easy to compute). Another particularity of our method is it needs to read no edge label: it is exclusively based on the topology of the suffix tree. The compact structure resulting after compression is the factor/suffix oracle introduced by Allauzen, Crochemore and Raffinot whose accepted language includes the accepted language of the corresponding suffix tree.
The interest of our paper is therefore threefold:
- 1. A topology-based compression method is defined for (compact) suffix trees.
2. A new property of a factor/suffix oracle is established, that is, like a DAG, it results from the corresponding suffix tree after a linear number of appropriate node mergings; unlike a DAG, the merged nodes do not necessarily have isomorphical subtrees.
3. A new algorithm to transform a suffix tree into a factor/suffix oracle is given, which has linear running time and thus improves the quadratic complexity previously known for the same task.
Let K denote a compact subset of the complex plane . We present correct proof that the stable rank of A(K) is one. Hereby, A (K) is the algebra of all continuous functions on K which are analytic in the interior of K.
Let G denote a plane domain whose boundary consists of finitely many closed, nonintersecting Jordan curves. We show that for a fixed function of gεC( ), g≠0, the following assertions are equivalent:
Every unimodular element (f, g) is reducible to the principal component exp(C( )).
The zero set Zg is polynomially convex, i.e., its complement Zg is connected.
Author Keywords: Bass' stable rank; reducible; unimodular; 1-stable; boundary principle 相似文献
1. dn, n 1, has no subsequence converging in probability, and
2. ∑n 1|an|p < ∞ whenever ∑n 1andn converges almost surely are equivalent for every sequence dn, n 1, of symmetric independent random elements taking values in B.
Author Keywords: Bounded in probability; convergence in probability; cotype; uniform tightness condition 相似文献
- (1) sensor-constrained: we are allowed a fixed number of sensors and want to minimize contaminationdetection time; and
(2) time-constrained: we must detect contamination within a given time limit and want to minimize the number of sensors required.
Our main results are as follows. First, we give a necessary and sufficient condition for source identification.Second, we show that the sensor and time constrained versions of the problem are polynomially equivalent. Finally, we show that the sensor-constrained version of the problem is polynomially equivalent to the asymmetric k-center problem and that the time-constrained version of the problem is polynomially equivalent to the dominating set problem. 相似文献
1. (i) (G − e) > (G), if e is not a cut edge of G, and
2. (ii) v(Gi) − (Gi) < v(G) − (G), I = 1, 2, if e is a cut edge and G1, G2 are the two components of G − e.
Recently, Katchalski et al. (1995) conjectured that: if G is a connected critical graph, then with equality possible if and only if G is a tree. In this paper we establish this conjecture. 相似文献
1. the use of fractional integral/differential operators;
2. a formula for Gegenbauer functions which is a fractional extension of the Rodrigues formula for Gegenbauer polynomials (see Theorem 3);
3. an intertwining relation concerning fractional integral/differential operators (see Theorem 1), which in the integer case reads (d/dx)2n+1 = (x−1 d/dx)nx2n+1(x−1 d/dx)n+1.
Thus we cover most of the known results on this type of integral equations and obtain considerable extensions. As a special illustration we present the Gegenbauer transform pair associated to the Radon transformation. 相似文献
1. [(i)] There exists a basis for V with respect to which the matrix representing A is diagonal and the matrix representing A* is irreducible tridiagonal.
2. [(ii)] There exists a basis for V with respect to which the matrix representing A* is diagonal and the matrix representing A is irreducible tridiagonal.
We call such a pair a Leonard pair on V. Refining this notion a bit, we introduce the concept of a Leonard system. We give a complete classification of Leonard systems. Integral to our proof is the following result. We show that for any Leonard pair A,A* on V, there exists a sequence of scalars β,γ,γ*,,* taken from such that both
where [r,s] means rs−sr. The sequence is uniquely determined by the Leonard pair if the dimension of V is at least 4. We conclude by showing how Leonard systems correspond to q-Racah and related polynomials from the Askey scheme. 相似文献
• We characterize those trees that can be drawn as Voronoi diagrams in the Euclidean metric.
• We characterize those sets of points whose Voronoi diagrams are trees in the Manhattan metric.
• We show that the maximum vertex degree of any tree that can be drawn as a Manhattan Voronoi diagram is at most five and prove that this bound is tight.
• We characterize those binary trees that can be drawn as Manhattan Voronoi diagrams.
Author Keywords: Graph drawing; Voronoi diagrams; Graph characterization; Geometric graphs 相似文献
1. a theory of laser stimulated vaporization of droplets,
2. a theory of internal heating resulting from vibration waves in linearly responding elastic material, and
3. flame theory.
There are applications to sending information through clouds on laser beams and to the control of temperature in ultrasonic welding, and improvement of the design of aircraft engines and the processes used for the destruction of toxic chemicals.
We develop a theory of thermal excursions resulting from ultrasonic welding in 3 and 7 dimensions, and interpret it as an elastic interaction with damping in a Voigt solid. It is hypothesized that with good control of temperature, one could achieve strong and uniform welds by this process and greatly reduce the cost of manufacturing aircraft, and other aluminum structures. We consider equations describing the conservation of mass, momentum, and energy coupled by an equation of state, and consider general mass, momentum, and energy transfer relationships in a compressible body subjected to external stimuli. For the Voigt solid theory, a linear elastic theory with damping forces, we show how some simple local time averaging gives us a dovetailed system consisting of the elastic wave equations whose solution provides the source term for an otherwise uncoupled heat equation. For the more general theory of droplet vaporization, we illustrate a general nonlinear energy equation which includes a radiation energy conductivity term. We get a class of exact solutions for a nonlinear flame front boundary value problem. 相似文献
1. each vertex corresponds to a distinct induced subgraph in G isomorphic to Y, and
2. two vertices are adjacent iff the intersection of their corresponding subgraphs contains an induced subgraph isomorphic to X.
This notion generalizes the classical concept of line graphs since the (K1,K2)-intersection graph of a graph G is precisely the line graph of G.
Let ( , respectively) denote the family of line graphs of bipartite graphs (bipartite multigraphs, respectively), and refer to a pair (X,Y) as a 2-pair if Y contains exactly two induced subgraphs isomorphic to X. Then and , respectively, are the smallest families amongst the families of (X,Y)-intersection graphs defined by so called hereditary 2-pairs and hereditary non-compact 2-pairs. Furthermore, they can be characterized through forbidden induced subgraphs. With this motivation, we investigate the properties of a 2-pair (X,Y) for which the family of (X,Y)-intersection graphs coincides with (or ). For this purpose, we introduce a notion of stability of a 2-pair and obtain the desired characterization for such stable 2-pairs. An interesting aspect of the characterization is that it is based on a graph determined by the structure of (X,Y). 相似文献
1. (1) Let S be any set of points in the plane, no three on a line. If |S| E(n, q), then there exists a convex n-gon whose points belong to S, for which the number of points of S in its interior is 0 (mod q).
2. (2) For fixed q, E(n,q) 2c(q)·n, c(q) is a constant depends on q only.
Part (1) was proved by Bialostocki et al. [2] and our proof is aimed to simplify the original proof. The proof of Part (2) is completely new and reduces the huge upper bound of [2] (a super-exponential bound) to an exponential upper bound. 相似文献