Information Processing Letters最新文献

In evolutionary biology, networks are becoming increasingly used to represent evolutionary histories for species that have undergone non-treelike or reticulate evolution. Such networks are essentially directed acyclic graphs with a leaf set that corresponds to a collection of species, and in which non-leaf vertices with indegree 1 correspond to speciation events and vertices with indegree greater than 1 correspond to reticulate events such as gene transfer. Recently forest-based networks have been introduced, which are essentially (multi-rooted) networks that can be formed by adding some arcs to a collection of phylogenetic trees (or phylogenetic forest), where each arc is added in such a way that its ends always lie in two different trees in the forest. In this paper, we consider the complexity of deciding whether a given network is proper forest-based, that is, whether it can be formed by adding arcs to some underlying phylogenetic forest which contains the same number of trees as there are roots in the network. More specifically, we show that it is NP-complete to decide whether a tree-child network with m roots is proper forest-based, for each $m\ge 2$. Moreover, for binary networks the problem remains NP-complete when $m\ge 3$ but becomes polynomial-time solvable for $m=2$. We also give a fixed parameter tractable (FPT) algorithm, with parameters the maximum outdegree of a vertex, the number of roots, and the number of indegree 2 vertices, for deciding if a semi-binary network is proper forest-based. A key element in proving our results is a new characterization for when a network with m roots is proper forest-based in terms of certain m-colorings.

We present a new complementation construction for nondeterministic automata on finite trees. The traditional complementation involves determinization of the corresponding bottom-up automaton (recall that top-down deterministic automata are less powerful than nondeterministic automata, whereas bottom-up deterministic automata are equally powerful).

The construction works directly in a top-down fashion, therefore without determinization. The main advantages of this construction are: (i) in the special case of finite words it boils down to the standard subset construction (which is not the case of the traditional bottom-up complementation construction), and $\left(ii\right)$ it illustrates the core argument of the complementation lemma for infinite trees, central in the proof of Rabin's tree theorem, in a simpler setting where issues related to acceptance conditions over infinite words and determinacy of infinite games are not present.

Given a set $P=\{p_1,p_2,\dots ,p_n\}$ of n points in $R^2$ and a positive integer k $(\le n)$, we wish to find a subset S of P of size k such that the cost of a subset S, $cost\left(S\right)=\min \left\{d\right(p,q\left)\right|p,q\in S\}$, is maximized, where $d(p,q)$ is the Euclidean distance between two points p and q. The problem is called the max-min k-dispersion problem. In this article, we consider the max-min k-dispersion problem, where a given set P of n points are vertices of a convex polygon. We refer to this variant of the problem as the convex k-dispersion problem.

We propose an 1.733-factor approximation algorithm for the convex k-dispersion problem. In addition, we study the convex k-dispersion problem for $k=4$. We propose an iterative algorithm that returns an optimal solution of size 4 in $O\left(n^3\right)$ time.

Recently, Jecker has introduced and studied the regular $D$-length of a monoid, as the length of its longest chain of regular $D$-classes. We use this parameter in order to improve the construction, originally proposed by Colcombet, of a deterministic automaton that allows to map a word to one of its forward Ramsey splits: these are a relaxation of factorisation forests that enjoy prefix stability, thus allowing a compositional construction. For certain monoids that have a small regular $D$-length, our construction produces an exponentially more succinct deterministic automaton. Finally, we apply it to obtain better complexity result for the problem of fast infix evaluation.

Let A, B, and C be three $n\times n$ matrices. We investigate the problem of verifying whether $AB=C$ over the ring of integers and finding the correct product AB. Given that C is different from AB by at most k entries, we propose an algorithm that uses $O(\sqrt{k}{n}^2+k^{2}n)$ operations. Let α be the largest absolute value of an entry in A, B, and C. The integers involved in the computation are of $O\left(n^3{\alpha }^2\right)$.

We study the problem of computing the center of cycle graphs whose vertices are weighted. The distance from a vertex to a point of the graph is defined as the weight of the vertex times the length of the shortest path between the vertex and the point. The weighted center of the graph is a point of the graph such that the maximum distance of the vertices of the graph to the point is minimum among all points of the graph. We present an $O\left(n\right)$-time algorithm for the discrete and continuous weighted center problem on cycle graphs with n vertices. Our algorithm improves upon the best known algorithm that takes $O(n\log n)$ time. Moreover, it is optimal for the weighted center problem of cycle graphs.

Recently, a class of quaternary sequences with period pq, where p and q are two distinct odd primes introduced by Zhang et al. were proved to possess high linear complexity and 4-adic complexity. In this paper, we determine the autocorrelation distribution of this class of quaternary sequence. Our results indicate that the studied quaternary sequence are weak with respect to the correlation property.

The qCCS model proposed by Feng et al. provides a powerful framework to describe and reason about quantum communication systems that could be entangled with the environment. However, they only studied weak bisimulation semantics. In this paper we propose a new branching bisimilarity for qCCS and show that it is a congruence. The new bisimilarity is based on the concept of ϵ-tree and preserves the branching structure of concurrent processes where both quantum and classical components are allowed. Furthermore, we present a polynomial time equivalence checking algorithm for the ground version of our branching bisimilarity.

In this paper we consider two vertex deletion problems. In the Block Vertex Deletion problem, the input is a graph G and an integer k, and the goal is to decide whether there is a set of at most k vertices whose removal from G result in a block graph (a graph in which every biconnected component is a clique). In the Pathwidth One Vertex Deletion problem, the input is a graph G and an integer k, and the goal is to decide whether there is a set of at most k vertices whose removal from G result in a graph with pathwidth at most one. We give a kernel for Block Vertex Deletion with $O\left(k^3\right)$ vertices and a kernel for Pathwidth One Vertex Deletion with $O\left(k^2\right)$ vertices. Our results improve the previous $O\left(k^4\right)$-vertex kernel for Block Vertex Deletion (Agrawal et al., 2016 [1]) and the $O\left(k^3\right)$-vertex kernel for Pathwidth One Vertex Deletion (Cygan et al., 2012 [3]).

In the Longest $(s,t)$-Detour problem, we look for an $(s,t)$-path that is at least k vertices longer than a shortest one. We study the parameterized complexity of Longest $(s,t)$-Detour when parameterized by k: this falls into the research paradigm of ‘parameterization above guarantee’. Whereas the problem is known to be fixed-parameter tractable (FPT) on undirected graphs, the status of Longest $(s,t)$-Detour on directed graphs remains highly unclear: it is not even known to be solvable in polynomial time for $k=1$. Recently, Fomin et al. made progress in this direction by showing that the problem is FPT on every class of directed graphs where the 3-Disjoint Paths problem is solvable in polynomial time. We improve upon their result by weakening this assumption: we show that only a polynomial-time algorithm for 2-Disjoint Paths is required.