Acta Informatica最新文献

Let G be a connected graph. For an edge (e=xy in E(G)), e is monitored by a vertex v if (d_G(v, y)ne d_{G-e}(v, y)) or (d_G(v, x)ne d_{G-e}(v, x)). A set M of vertices of a graph G is distance-edge-monitoring (DEM for short) set if every edge e of G is monitored by some vertex of M. A DEM set X for a graph G is called fault-tolerant DEM set if (Xsetminus {v}) is also DEM set for each v in X. Denote (operatorname {dem}(G)) and (operatorname {Fdem}(G)) the smallest size of DEM set and fault-tolerant DEM sets, respectively. In this paper, we first study the relation between (operatorname {Fdem}(G)) and (operatorname {dem}(G)) for a graph G. Next, we show that (2 le operatorname {Fdem}(G) le n) for any graph G with order n. Furthermore, the extremal graphs attaining lower and upper bounds are characterized. In the end, the exact values for some networks are given. Furthermore, it is shown that for (2le s<tle n), there exists a graph G of order n such that (operatorname {dem}(G)=s) and (operatorname {Fdem}(G)=t).

The current study advances prior research on non-binary Fibonacci codes by introducing new families of universal codes. These codes demonstrate the advantage of accommodating a larger number of codewords for sufficiently large lengths. They retain the properties of instantaneous decipherability and robustness against transmission errors. This work presents these dense codes as a promising alternative for compressing extensive lists of very large integers, commonly encountered in cryptographic applications.

In this paper, we investigate a slightly simplified version of Birkhoff–von Neumann quantum logic enriched with entanglement quantifiers which is proposed in Ying (Birkhoff–von Neumann quantum logic as an assertion language for quantum programs, 2022. arXiv:2205.01959). The main result is a coincidence theorem, which says that every formula is interpreted by a closed subspace in the Hilbert space corresponding to the free variables of the formula. We also prove that many instances of semantic consequence, which are used in the proof of the prenex normal form theorem in first-order logic, also hold in this logic. The technical work is about the interplay among the three operations on density operators, namely, tensor product, support and partial trace.

Motivated by a phylogeny reconstruction problem in evolutionary biology, we study the minimum Steiner arborescence problem on directed hypercubes (MSA-DH). Given m, representing the directed hypercube (vec {Q}_m), and a set of terminals (R), the problem asks to find a Steiner arborescence that spans (R) with minimum cost. As (m) implicitly represents (vec {Q}_{m}) comprising (2^{m}) vertices, the running time analyses of traditional Steiner tree algorithms on general graphs does not give a clear understanding of the actual complexity of this problem. We present algorithms that exploit the structure of the hypercube and run in FPT time. We explore the MSA-DH problem on three natural parameters—(|R|), and two above-guarantee parameters, number of Steiner nodes p and penalty q (defined as the extra cost above m incurred by the solution). For above-guarantee parameters, the parameterized MSA-DH problem take (p ge 0) or (qge 0) as input, and outputs a Steiner arborescence with at most (|R|+ p - 1) or (m+ q) edges respectively. We present the following results ((tilde{{mathcal {O}}}) hides the polynomial factors):

1. 1.

   An exact algorithm that runs in (tilde{{mathcal {O}}}(3^{|R|})) time.

2. 2.

   A randomized algorithm that runs in (tilde{{mathcal {O}}}(9^q)) time with success probability (ge 4^{-q}).

3. 3.

   An exact algorithm that runs in (tilde{{mathcal {O}}}(36^q)) time.

4. 4.

   A ((1+q))-approximation algorithm that runs in (tilde{{mathcal {O}}}(1.25284^q)) time.

5. 5.

   An ({mathcal {O}}left( pell _{textrm{max}}right) )-additive approximation algorithm that runs in (tilde{{mathcal {O}}}(ell _{textrm{max}}^{p+2})) time, where (ell _{textrm{max}}) is the maximum distance of any terminal from the root.

Let H(V, E) be a k-regular connected hypergraph with rank R on n vertices and m edges. A set of vertices (Ssubseteq V) is an independent set if every two vertices in S are not adjacent. The independence number is the maximum cardinality of an independent set, denoted by (alpha (H)). In this paper, we prove the following inequality: (alpha (H)ge frac{m-(k-2)n-1}{R}), and the equality holds if and only if H is a hypertree with R-perfect matching. Based on the proofs, some combinatorial algorithms on the independence number are designed.

It is a current trend of sparse architectures employed for superconducting quantum chips, which have the advantage of low coupling and crosstalk properties. Existing qubit mapping algorithms do not take the sparsity of quantum architectures into account. To this end, we propose a qubit mapping method based on binary integer programming, called QMBIP. First, we slice a given quantum circuit by taking into account the sparsity of target architectures. Then, the constraints and the objective function are formulated and rendered to the binary integer programming problem by matrix transformation. The behavior of a (textbf{SWAP}) gate is characterized by an elementary row transformation on the mapping matrix between the physical and logical qubits. To reduce the search space, we introduce path variables and isomorphic pruning, as well as a look-ahead mechanism. Finally, we compare with typical qubit mapping algorithms such as SABRE and SATMAP on the sparse architectures ibmq_sydney, ibmq_manhattan, ibmq_singapore, and a dense architecture ibmq_tokyo. Experiments show that QMBIP effectively maintains the fidelity of the compiled quantum circuits. For example, on ibmq_sydney, the fidelity of the quantum circuits compiled by our approach outperforms SABRE and SATMAP by 53.9% and 46.8%, respectively.

P systems are distributed, parallel computing models inspired by biology. Tissue-like P systems are an important variant of P systems, where the environment can provide objects for cells. Hence, the environment plays a critical role. Nevertheless, in actual biological tissues, there exists a peculiar biological phenomenon called “homeostasis”; that is, the internal organisms maintain stable, thereby reducing their dependence on external conditions (i.e., the environment). In this work, considering cell separation, we construct a novel variant to simulate the mechanism of biological homeostasis, called homeostasis tissue-like P systems with cell separation. In this variant, the number of object is finite, and certain substance changes occur inside the cells; moreover, an exponential workspace can be obtained with cell separation in feasible time. The computational power of this model is studied by simulating register machines, and the results show that the variant is computationally complete as number computing devices. Furthermore, to explore the computational efficiency of the model, we use the variant to solve a classic (textbf{NP})-complete problem, the SAT problem, obtaining a uniform solution with a rule length of at most 3.

A connected feedback vertex set of a graph is a connected subgraph of the graph whose removal makes the graph cycle free. In this paper, we provide an approximation algorithm for connected feedback vertex set in AT-free graphs. Given an (alpha )-approximate solution for feedback vertex set on 2-connected AT-free graph, our algorithm produces a solution of size (((alpha +0.9091)OPT+6)) for connected feedback vertex set on the same graph. The complexity of our algorithm is (O(f(n)+(m+n))), where the time required to obtain the (alpha )-approximate solution is O(f(n)). Our result leads to the following two observations. The optimal feedback vertex set algorithm for AT-free graphs combined with our result provides an algorithm which produces a solution of size ((1.9091OPT+6)) with running time (O(n^8m^2)) for 2-connected AT-free graphs. The 2-approximation algorithm for feedback vertex set in general graphs along with our result provides an algorithm which produces a solution of size ((2.9091OPT+6)) with running time (O(min{m(log(n)),n^2})). Using the same method we also obtain a (((alpha +1)OPT+6))-approximation for this problem on general AT-free graphs. We note that, the complexity status of this problem is not known.

DNA technologies have evolved significantly in the past years enabling the sequencing of a large number of genomes in a short time. Nevertheless, the underlying problem of assembling sequence fragments is computationally hard and many technical factors and limitations complicate obtaining the complete sequence of a genome. Many genomes are left in a draft state, in which each chromosome is represented by a set of sequences with partial information on their relative order. Recently, some approaches have been proposed to compare draft genomes by comparing paths in de Bruijn graphs, which are constructed by many practical genome assemblers. In this article we describe in more detail a method for comparing genomes represented as succinct colored de Bruijn graphs directly and without resorting to sequence alignments, called (texttt {gcBB}), that evaluates the entropy and expectation measures based on the Burrows-Wheeler Similarity Distribution. We also introduce an improved version of (texttt {gcBB}), called (texttt {multi-gcBB}), that improves the time and space performance considerably through the selection of different data structures. We have compared phylogenies of 12 Drosophila species obtained by other methods to those obtained with (texttt {gcBB}), achieving promising results.