Journal of Computer and System Sciences最新文献

We treat user equipments (UEs) and mobile edge clouds (MECs) as M/G/1 queueing systems, which are the most suitable, powerful, and manageable models. We propose a computation offloading strategy which can satisfy all UEs served by an MEC and develop an efficient method to find such a strategy. We use discrete-time Markov chains, continuous-time Markov chains, and semi-Markov processes to characterize the mobility of UEs, and calculate the joint probability distribution of the locations of UEs at any time. We extend our Markov chains to incorporate mobility cost into consideration, and are able to obtain the average response time of a UE with location change penalty. We can algorithmically predict the overall average response time of tasks generated on a UE and also demonstrate numerical data and examples. We consider the power constrained MEC speed setting problem and develop an algorithm to solve the problem for two power consumption models.

This paper studies the relationship between undirected (unrooted) and directed (rooted) phylogenetic networks. We describe a polynomial-time algorithm for deciding whether an undirected nonbinary phylogenetic network, given the locations of the root and reticulation vertices, can be oriented as a directed nonbinary phylogenetic network. Moreover, we characterize when this is possible and show that, in such instances, the resulting directed nonbinary phylogenetic network is unique. In addition, without being given the location of the root and the reticulation vertices, we describe an algorithm for deciding whether an undirected binary phylogenetic network N can be oriented as a directed binary phylogenetic network of a certain class. The algorithm is fixed-parameter tractable (FPT) when the parameter is the level of N and is applicable to classes of directed phylogenetic networks that satisfy certain conditions. As an example, we show that the well-studied class of binary tree-child networks satisfies these conditions.

In their 2006 seminal paper in Distributed Computing, Angluin et al. present a construction that, given any Presburger predicate, outputs a leaderless population protocol that decides the predicate. The protocol for a predicate of size m runs in $O(m\cdot n^2\log n)$ expected number of interactions, which is almost optimal in n, the number of interacting agents. However, the number of states is exponential in m. Blondin et al. presented at STACS 2020 another construction that produces protocols with a polynomial number of states, but exponential expected number of interactions. We present a construction that produces protocols with $O\left(m\right)$ states that run in expected $O(m^7\cdot n^2)$ interactions, optimal in n, for all inputs of size $\Omega \left(m\right)$. For this, we introduce population computers, a generalization of population protocols, and show that our computers for Presburger predicates can be translated into fast and succinct population protocols.

The maximum parsimony distance $d_{\text{MP}}(T_1,T_2)$ and the bounded-state maximum parsimony distance $d_{\text{MP}}^t(T_1,T_2)$ measure the difference between two phylogenetic trees $T_1,T_2$ in terms of the maximum difference between their parsimony scores for any character (with t a bound on the number of states in the character, in the case of $d_{\text{MP}}^t(T_1,T_2)$). While computing $d_{\text{MP}}(T_1,T_2)$ was previously shown to be fixed-parameter tractable with a linear kernel, no such result was known for $d_{\text{MP}}^t(T_1,T_2)$. In this paper, we prove that computing $d_{\text{MP}}^t(T_1,T_2)$ is fixed-parameter tractable for all t. Specifically, we prove that this problem has a kernel of size $O(k\lg k)$, where $k=d_{\text{MP}}^t(T_1,T_2)$. As the primary analysis tool, we introduce the concept of leg-disjoint incompatible quartets, which may be of independent interest.

We propose a generic method for proving the decidability of the finite satisfiability problem for PCTL fragments and demonstrate its applicability in several non-trivial examples.

The NP-hard Multiple Hitting Set problem is the problem of finding a minimum-cardinality set intersecting each of the sets in a given input collection a given number of times. Generalizing a well-known data reduction algorithm due to Weihe, we show a problem kernel for Multiple Hitting Set parameterized by the Dilworth number, a graph parameter introduced by Foldes and Hammer in 1978 yet seemingly so far unexplored in the context of parameterized complexity theory. Using matrix multiplication, we speed up the algorithm to quadratic sequential time and logarithmic parallel time. We experimentally evaluate our algorithms. By implementing our algorithm on GPUs, we show the feasibility of realizing kernelization algorithms on SIMD (Single Instruction, Multiple Data) architectures.

We generalize the tree doubling and Christofides algorithm to parameterized approximations for ATSP (constant factor approximations that invest more runtime with respect to a chosen parameter). The parameters we consider are upper bounded by the number of asymmetric distances, which yields algorithms to efficiently compute good approximations for moderately asymmetric TSP instances. As generalization of the Christofides algorithm, we derive a parameterized 2.5-approximation, with the size of a vertex cover for the subgraph induced by the edges with asymmetric distances as parameter. Our generalization of tree doubling gives a parameterized 3-approximation, where the parameter is the minimum number of asymmetric distances in a minimum spanning arborescence. Further, we combine these with a notion of symmetry relaxation which allows to trade approximation guarantee for runtime. Since the parameters we consider are theoretically incomparable, we present experimental results showing that generalized tree doubling frequently outperforms generalized Christofides with respect to parameter size.

The asynchronous automaton of a Boolean network $f:{\{0,1\}}^n\to {\{0,1\}}^n$, considered in many applications, is the finite deterministic automaton where the set of states is ${\{0,1\}}^n$, the alphabet is $\left[n\right]$, and the action of letter i on a state x consists in either switching the ith component if $f_i\left(x\right)\ne x_i$ or doing nothing otherwise. In this paper, we ask for the existence of synchronizing words for this automaton, and their minimal length, when f is the and-net over an arc-signed digraph G on $\left[n\right]$: for every $i\in \left[n\right]$, $f_i\left(x\right)=1$ if and only if $x_j=1$ ($x_j\ne 0$) for every positive (negative) arc from j to i. Our main result is that if G is strongly connected and has no positive cycles, then either there exists a synchronizing word of length at most $10{(\sqrt{5}+1)}^n$ or G is a cycle and there are no synchronizing words. We also give complexity results showing that the situation is much more complex if one of the two hypothesis made on G is removed.

Unambiguous automata are nondeterministic automata in which every word has at most one accepting run. In this paper we give a polynomial-time algorithm for model checking discrete-time Markov chains against ω-regular specifications represented as unambiguous automata. We furthermore show that the complexity of this model checking problem lies in NC: the subclass of P comprising those problems solvable in poly-logarithmic parallel time. These complexity bounds match the known bounds for model checking Markov chains against specifications given as deterministic automata, notwithstanding the fact that unambiguous automata can be exponentially more succinct than deterministic automata. We report on an implementation of our procedure, including an experiment in which the implementation is used to model check LTL formulas on Markov chains.

We analyze the complexity of two fundamental verification problems within a generalization of the two-handed tile self-assembly model (2HAM) where initial system assemblies are not restricted to be singleton tiles, but may be larger prebuilt assemblies. Within this model we consider the producibility problem, which asks if a given tile system builds, or produces, a given assembly, and the unique assembly verification (UAV) problem, which asks if a given system uniquely produces a given assembly. We show that producibility is NP-complete and UAV is coNP${}^{NP}$-complete even when the initial assembly size and temperature threshold are both bounded by a constant. This is in stark contrast to results in the standard model with singleton input tiles where producibility is in P and UAV is coNP-complete with constant temperature. We further provide preliminary polynomial time results for producibility and UAV in the case of 1-dimensional linear assemblies with pre-built assemblies, as well as extend our results to the abstract Tile Assembly Model (aTAM) with constant-size attachable assemblies.