Journal of Computer and System Sciences最新文献

Given a graph G on n vertices and two integers k and d, the Contraction(vc) problem asks whether one can contract at most k edges to reduce the vertex cover number of G by at least d. Recently, Lima et al. [JCSS 2021] proved that Contraction(vc) admits an XP algorithm running in time $f\left(d\right)\cdot n^{O\left(d\right)}$. They asked whether this problem is FPT under this parameterization. In this article, we prove that: (i) Contraction(vc) is W[1]-hard parameterized by $k+d$. Moreover, unless the ETH fails, the problem does not admit an algorithm running in time $f(k+d)\cdot n^{o(k+d)}$ for any function f. This answers negatively the open question stated in Lima et al. [JCSS 2021]. (ii) Contraction(vc) is NP-hard even when $k=d$. (iii) Contraction(vc) can be solved in time $2^{O\left(d\right)}\cdot n^{k-d+O\left(1\right)}$. This improves the algorithm of Lima et al. [JCSS 2021], and shows that when $k=d$, Contraction(vc) is FPT parameterized by d (or by k).

Given a graph G and two independent sets $I_s$ and $I_t$ of size k, the Independent Set Reconfiguration problem asks whether there exists a sequence of independent sets that transforms $I_s$ to $I_t$ such that each independent set is obtained from the previous one using a so-called reconfiguration step. Viewing each independent set as a collection of k tokens placed on the vertices of a graph G, the two most studied reconfiguration steps are token jumping and token sliding. Over a series of papers, it was shown that the Token Jumping problem is fixed-parameter tractable (for parameter k) when restricted to sparse graph classes, such as planar, bounded treewidth, and nowhere dense graphs. As for the Token Sliding problem, almost nothing is known. We remedy this situation by showing that Token Sliding is fixed-parameter tractable on graphs of bounded degree, planar graphs, and chordal graphs of bounded clique number.

We contribute to the refined understanding of language-logic-algebra interplay in a recent algebraic framework over countable words. Algebraic characterizations of the one variable fragment of FO as well as the boolean closure of the existential fragment of FO are established. We develop a seamless integration of the block product operation in the countable setting, and generalize well-known decompositional characterizations of FO and its two variable fragment. We propose an extension of FO admitting infinitary quantifiers to reason about inherent infinitary properties of countable words, and obtain a natural hierarchical block-product based characterization of this extension. Properties expressible in this extension can be simultaneously expressed in the classical logical systems such as WMSO and FO[cut]. We also rule out the possibility of a finite-basis for a block-product based characterization of these logical systems. Finally, we report algebraic characterizations of one variable fragments of the hierarchies of the new extension.

We consider Internet of Things (IoT) sensors deployed inside an area to be monitored. Drones can be used to collect the data from the sensors, but they are constrained in energy and storage. Therefore, all drones need to select a subset of sensors whose data are the most relevant to be acquired, modeled by assigning a reward. We present an optimization problem called Multiple-drone Data-collection Maximization Problem (MDMP) whose objective is to plan a set of drones' missions aimed at maximizing the overall reward from the collected data, and such that each individual drone's mission energy cost and total collected data are within the energy and storage limits, respectively. We optimally solve MDMP by proposing an Integer Linear Programming based algorithm. Since MDMP is NP-hard, we devise suboptimal algorithms for single- and multiple-drone scenarios. Finally, we thoroughly evaluate our algorithms on the basis of random generated synthetic data.

Floyd and Knuth investigated in 1990 register machines which can add, subtract and compare integers as primitive operations. They asked whether their current bound on the number of registers for multiplying and dividing fast (running in time linear in the size of the input) can be improved and whether one can output fast the powers of two summing up to a positive integer in subquadratic time. Both questions are answered positively. Furthermore, it is shown that every function computed by only one register is automatic and that the automatic functions with one input can be computed with four registers in linear time; automatic functions with a larger number of inputs can be computed with 5 registers in linear time. There is a nonautomatic function with one input which can be computed with two registers in linear time.

A garden is populated by n bamboos, each with its own daily growth rate. The Bamboo Garden Trimming Problem (BGT) is to design for a robotic gardener a perpetual schedule of cutting bamboos to keep the elevation of the garden as low as possible. The frequency of cutting is constrained by the time needed to move from one bamboo to the next, which is one day in Discrete BGT and is defined by the distance between the two bamboos in Continuous BGT. The bamboo garden is a metaphor for a collection of machines which have to be serviced, with different frequencies, by a robot which can service only one machine at a time. For Discrete BGT, we show tighter approximation algorithms, with one of them settling a long-standing conjecture about the related Pinwheel problem. For Continuous BGT, we propose approximation algorithms which achieve logarithmic approximation ratios.

A temporal graph G is a pair $(G,\lambda )$ where G is a graph and λ is a function on the edges of G describing when each edge is active. Temporal connectivity then concerns only paths that respect the flow of time. In this context, it is known that Menger's Theorem does not hold. In a seminal paper, Kempe, Kleinberg and Kumar (STOC'2000) defined a graph to be Mengerian if equality holds for every time-function. They then proved that, if each edge is allowed to be active only once in $(G,\lambda )$, then G is Mengerian if and only if G has no gem as topological minor. In this paper, we generalize their result by allowing edges to be active more than once, giving a characterization also in terms of forbidden structures. We additionally provide a polynomial time recognition algorithm.

We study the problem of representing a graph as a storyplan, a recently introduced model for dynamic graph visualization. It is based on a sequence of frames, each showing a subset of vertices and a planar drawing of their induced subgraphs, where vertices appear and disappear over time. Namely, in the StoryPlan problem, we are given a graph and we want to decide whether there exists a total vertex appearance order for which a storyplan exists. We prove that the problem is NP-complete, and complement this hardness with two parameterized algorithms, one in the vertex cover number and one in the feedback edge set number of the input graph. We prove that partial 3-trees always admit a storyplan, which can be computed in linear time. Finally, we show that the problem remains NP-complete if the vertex appearance order is given and we have to choose how to draw the frames.

Standardized Ethereum tokens, e.g., ERC-20 tokens, have become the norm in fundraising (through ICOs) and kicking off blockchain-based DeFi applications. However, they require the user's wallet to hold both tokens and ether to pay the gas fee for making a transaction. This makes for a cumbersome user experience, and complicates, from the user perspective, the process of transitioning to a different smart-contract enabled blockchain, or to a newly launched blockchain. We formalize, instantiate, and analyze in a composable manner a system that we call Etherless Ethereum Tokens (in short, EETs), which allows the token users to transact in a closed-economy manner, i.e., having only tokens on their wallet and paying any transaction fees in tokens rather than Ether/Gas. In the process, we devise a methodology for capturing Ethereum token-contracts in the Universal Composability (UC) framework, which can be of independent interest.

We study the complexity of testing whether a biconnected graph $G=(V,E)$ is planar with the constraint that some cyclic orders of the edges incident to its vertices are allowed while some others are forbidden. The allowed cyclic orders are described by associating every vertex v of G with a set $D\left(v\right)$ of FPQ-trees. Let tw be the treewidth of G and let $D_{\max }$ be the maximum number of FPQ-trees per vertex. We show that the problem is FPT when parameterized by $\text{tw}+D_{\max }$, paraNP-hard when parameterized by $D_{\max }$, and W[1]-hard when parameterized by tw. We also consider NodeTrix planar representations of clustered graphs, where clusters are adjacency matrices and inter-cluster edges are non-intersecting simple curves. We prove that NodeTrix planarity with fixed sides is FPT when parameterized by the size of clusters plus the treewidth of the graph obtained by collapsing clusters to single vertices, provided that this graph is biconnected.