Journal of Computer and System Sciences最新文献

In this paper, we study the problem of PAC learning halfspaces in the non-interactive local differential privacy model (NLDP). To breach the barrier of exponential sample complexity, previous results studied a relaxed setting where the server has access to some additional public but unlabeled data. We continue in this direction. Specifically, we consider the problem under the standard setting instead of the large margin setting studied before. Under different mild assumptions on the underlying data distribution, we propose two approaches that are based on the Massart noise model and self-supervised learning and show that it is possible to achieve sample complexities that are only linear in the dimension and polynomial in other terms for both private and public data, which significantly improve the previous results. Our methods could also be used for other private PAC learning problems.

We introduce the notions of blackout-tolerant temporal α-spanner of a temporal graph G which is a subgraph of G that preserves the distances between pairs of vertices of interest in G up to a multiplicative factor of α, even when the graph edges at a single time-instant become unavailable. In particular, we consider the single-source, single-pair, and all-pairs cases and, for each case we look at three quality requirements: exact distances (i.e., $\alpha =1$), almost-exact distances (i.e., $\alpha =1+\epsilon$ for an arbitrarily small constant $\epsilon >0$), and connectivity (i.e., unbounded α). We provide almost tight bounds on the size of such spanners for general temporal graphs and for temporal cliques, showing that they are either very sparse (i.e., they have $\tilde{O}\left(n\right)$ edges) or they must have size $\Omega \left(n^2\right)$ in the worst case, where n is the number of vertices of G. We also investigate multiple blackouts and k-edge fault-tolerant temporal spanners.

Time-space tradeoff has been studied in a variety of models, such as Turing machines, branching programs, and finite automata, etc. While communication complexity as a technique has been applied to study finite automata, it seems it has not been used to study time-space tradeoffs of finite automata. We design a new technique showing that separations of query complexity can be lifted, via communication complexity, to separations of time-space complexity of two-way finite automata. As an application, one of our main results exhibits the first example of a language L such that the time-space complexity of two-way probabilistic finite automata with a bounded error (2PFA) is $\tilde{\Omega }\left(n^2\right)$, while of exact two-way quantum finite automata with classical states (2QCFA) is $\tilde{O}\left(n^{5/3}\right)$, that is, we demonstrate for the first time that exact quantum computing has an advantage in time-space complexity comparing to classical computing.

A bipartite graph $G=(A,B,E)$ is $H$-convex for some family of graphs $H$ if there exists a graph $H\in H$ with $V\left(H\right)=A$ such that the neighbours in A of each $b\in B$ induce a connected subgraph of H. Many $\mathrm{NP}$-complete problems are polynomial-time solvable for $H$-convex graphs when $H$ is the set of paths. The underlying reason is that the class has bounded mim-width. We extend this result to families of $H$-convex graphs where $H$ is the set of cycles, or $H$ is the set of trees with bounded maximum degree and a bounded number of vertices of degree at least 3. As a consequence, we strengthen many known results via one general and short proof. We also show that the mim-width of $H$-convex graphs is unbounded if $H$ is the set of trees with arbitrarily large maximum degree or an arbitrarily large number of vertices of degree at least 3.

The Probabilistic Serial mechanism is valued for its fairness and efficiency in addressing the random assignment problem. However, it lacks truthfulness, meaning it works well only when agents' stated preferences match their true ones. Significant utility gains from strategic actions may lead self-interested agents to manipulate the mechanism, undermining its practical adoption. To gauge the potential for manipulation, we explore an extreme scenario where a manipulator has complete knowledge of other agents' reports and unlimited computational resources to find their best strategy. We establish tight incentive ratio bounds of the mechanism. Furthermore, we complement these worst-case guarantees by conducting experiments to assess an agent's average utility gain through manipulation. The findings reveal that the incentive for manipulation is very small. These results offer insights into the mechanism's resilience against strategic manipulation, moving beyond the recognition of its lack of incentive compatibility.

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.