Journal of Computer and System Sciences最新文献

An automata network with n components over a finite alphabet Q of size q is a discrete dynamical system described by the successive iterations of a function $f:Q^n\to Q^n$. In most applications, the main parameter is the interaction graph of f: the digraph with vertex set $\left[n\right]$ that contains an arc from j to i if $f_i$ depends on input j. What can be said on the set $G\left(f\right)$ of the interaction graphs of the automata networks isomorphic to f? It seems that this simple question has never been studied. Here, we report some basic facts. First, we prove that if $n\ge 5$ or $q\ge 3$ and f is neither the identity nor constant, then $G\left(f\right)$ always contains the complete digraph $K_n$, with $n^2$ arcs. Then, we prove that $G\left(f\right)$ always contains a digraph whose minimum in-degree is bounded as a function of q. Hence, if n is large with respect to q, then $G\left(f\right)$ cannot only contain $K_n$. However, we prove that $G\left(f\right)$ can contain only dense digraphs, with at least $\lfloor n^2/4\rfloor$ arcs.

We study two “above guarantee” versions of the classical Longest Path problem on undirected and directed graphs and obtain the following results. In the first variant of Longest Path that we study, called Longest Detour, the task is to decide whether a graph has an $(s,t)$-path of length at least ${\mathrm{dist}}_G(s,t)+k$. Bezáková et al. [7] proved that on undirected graphs the problem is fixed-parameter tractable ($\mathrm{FPT}$). Our first main result establishes a connection between Longest Detour on directed graphs and 3- Disjoint Paths on directed graphs. Using these new insights, we design a $2^{O\left(k\right)}\cdot n^{O\left(1\right)}$ time algorithm for the problem on directed planar graphs. Furthermore, the new approach yields a significantly faster $\mathrm{FPT}$ algorithm on undirected graphs. In the second variant of Longest Path, namely Longest Path above Diameter, the task is to decide whether the graph has a path of length at least $\mathrm{diam}\left(G\right)+k$. We obtain dichotomy results about Longest Path above Diameter on undirected and directed graphs.

We present a linear-time, space and communication data-oblivious algorithm for securely merging two private, sorted lists into a single sorted, secret-shared list in the two party setting. Although merging two sorted lists can be done insecurely in linear time, previous secure merge algorithms all require super-linear time and communication. A key feature of our construction is a novel method to obliviously traverse permuted lists in sorted order. Our algorithm only requires black-box use of the underlying additively homomorphic cryptosystem and generic secure computation protocols for comparison and equality testing.

We identify two new clusters of proof complexity measures equal up to polynomial and $\log n$ factors. The first cluster contains the logarithm of tree-like resolution size, regularized clause and monomial space, and clause space, ordinary and regularized, in regular and tree-like resolution. Consequently, separating clause or monomial space from the logarithm of tree-like resolution size is equivalent to showing strong trade-offs between clause space and length, and equivalent to showing super-critical trade-offs between clause space and depth. The second cluster contains width, ${\Sigma }_2$ space (a generalization of clause space to depth 2 Frege systems), ordinary and regularized, and the logarithm of tree-like $R(\log )$ size. As an application, we improve a known size-space trade-off for polynomial calculus with resolution. We further show a quadratic lower bound on tree-like resolution size for formulas refutable in clause space 4, and introduce a measure intermediate between depth and the logarithm of tree-like resolution size.

Temporal graphs are graphs whose topology is subject to discrete changes over time. Given a static underlying graph G, a temporal graph is represented by assigning a set of integer time-labels to every edge e of G, indicating the discrete time steps at which e is active. We introduce and study the complexity of a natural temporal extension of the classical graph problem Maximum Matching, taking into account the dynamic nature of temporal graphs. In our problem, Maximum Temporal Matching, we are looking for the largest possible number of time-labeled edges (simply time-edges) $(e,t)$ such that no vertex is matched more than once within any time window of Δ consecutive time slots, where $\Delta \in N$ is given. We prove strong computational hardness results for Maximum Temporal Matching, even for elementary cases, as well as fixed-parameter algorithms with respect to natural parameters and polynomial-time approximation algorithms.

Many Internet protocol (IP) lookup algorithms have been formulated to improve network performance. This study reviewed and experimentally evaluated technologies for trie-based methods that reduce memory access, memory consumption and IP lookup time. Experiments involving binary tries (for simplicity) were conducted on four real-world data sets, two of which were on IPv4 router tables (855,997 and 876,489 active prefixes) and two of which were on IPv6 router tables (155,310 and 157,579 active prefixes). Technologies designed to reduce time taken (at the expense of memory consumption) worked well for IPv4, and those designed to reduce memory consumption worked well for IPv6. Various combinations of these technologies were applied together in the experiments.

We introduce and study two natural generalizations of the Connected Vertex Cover (VC) problem: the p-Edge-Connected and p-Vertex-Connected VC problem (where $p\ge 2$ is a fixed integer). We obtain an $2^{O\left(pk\right)}{n}^{O\left(1\right)}$-time algorithm for p-Edge-Connected VC and an $2^{O\left(k^2\right)}{n}^{O\left(1\right)}$-time algorithm for p-Vertex-Connected VC. Thus, like Connected VC, both constrained VC problems are FPT. Furthermore, like Connected VC, neither problem admits a polynomial kernel unless NP ⊆ coNP/poly, which is highly unlikely. We prove however that both problems admit time efficient polynomial sized approximate kernelization schemes. Finally, we describe a $2(p+1)$-approximation algorithm for the p-Edge-Connected VC. The proofs for the new VC problems require more sophisticated arguments than for Connected VC. In particular, for the approximation algorithm we use Gomory-Hu trees and for the approximate kernels a result on small-size spanning p-vertex/edge-connected subgraphs of a p-vertex/edge-connected graph by Nishizeki and Poljak (1994) [30] and Nagamochi and Ibaraki (1992) [27].

In a multiple access channel, autonomous stations are able to transmit and listen to a shared device. A fundamental problem, called contention resolution, is to allow any station to successfully deliver its message by resolving the conflicts that arise when several stations transmit simultaneously. Despite a long history on such a problem, most of the results deal with the static setting when all stations start simultaneously, while many fundamental questions remain open in the realistic scenario when stations can join the channel at arbitrary times. In this paper, we explore the impact that three major channel features (asynchrony among stations, knowledge of the number of contenders and possibility of switching off stations after a successful transmission) can have on the time complexity of non-adaptive deterministic algorithms. We establish upper and lower bounds allowing to understand which parameters permit time-efficient contention resolution and which do not.

In this paper, we focus on Hitting-Set, a fundamental problem in combinatorial optimization, through the lens of sublinear time algorithms. Given access to the hypergraph through a subset query oracle in the query model, we give sublinear time algorithms for Hitting-Set with almost tight parameterized query complexity. In parameterized query complexity, we estimate the number of queries to the oracle based on the parameter k, the size of the Hitting-Set. The subset query oracle we use in this paper is called Generalized d-partite Independent Set query oracle (GPIS) and it was introduced by Bishnu et al. (ISAAC'18). GPIS is a generalization to hypergraphs of the Bipartite Independent Set query oracle (BIS) introduced by Beame et al. (ITCS'18 and TALG'20) for estimating the number of edges in graphs. Since its introduction GPIS query oracle has been used for estimating the number of hyperedges independently by Dell et al. (SODA'20 and SICOMP'22) and Bhattacharya et al. (STACS'22), and for estimating the number of triangles in a graph by Bhattacharya et al. (ISAAC'19 and TOCS'21). Formally, GPIS is defined as follows: GPIS oracle for a d-uniform hypergraph $H$ takes as input d pairwise disjoint non-empty subsets $A_1,\dots ,A_d$ of vertices in $H$ and answers whether there is a hyperedge in $H$ that intersects each set $A_i$, where $i\in \{1,2,\dots ,d\}$. For $d=2$, the GPIS oracle is nothing but BIS oracle.

We show that d-Hitting-Set, the hitting set problem for d-uniform hypergraphs, can be solved using ${\tilde{O}}_d(k^d\log n)$ GPIS queries. Additionally, we also showed that d-Decision-Hitting-Set, the decision version of d-Hitting-Set can be solved with