Journal of Computer and System Sciences最新文献

A temporal (directed) graph is one where edges are available only at specific times during its lifetime, τ. Paths in these graphs are sequences of adjacent edges whose appearing times are either strictly increasing or non-strictly increasing. Classical concepts of connected and unilateral components can be naturally extended to temporal graphs. We address fundamental questions in temporal graphs. (i) What is the complexity of deciding the existence of a component of size k, parameterized by τ, k, and $k+\tau$? The answer depends on the component definition and whether the graph is directed or undirected. (ii) What is the minimum running time to check if a subset of vertices is pairwise reachable? A quadratic-time algorithm exists, but a faster time is unlikely unless SETH fails. (iii) Can we verify if a subset of vertices forms a component in polynomial time? This is NP -complete depending on the temporal component definition.

We introduce backdoor DNFs, as a tool to measure the theoretical hardness of CNF formulas. Like backdoor sets and backdoor trees, backdoor DNFs are defined relative to a tractable class of CNF formulas. Each conjunctive term of a backdoor DNF defines a partial assignment that moves the input CNF formula into the base class. Backdoor DNFs are more expressive and potentially smaller than their predecessors backdoor sets and backdoor trees. We establish the fixed-parameter tractability of the backdoor DNF detection problem. Our results hold for the fundamental base classes Horn and 2CNF, and their combination. We complement our theoretical findings by an empirical study. Our experiments show that backdoor DNFs provide a significant improvement over their predecessors.

We study spreading processes in temporal graphs, that is, graphs whose connections change over time. More precisely, we investigate how such a spreading process, emerging from a given set of sources, can be contained to a small part of the graph. We consider two ways of modifying the graph, which are (1) deleting and (2) delaying connections. We show a close relationship between the two associated problems. It is known that both problems are W[1]-hard when parameterized by the number of modifications. We consider the number of vertices to which the spread is contained as a parameter. Surprisingly, we prove W[1]-hardness for the deletion variant but fixed-parameter tractability for the delaying variant. Furthermore, we give a polynomial time algorithm for both problem variants when the graph has a tree structure and show how to generalize this result to an FPT-algorithm for the so-called timed feedback vertex number as a parameter.

The $\mathrm{NP}$-complete graph problem Cluster Editing seeks to transform a static graph into a disjoint union of cliques by making the fewest possible edits to the edges. We introduce a natural interpretation of this problem in temporal graphs, whose edge sets change over time. This problem is $\mathrm{NP}$-complete even when restricted to temporal graphs whose underlying graph is a path, but we obtain two polynomial-time algorithms for restricted cases. In the static setting, it is well-known that a graph is a disjoint union of cliques if and only if it contains no induced copy of $P_3$; we demonstrate that no general characterisation involving sets of at most four vertices can exist in the temporal setting, but obtain a complete characterisation involving forbidden configurations on at most five vertices. This characterisation gives rise to an $\mathrm{FPT}$ algorithm parameterised simultaneously by the permitted number of modifications and the lifetime of the temporal graph.

One strategy for inference of phylogenetic networks is to solve the phylogenetic network problem, which involves inferring phylogenetic trees first and subsequently computing the smallest phylogenetic network that displays all the trees. This approach capitalizes on exceptional tools available for inferring phylogenetic trees from biomolecular sequences. Since the vast space of phylogenetic networks poses difficulties in obtaining comprehensive sampling, the researchers switch their attention to inferring tree-child networks from multiple phylogenetic trees, where in a tree-child network each non-leaf node must have at least one child that is an indegree-one node. Three results are obtained in this work: (1) The shortest common supersequence problem remains NP-hard even for permutation strings. (2) Derived from the first result, the tree-child network inference problem is also established as NP-hard even for line trees (also known as caterpillar trees). (3) The parsimonious tree-child networks that display all the line trees are the same as those displaying all the binary trees and their hybridization number is $\Theta \left(n^3\right)$ for n taxa.

Minimum vertex bisection is a graph partitioning problem in which the aim is to find a partition of the vertices into two equal parts that minimizes the number of vertices in one partition set that have a neighbor in the other set. In this work we are interested in providing asymptotically almost surely upper bounds on the minimum vertex bisection of random d-regular graphs, for constant values of d. Our approach is based on analyzing a greedy algorithm by using the differential equation method. In this way, we obtain the first known non-trivial upper bounds for the vertex bisection number in random regular graphs. The numerical approximations of these theoretical bounds are compared with the emprical ones, and with the lower bounds from Kolesnik and Wormald (2014) [30].

We study a generalization of the advice complexity model of online computation in which the advice is provided by an untrusted source. Our objective is to quantify the impact of untrusted advice so as to design and analyze online algorithms that are robust if the advice is adversarial, and efficient is the advice is foolproof. We focus on four well-studied online problems, namely ski rental, online bidding, bin packing and list update. For ski rental and online bidding, we show how to obtain algorithms that are Pareto-optimal with respect to the competitive ratios achieved, whereas for bin packing and list update, we give online algorithms with worst-case tradeoffs in their competitiveness, depending on whether the advice is trusted or adversarial. More importantly, we demonstrate how to prove lower bounds, within this model, on the tradeoff between the number of advice bits and the competitiveness of any online algorithm.

Message-based systems usually consist of distributed components that communicate using asynchronous message passing. In such systems, particular message orderings may violate some required properties. Given an automata-based specification of unwanted message sequences, we propose a decentralized deadlock-free runtime enforcement algorithm to prevent the formation of such sequences. In our approach, components are equipped with monitors executed concurrently. A component is only blocked before sending or receiving the last message of a sequence, until its associated monitor checks that such a message does not complete an unwanted sequence. According to the specification of unwanted sequences, some blocked components may suffer from a deadlock. Our deadlock-free algorithm guarantees that monitors detect and resolve such deadlocks by improving the existing deadlock detection algorithms. We evaluate the efficiency and scalability of our approach in terms of the communication overhead, the prevention latency, and the overhead of deadlock detection through simulation.

We show that the topes of a complex of oriented matroids (abbreviated COM) of VC-dimension d admit a proper labeled sample compression scheme of size d. This considerably extends results of Moran and Warmuth on ample classes, of Ben-David and Litman on affine arrangements of hyperplanes, and of the authors on complexes of uniform oriented matroids, and is a step towards the sample compression conjecture – one of the oldest open problems in computational learning theory. On the one hand, our approach exploits the rich combinatorial cell structure of COMs via oriented matroid theory. On the other hand, viewing tope graphs of COMs as partial cubes creates a fruitful link to metric graph theory.

We provide new parameterized complexity results for Interval Scheduling on Eligible Machines. In this problem, a set of n jobs is given to be processed non-preemptively on a set of m machines. Each job has a processing time, a deadline, a weight, and a set of eligible machines that can process it. The goal is to find a maximum weight subset of jobs that can each be processed on one of its eligible machines such that it completes exactly at its deadline. We focus on two parameters: The number m of machines, and the largest processing time $p_{\max }$. Our main contribution is showing W[1]-hardness when parameterized by m. This answers Open Problem 8 of Mnich and van Bevern's list of 15 open problems in parameterized complexity of scheduling problems [Computers & Operations Research, 2018]. Furthermore, we show NP-hardness even when $p_{\max }=O\left(1\right)$ and present an FPT-algorithm with for the combined parameter $m+p_{\max }$.