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JOURNAL OF COMPUTER AND SYSTEM SCIENCES 2025年 147卷

作者： Mertzios, George Michail, Othon Skretas, George Spirakis, Paul G. Theofilatos, Michail Univ Durham Dept Comp Sci Durham England Univ Liverpool Dept Comp Sci Liverpool England Univ Potsdam Hasso Plattner Inst Potsdam Germany

We study a new algorithmic process of graph growth which starts from a single initial vertex and operates in discrete time-steps, called slots. In every slot, the graph grows via two operations (i) vertex generation and (ii) edge activation. The process completes at the last slot where a (possibly empty) subset of the edges of the graph are removed. Removed edges are called excess edges. The main problem investigated in this paper is: Given a target graph G, design an algorithm that outputs a process that grows G, called a growth schedule. Additionally, we aim to minimize the total number of slots k and of excess edges P used by the process. We provide both positive and negative results, with our main focus being either schedules with sub-linear number of slots or with no excess edges. (c) 2024 Published by Elsevier Inc.

关键词： Dynamic graph Temporal graph Cop-win graph Graph process polynomial-time algorithm Lower bound NP-complete Hardness result

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Adapting stable matchings to forced and forbidden pairs

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JOURNAL OF COMPUTER AND SYSTEM SCIENCES 2025年 147卷

作者： Boehmer, Niclas Heeger, Klaus TU Berlin Ernst Reuter Pl 7 D-10587 Berlin Germany Univ Potsdam Hasso Plattner Inst Potsdam Germany Ben Gurion Univ Negev Beer Sheva Israel

We introduce the problem of adapting a stable matching to forced and forbidden pairs. Given a stable matching M-1, a set Q of forced pairs, and a set P of forbidden pairs, we want to find a stable matching that includes all pairs from Q, no pair from P, and is as close as possible to M-1. We study this problem in four classic stable matching settings: Stable Roommates (with Ties) and Stable Marriage (with Ties). Our main contribution is a polynomial-time algorithm, based on the theory of rotations, for adapting Stable Roommates matchings to forced pairs. In contrast, we show that the same problem for forbidden pairs is NP-hard. However, our polynomial-time algorithm for forced pairs can be extended to a fixed-parameter tractable algorithm with respect to the number of forbidden pairs. Moreover, we study the setting where preferences contain ties: Some of our algorithmic results can be extended while other problems become intractable. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).

关键词： Stable Marriage Stable Roommates Forced and forbidden pairs Incremental algorithms Rotations NP-hardness polynomial-time algorithm W[1]-hardness FPT

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The complexity of transitively orienting temporal graphs

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JOURNAL OF COMPUTER AND SYSTEM SCIENCES 2025年 150卷

作者： Mertzios, George B. Molter, Hendrik Renken, Malte Spirakis, Paul G. Zschoche, Philipp Univ Durham Dept Comp Sci Durham England Ben Gurion Univ Negev Dept Comp Sci Beer Sheva Israel Tech Univ Berlin Algorithm & Computat Complex Berlin Germany Univ Liverpool Dept Comp Sci Liverpool England

In a temporal network with discrete time-labels on its edges, information can only "flow" along sequences of edges with non-decreasing (resp. increasing) time-labels. In this paper we make a first attempt to understand how the direction of information flow on one edge can impact the direction of information flow on other edges. By naturally extending the classical notion of a transitive orientation in static graphs, we introduce the fundamental notion of a temporal transitive orientation, and we systematically investigate its algorithmic behavior. Our main result is a conceptually simple, yet technically quite involved, polynomial-time algorithm for recognizing whether a temporal graph G is transitively orientable. In wide contrast we prove that, surprisingly, it is NP-hard to recognize whether G is strictly transitively orientable. Additionally we introduce further related problems to temporal transitivity, notably among them the temporal transitive completion problem, for which we prove both algorithmic and hardness results. (c) 2025 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://***/licenses/by/4.0/).

关键词： Temporal graph Transitive orientation Transitive closure polynomial-time algorithm NP-hardness Satisfiability

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A near-linear time algorithm and a min-cost flow approach for determining the optimal landing times of a fixed sequence of planes

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ANNALS OF OPERATIONS RESEARCH 2025年第1期344卷 479-498页

作者： Cao, Bin Xu, Chao Jinan Univ Sch Management Guangzhou 510632 Peoples R China Univ Elect Sci & Technol China Sch Comp Sci & Engn Chengdu 610054 Peoples R China

The aircraft landing problem (ALP) is an important issue of assigning an airport's runways to the arrival aircrafts as well as to schedule the landing time of these aircrafts in practice. A large number of the extant studies have tried to address such a practical problem with using various algorithms for one or more runways. For a static single-runway of the ALP, this paper proposes a new approach to develop an alternative powerful algorithm. For a given sequence of planes, we develop a faster algorithm for solving the ALP with the running time O(nlogn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(n \log n)$$\end{document}, where n is the number of aircrafts in the schedule. Alternatively, we reduce the proposed problem of minimizing the total cost by determining the landing times for a given landing sequence into a min-cost flow problem. We conduct a set of experimental studies to compare the performance of our near-linear time algorithm to the quadratic time algorithm whose time complexity is O(n2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(n<^>2)$$\end{document}, for computing the optimal landing times. The computational results show that the proposed heuristic based on our algorithm could be much faster than both such quadratic time algorithm and the one using linear programming.

关键词： Aircraft landing problem static single-runway system Scheduling Min-cost flow polynomial-time algorithm

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Graph Bipartization and Via Minimization for Intersection Graphs

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JOURNAL OF INTERCONNECTION NETWORKS 2025年第2期25卷

作者： Lin, Lan Lin, Yixun Tongji Univ Sch Elect & Informat Engn Shanghai 200092 Peoples R China Zhengzhou Univ Sch Math & Stat Zhengzhou 450001 Henan Peoples R China

The graph bipartization problem, arising from via minimization in VLSI design and related areas, consists in finding a vertex subset S of graph G such that the induced subgraph G[S] is bipartite and |S| is maximized. The problem has been proved to be NP-hard even for planar graphs and cubic graphs. On the other hand, the study of polynomial-time algorithms for typical graph classes is significant in both theoretical and applied aspects. This paper focuses on several intersection graph classes, such as line graphs, circular-arc graphs, and directed path graphs. For the line graphs, we show the NP-hardness results in general and present the polynomial-time algorithms for special cases. For circular-arc graphs and directed path graphs, we propose algorithms that improve on the previously known ones.

关键词： Bipartite induced subgraph odd-cycle transversal via minimization NP-hardness polynomial-time algorithm

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polynomial-time algorithms for Phylogenetic Inference Problems Involving Duplication and Reticulation

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IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2020年第1期17卷 14-26页

作者： van Iersel, Leo Janssen, Remie Jones, Mark Murakami, Yukihiro Zeh, Norbert Delft Univ Technol Delft Inst Appl Math Mourik Broekmanweg 6 NL-2628 XE Delft Netherlands Dalhousie Univ Fac Comp Sci 6050 Univ Ave Halifax NS B3H 1W5 Canada

A common problem in phylogenetics is to try to infer a species phylogeny from gene trees. We consider different variants of this problem. The first variant, called Unrestricted Minimal Episodes Inference, aims at inferring a species tree based on a model with speciation and duplication where duplications are clustered in duplication episodes. The goal is to minimize the number of such episodes. The second variant, Parental Hybridization, aims at inferring a species network based on a model with speciation and reticulation. The goal is to minimize the number of reticulation events. It is a variant of the well-studied Hybridization Number problem with a more generous view on which gene trees are consistent with a given species network. We show that these seemingly different problems are in fact closely related and can, surprisingly, both be solved in polynomial time, using a structure we call "beaded trees". However, we also show that methods based on these problems have to be used with care because the optimal species phylogenies always have a restricted form. To mitigate this problem, we introduce a new variant of Unrestricted Minimal Episodes Inference that minimizes the duplication episode depth. We prove that this new variant of the problem can also be solved in polynomial time.

关键词： Phylogenetics duplication MINIMUM EPISODES problem HYBRIDIZATION NUMBER problem gene trees inference polynomial-time algorithm

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polynomial-time algorithms for Checking Some Properties of Boolean Functions Given by polynomials

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THEORY OF COMPUTING SYSTEMS 2016年第3期58卷 383-391页

作者： Selezneva, Svetlana N. Bukhman, Anton V. Moscow MV Lomonosov State Univ Fac Computat Math & Cybernet Moscow Russia

In this paper, we show that checking some properties of Boolean functions which are given by the lists of monomials in their polynomial representations can be implemented in polynomial time. Multi-linear polynomials over GF(2) are often a convenient way to represent Boolean functions. There is a single polynomial for each Boolean function, and the length of the polynomial (i.e. the number of its monomials) which represents a function of n variables can be far less than 2(n). Therefore, in some cases, polynomials are a compressed description of Boolean functions. Besides, polynomial representations of Boolean functions have applications in circuit lower bounds, computational learning, error-correcting codes, cryptography. We construct polynomial-time algorithms for checking some properties of Boolean functions which are given by the lists of monomials in their polynomial representations. The considered properties are self-anti-duality (evenness), self-duality, periodicity, 1-invariance (Mobius transform invariance, coincidence). Note that checking each of these properties directly by definition gives, in the general case, only exponential-time algorithms. The approach to construct our algorithms is the following. Firstly, we prove that if a Boolean function has a certain property then its polynomial has a special structure. And secondly, we check the property by its characterization, cutting negative cases by proven facts. More precisely, we analyze an exponential time algorithm and prove that if the number of steps of the algorithm exceeds a bound, which is polynomial in the input size, and may be computed in advance, then the input will be necessarily rejected.

关键词： Boolean function polynomial representation List of monomials Computational complexity polynomial-time algorithm

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polynomial-time algorithms for solving a class of critical node problems on trees and series-parallel graphs

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NETWORKS 2012年第2期60卷 103-119页

作者： Shen, Siqian Smith, J. Cole Univ Florida Dept Ind & Syst Engn Gainesville FL 32611 USA

We examine variants of the critical node problem on specially structured graphs, which aim to identify a subset of nodes whose removal will maximally disconnect the graph. These problems lie at the intersection of network interdiction and graph theory research and are relevant to several practical optimization problems. The two different connectivity metrics that we consider regard the number of maximal connected components (which we attempt to maximize) and the largest component size (which we attempt to minimize). We develop optimal polynomial-time dynamic programming algorithms for solving these problems on tree structures and on series-parallel graphs, corresponding to each graph-connectivity metric. We also extend our discussion by considering node deletion costs, node weights, and solving the problems on generalizations of tree structures. Finally, we demonstrate the computational efficacy of our approach on randomly generated graph instances. (c) 2011 Wiley Periodicals, Inc. NETWORKS, 2012

关键词： critical node problem tree series-parallel graph dynamic programming polynomial-time algorithm

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polynomial-time algorithms for SUBGRAPH ISOMORPHISM in small graph classes of perfect graphs

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DISCRETE APPLIED MATHEMATICS 2016年 199卷 37-45页

作者： Konagaya, Matsuo Otachi, Yota Uehara, Ryuhei Japan Adv Inst Sci & Technol Sch Informat Sci Nomi Ishikawa 9231292 Japan

Given two graphs, SUBGRAPH ISOMORPHISM is the problem of deciding whether the first graph (the base graph) contains a subgraph isomorphic to the second one (the pattern graph). This problem is NP-complete even for very restricted graph classes such as connected proper interval graphs. Only a few cases are known to be polynomial-time solvable even if we restrict the graphs to be perfect. For example, if both graphs are co-chain graphs, then the problem can be solved in linear time. In this paper, we present a polynomial-time algorithm for the case where the base graphs are chordal graphs and the pattern graphs are co-chain graphs. We also present a linear-time algorithm for the case where the base graphs are trivially perfect graphs and the pattern graphs are threshold graphs. These results answer some of the open questions of Kijima et al. (2012). To present a complexity contrast, we then show that even if the base graphs are somewhat restricted perfect graphs, the problem of finding a pattern graph that is a chain graph, a co-chain graph, or a threshold graph is NP-complete. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Subgraph isomorphism Graph class polynomial-time algorithm NP-completeness

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polynomial-time algorithms for special cases of the maximum confluent flow problem

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DISCRETE APPLIED MATHEMATICS 2014年第part2期163卷 142-154页

作者： Dressler, Daniel Strehler, Martin TU Berlin Inst Math D-10623 Berlin Germany Brandenburg Tech Univ Cottbus Math Inst D-03013 Cottbus Germany

A flow on a directed network is said to be confluent if the flow uses at most one outgoing arc at each node. Confluent flows arise naturally in destination-based routing. We study the maximum confluent flow problem (MAXCONF) with a single commodity but multiple sources and sinks and heterogeneous arc capacities. It was recently shown that MAXCONF is N P-hard even on trees. We improve the classification of easy and hard confluent flow problems by providing polynomial-time algorithms for outerplanar graphs with a single sink, as well as trees with a constant number of either sources or sinks. Furthermore, we present an FPTAS for graphs with bounded treewidth. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Confluent flow Outerplanar graph polynomial-time algorithm Treewidth FPTAS

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