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,...
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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.(c) 2023 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/).
A procedure is given for recognizing sets of inference rules that generate polynomialtime decidable inference relations. The procedure can automatically recognize the tractability of the inference rules underlying co...
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A procedure is given for recognizing sets of inference rules that generate polynomialtime decidable inference relations. The procedure can automatically recognize the tractability of the inference rules underlying congruence closure. The recognition of tractability for that particular rule set constitutes mechanical verification of a theorem originally proved independently by Kozen and Shostak. The procedure is algorithmic, rather than heuristic, and the class of automatically recognizable tractable rule sets can be precisely characterized. A series of examples of rule sets whose tractability is nontrivial, yet machine recognizable, is also given. The technical framework developed here is viewed as a first step toward a general theory of tractable inference relations.
作者:
Gao, YuanZhengzhou Univ
Sch Math & Stat Zhengzhou 450001 Henan Peoples R China Zhengzhou Univ
Sch Informat Engn Zhengzhou 450001 Henan Peoples R China
We study the Pareto optimization scheduling on an unbounded parallel-batch machine with jobs having agreeable release dates and processing times for minimizing makespan and maximum cost simultaneously. The jobs consid...
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We study the Pareto optimization scheduling on an unbounded parallel-batch machine with jobs having agreeable release dates and processing times for minimizing makespan and maximum cost simultaneously. The jobs considered in this paper are of two types: batch jobs and drop-line jobs. For batch jobs, the completion time of a job is given by the completion time of the batch containing this job. For drop-line jobs, the completion time of a job is given by the starting time of the batch containing this job plus the processing time of this job. For both of batch jobs and drop-line jobs, we present polynomial-time algorithms for finding all Pareto optimal points.
Matched designs are commonly used in non-randomized studies to evaluate causal effects for dichotomous treatment. Optimal matching algorithms have been devised to form matched pairs or sets between treatment and contr...
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Matched designs are commonly used in non-randomized studies to evaluate causal effects for dichotomous treatment. Optimal matching algorithms have been devised to form matched pairs or sets between treatment and control groups in various designs, including 1-k matching and full matching. With multiple treatment arms, however, the optimal matching problem cannot be solved in polynomial-time. This is a major challenge for implementing matched designs with multiple arms, which are important for evaluating causal effects with different dose levels or constructing evidence factors with multiple control groups. A polymatching framework for generating matched sets among multiple groups is proposed. An iterative multi-way algorithm for implementation is developed, which takes advantage of the existing optimal two-group matching algorithm repeatedly. An upper bound for the total distance attained by our algorithm is provided to show that the distance result is close to the optimal solution. Simulation studies are conducted to compare the proposed algorithm with the nearest neighbor algorithm under different scenarios. The algorithm is also used to construct a difference-in-difference matched design among four groups, to examine the impact of Medicaid expansion on the health status of Ohioans. (C) 2021 Elsevier B.V. All rights reserved.
Evolutionary histories for species that cross with one another or exchange genetic material can be represented by leaf-labelled, directed graphs called phylogenetic networks. A major challenge in the burgeoning area o...
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Evolutionary histories for species that cross with one another or exchange genetic material can be represented by leaf-labelled, directed graphs called phylogenetic networks. A major challenge in the burgeoning area of phylogenetic networks is to develop algorithms for building such networks by amalgamating small networks into a single large network. The level of a phylogenetic network is a measure of its deviation from being a tree;the higher the level of a network, the less treelike it becomes. Various algorithms have been developed for building level-1 networks from small networks. However, level-1 networks may not be able to capture the complexity of some data sets. In this paper, we present a polynomial-time algorithm for constructing a rooted binary level-2 phylogenetic network from a collection of 3-leaf networks or trinets. Moreover, we prove that the algorithm will correctly reconstruct such a network if it is given all of the trinets in the network as input. The algorithm runs in time O (t middot n + n4) with t the number of input trinets and n the number of leaves. We also show that there is a fundamental obstruction to constructing level-3 networks from trinets, and so new approaches will need to be developed for constructing level-3 and higher level-networks.(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://***/licenses/by/4.0/).
We define the d-defective incidence chromatic number of a graph, generalizing the notion of incidence chromatic number, and determine it for some classes of graphs including trees, complete bipartite graphs, complete ...
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We define the d-defective incidence chromatic number of a graph, generalizing the notion of incidence chromatic number, and determine it for some classes of graphs including trees, complete bipartite graphs, complete graphs, and outerplanar graphs. Fast algorithms for constructing the optimal d-defective incidence colorings of those graphs are presented. (c) 2022 Elsevier Inc. All rights reserved.
We investigate the computational complexity of finding temporally disjoint paths and walks in temporal graphs. There, the edge set changes over discrete time steps. Temporal paths and walks use edges that appear at mo...
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We investigate the computational complexity of finding temporally disjoint paths and walks in temporal graphs. There, the edge set changes over discrete time steps. Temporal paths and walks use edges that appear at monotonically increasing time steps. Two paths (or walks) are temporally disjoint if they never visit the same vertex at the same time;otherwise, they interfere. This reflects applications in robotics, traffic routing, or finding safe pathways in dynamically changing networks. At one extreme, we show that on general graphs the problem is computationally hard. The path version is NP-hard even if we want to find only two temporally disjoint paths. The walk version is W-hard (Klobas in IJCAI 4090-4096, 2021) when parameterized by the number of walks. However, it is polynomial-time solvable for any constant number of walks. At the other extreme, restricting the input temporal graph to have a path as underlying graph, quite counter-intuitively, we find NP-hardness in general but also identify natural tractable cases.
We present a deterministic polynomial-time algorithm for the A B C problem, which is the membership problem for 2-generated commutative linear semigroups over an algebraic number field. We also obtain a polynomial-tim...
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We present a deterministic polynomial-time algorithm for the A B C problem, which is the membership problem for 2-generated commutative linear semigroups over an algebraic number field. We also obtain a polynomial-time algorithm for the (easier) membership problem for 2-generated abelian linear groups. Furthermore, we provide a polynomial-sized encoding for the set of all solutions.
The paper is concerned with scheduling traffic on a single track between two stations which generate requests for transportation with different release times. These requests are served by a fleet of identical vehicles...
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The paper is concerned with scheduling traffic on a single track between two stations which generate requests for transportation with different release times. These requests are served by a fleet of identical vehicles, each of which can serve (carry) several requests for transportation simultaneously. The single track, used by the vehicles, does not permit traffic in both directions simultaneously. The presented polynomial-time algorithms are based on dynamic programming.
We study the network facility location problem with constraints on the capacities of communication lines, called Restricted Facility Location Problem (RFLP). It is required to locate facilities at the vertices of a gi...
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We study the network facility location problem with constraints on the capacities of communication lines, called Restricted Facility Location Problem (RFLP). It is required to locate facilities at the vertices of a given network graph so as to simultaneously satisfy at minimum cost the demands of customers located at the vertices of the graph. We consider two statements of the problem: the multiple allocation RFLP, where the demand of a customer can be satisfied jointly by several facilities, and the single allocation RFLP, where the demand of a customer must be entirely satisfied by a single facility. We show that the single allocation RFLP is NP-hard even if the network is a simple path and strongly NP-hard if the network is a tree. The multiple allocation RFLP is weakly NP-hard on trees. For this problem, we propose a pseudopolynomial-time algorithm for the case where the network graph has constant treewidth and a linear-timealgorithm for the case where the network is a simple path.
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