For a wide family of formations a it is proved that the a-residual of a permutation finite group can be computed in polynomialtime. Moreover, if in the previous case a is hereditary, then the a -subnormality of a sub...
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For a wide family of formations a it is proved that the a-residual of a permutation finite group can be computed in polynomialtime. Moreover, if in the previous case a is hereditary, then the a -subnormality of a subgroup can be checked in polynomialtime.(c) 2023 Elsevier Ltd. All rights reserved.
This paper studies single vehicle scheduling problems with two agents on a line-shaped network. Each of two agents has some customers that are situated at some vertices on the network. A vehicle has to start from upsi...
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This paper studies single vehicle scheduling problems with two agents on a line-shaped network. Each of two agents has some customers that are situated at some vertices on the network. A vehicle has to start from upsilon(0) to serve all customers. The objective is to schedule the customers to minimize C-max(A) + theta C-max(B), where C-max(X) is the latest completion time of the customers for agent X and X is an element of{A,B}. We first propose a polynomial time algorithm for the problem without release time. Next, the problem with release time is proved to be NP-hard despite of a network with only two vertices. Then, we present a 3+root 5/2 -approximation algorithm. Finally, numerical experiments are carried out to verify the approximation algorithm is effective.
For a matrix W \in Zmx n, m \leq n, and a convex function g : Rm \rightarrowR, we are interested in minimizing f(x) = g(Wx) over the set {0, 1\} n. We will study separable convex functions and sharp convex functions g...
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For a matrix W \in Zmx n, m \leq n, and a convex function g : Rm \rightarrowR, we are interested in minimizing f(x) = g(Wx) over the set {0, 1\} n. We will study separable convex functions and sharp convex functions g. Moreover, the matrix W is unknown to us. Only the number of rows m \leq n and II W II,, are revealed. The composite function f (x) is presented by a zeroth and first order oracle only. Our main result is a proximity theorem that ensures that an integral minimum and a continuous minimum for separable convex and sharp convex functions are always ``close"" by. This will be a key ingredient in developing an algorithm for detecting an integer minimum that achieves a running time of roughly (mII W II,,)O(m3) \cdot poly(n). In the special case when (i) W is given explicitly and (ii) g is separable convex one can also adapt an algorithm of Hochbaum and Shanthikumar [J. ACM, 37 (1990), pp. 843--862]. The running time of this adapted algorithm matches the running time of our general algorithm.
This paper studies the days off scheduling problem when the demand for staffing may differ from day to another and when the total load is fixed in advance for each employee. The scheduling problem is then to assign on...
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ISBN:
(纸本)9783031692567;9783031692574
This paper studies the days off scheduling problem when the demand for staffing may differ from day to another and when the total load is fixed in advance for each employee. The scheduling problem is then to assign on-days and days-off to employees with different objectives: (1) exactly met the demand and the offer requirement (2) satisfy as best as possible the requirements. For each one, we propose a polynomial time algorithm based on network flow to construct a feasible scheduling.
Let Gbe a vertex-colored connected graph. A subset X of the vertex-set of G is called proper if any two adjacent vertices in X have distinct colors. The graph G is called proper vertex-disconnected if for any two vert...
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Let Gbe a vertex-colored connected graph. A subset X of the vertex-set of G is called proper if any two adjacent vertices in X have distinct colors. The graph G is called proper vertex-disconnected if for any two vertices x and y of G, there exists a vertex subset S of G such that when x and y are nonadjacent, Sis proper and x and y belong to different components of G - S;where as when x and y are adjacent, S + x or S + y is proper and x and y belong to different components of (G - xy) - S. For a connected graph G, the proper vertex-disconnection number of G, denoted by pvd( G), is the minimum number of colors that are needed to make G proper vertex-disconnected. In this paper, we firstly characterize the graphs of order n with proper vertex-disconnection number k for k.{1, n - 2, n - 1, n}. Secondly, we give some sufficient conditions for a graph G such that pvd(G) =.(G), and show that almost all graphs G have pvd(G) =.(G) and pvd(G) =.(G). We also give an equivalent statement of the famous Four Color Theorem. Furthermore, we study the relationship between the proper disconnection number pd(G) of G and the proper vertex-disconnection number pvd(L(G)) of the line graph L(G) of G. Finally, we show that it is NP-complete to decide whether a given vertex-colored graph is proper vertex-disconnected, and it is NP-hard to decide for a fixed integer k = 3, whether the pvd-number of a graph G is no more than k, even if k = 3 and G is a planar graph with Delta(G) = 12. We also show that it is solvable in polynomialtime to determine the proper vertex-disconnection number for a graph with maximum degree less than four. (c) 2022 Elsevier B.V. All rights reserved.
Given an edge weighted graph, and an acyclic edge set, the target of the partial inverse maximum spanning tree problem (PIMST) is to get a new weight function such that the given set is included in some maximum spanni...
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Given an edge weighted graph, and an acyclic edge set, the target of the partial inverse maximum spanning tree problem (PIMST) is to get a new weight function such that the given set is included in some maximum spanning tree associated with the new function, and the difference between the two functions is minimum. In this paper, we research PIMST under the Chebyshev norm. Firstly, the definition of extreme optimal solution is introduced, and its some properties are gained. Based on these properties, a polynomial scale optimal value candidate set is obtained. Finally, strongly polynomial-timealgorithms for solving this problem are proposed. Thus, the computational complexity of PIMST is completely solved.
We study the design of large-scale group testing schemes under a heterogeneous population (i.e., subjects with potentially different risk) and with the availability of multiple tests. The objective is to classify the ...
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We study the design of large-scale group testing schemes under a heterogeneous population (i.e., subjects with potentially different risk) and with the availability of multiple tests. The objective is to classify the population as positive or negative for a given binary characteristic (e.g., the presence of an infectious disease) as efficiently and accurately as possible. Our approach examines components often neglected in the literature, such as the dependence of testing cost on the group size and the possibility of no testing, which are especially relevant within a heterogeneous setting. By developing key structural properties of the resulting optimization problem, we are able to reduce it to a network flow problem under a specific, yet not too restrictive, objective function. We then provide results that facilitate the construction of the resulting graph and finally provide a polynomial time algorithm. Our case study, on the screening of HIV in the United States, demonstrates the substantial benefits of the proposed approach over conventional screening methods. Summary of Contribution: This paper studies the problem of testing heterogeneous populations in groups in order to reduce costs and hence allow for the use of more efficient tests for high-risk groups. The resulting problem is a difficult combinatorial optimization problem that is NP-complete under a general objective. Using structural properties specific to our objective function, we show that the problem can be cast as a network flow problem and provide a polynomial time algorithm.
An Italian dominating function on a simple undirected graph G is a function f : V(G) -> {0, 1, 2} satisfying the condition that for each vertex v with f (v) = 0, Sigma(u epsilon NG(v)) f(u) >= 2. An Italian domi...
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An Italian dominating function on a simple undirected graph G is a function f : V(G) -> {0, 1, 2} satisfying the condition that for each vertex v with f (v) = 0, Sigma(u epsilon NG(v)) f(u) >= 2. An Italian dominating function f on G is called a perfect Italian dominating function on G if for each vertex v with f (v) = 0, Sigma(u epsilon NG(v)) f (u) = 2. The weight of a function f on a graph G, denoted by w(f), is the sum Sigma(u epsilon V(G)) f (v). For a simple undirected graph G, Min-PIDF is the problem of finding the minimum weight of a perfect Italian dominating function on G. First, we discuss the complexity difference between Min-PIDF and the problem of finding the minimum weight of an Italian dominating function. We then establish the NP-completeness of the decision version of Min-PIDF in chordal graphs and investigate the hardness of approximation of Min-PIDF in general graphs. Finally, we present linear timealgorithms for computing the minimum weight of a perfect Italian dominating function in block graphs and series-parallel graphs. (c) 2021 Elsevier B.V. All rights reserved.
A matching is called stable if it has no blocking pair, where a blocking pair is a man-woman pair, say (m, w), such that m and w are not matched with each other in the matching but if they get matched with each other,...
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ISBN:
(纸本)9783031252105;9783031252112
A matching is called stable if it has no blocking pair, where a blocking pair is a man-woman pair, say (m, w), such that m and w are not matched with each other in the matching but if they get matched with each other, then both of them become better off. A matching is called non-crossing if it does not admit any pair of edges that cross each other when all men and women are arranged in two parallel vertical lines with men on one line and women on the other. Two notions of matchings that are stable as well as non-crossing have been identified in the literature, namely (i) weakly stable non-crossing matching (WSNM) and (ii) strongly stable non-crossing matching (SSNM). An SSNM is a non-crossing matching which is stable in the classical sense, whereas in a WSNM, a blocking pair satisfies an extra condition that it must not cross any matching edge. It is known that the problem of finding a WSNM, which always exists in an SMI instance, is polynomialtime solvable. However, the problem of determining the existence of an SSNM in SMTI is known to be NP-complete. We show that this problem is fixed-parameter tractable (FPT) when parameterized by total length of ties. We introduce a new notion of stable non-crossing matching, namely semi-strongly stable non-crossing matching (SSSNM). We prove that the problem of determining the existence of an SSSNM in SMI is NP-complete even if size of every man's preference list is at most two. On the positive side, we show that this problem is polynomialtime solvable if every man's preference list contains at most one woman.
Let G = (V, E) be a finite undirected graph. An edge set E' subset of E is a dominating induced matching (d.i.m.) in G if every edge in E is intersected by exactly one edge of E'. The Dominating Induced Matchi...
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Let G = (V, E) be a finite undirected graph. An edge set E' subset of E is a dominating induced matching (d.i.m.) in G if every edge in E is intersected by exactly one edge of E'. The Dominating Induced Matching (DIM) problem asks for the existence of a d.i.m. in G;this problem is also known as the Efficient Edge Domination problem;it is the Efficient Domination problem for line graphs. The DIM problem is NP-complete even for very restricted graph classes such as planar bipartite graphs with maximum degree 3 and is solvable in linear time for P-7-free graphs, and in polynomialtime for S-1,S-2,S-4-free graphs as well as for S-2,S-2,S-2-free graphs. In this paper, combining two distinct approaches, we solve it in polynomialtime for S-2,S-2,S-3-free graphs. (C) 2020 Elsevier B.V. All rights reserved.
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