This paper deals with the Efficient Edge Domination Problem (EED, for short), also known as Dominating Induced Matching Problem. For an undirected graph G = (V, E) FED asks for an induced matching M subset of E that s...
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(纸本)9783642121999
This paper deals with the Efficient Edge Domination Problem (EED, for short), also known as Dominating Induced Matching Problem. For an undirected graph G = (V, E) FED asks for an induced matching M subset of E that simultaneously dominates all edges of G. Thus, the distance between edges of M is at least two and every edge in E is adjacent to an edge of M. EED is related to parallel resource allocation problems, encoding theory and network routing. The problem is NP-complete even for restricted classes like planar bipartite and bipartite graphs with maximum degree three. However, the complexity has been open for chordal bipartite graphs. This paper shows that EED can be solved in polynomialtime on hole-free graphs. Moreover, it provides even linear time for chordal bipartite graphs. Finally, we strengthen the NP-completeness result to planar bipartite graphs of maximum degree three.
Let G = (V, E) be a finite undirected graph. An edge set E ' c 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 (DI...
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Let G = (V, E) be a finite undirected graph. An edge set E ' c 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 but is solvable in polynomialtime for P9 -free graphs [and in linear time for P7 -free graphs] as well as for S1,2,4 -free, for S2,2,2 -free, and for S2,2,3 -free graphs. In this paper, combining two distinct approaches, we solve it in polynomialtime for P10 -free graphs and introduce a partial result for the general case.
We consider two versions of two-machine flow shop scheduling problems, where each job requires an additional resource from the start of its first operation till the end of its second operation. We refer to this resour...
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We consider two versions of two-machine flow shop scheduling problems, where each job requires an additional resource from the start of its first operation till the end of its second operation. We refer to this resource as storage space. The storage requirement of each job is determined by the processing time of its first operation. The two problems differ from each other in the way resources are allocated for each job. In the first case, the job captures all the necessary units of storage space at the beginning of processing its first operation. In the second case, the job takes up storage space gradually as its first operation is performed. In both problems, the goal is to minimize the makespan. In our paper, we establish the exact borderline between the NP-hard and polynomial-time solvable instances of the problems with respect to the ratio between the storage size and the maximum operation length.
Given a rational matrix A, and a set of rational matrices B, C,… which commute with A, we give polynomial time algorithms to compute exactly the Jordan Normal Form of A, as well as the transformed matrices of B, C,…...
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Given a rational matrix A, and a set of rational matrices B, C,… which commute with A, we give polynomial time algorithms to compute exactly the Jordan Normal Form of A, as well as the transformed matrices of B, C,…. We also obtain the transformation matrix and its inverse exactly in polynomialtime.
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.
PREMAGE CONSTRUCTION problem by Kratsch and Hemaspaandra naturally arose from the famous graph reconstruction conjecture. It deals with the algorithmic aspects of the conjecture. We present an O(n(8)) timealgorithm f...
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PREMAGE CONSTRUCTION problem by Kratsch and Hemaspaandra naturally arose from the famous graph reconstruction conjecture. It deals with the algorithmic aspects of the conjecture. We present an O(n(8)) timealgorithm for PREIMAGE CONSTRUCTION on permutation graphs and an O(n(4)(n + m)) timealgorithm for PREIMAGE CONSTRUCTION on distance-hereditary graphs, where n is the number of graphs in the input, and m is the number of edges in a preimage: Since each graph of the input has n - 1 vertices and O(n(2)) edges, the input size is O(n(3)) (, or O(nm)). There are polynomialtime isomorphism algorithms for permutation graphs and distance-hereditary graphs. However the number of permutation (distance-hereditary) graphs obtained by adding a vertex to a permutation (distance-hereditary) graph is generally exponentially large. Thus exhaustive checking of these graphs does not achieve any polynomial time algorithm. Therefore reducing the number of preimage candidates is the key point.
The shop-scheduling problem with two jobs and m machines is considered under the condition that the machine order is fixed in advance for the first job and nonfixed for the second job. The problems of makespan and mea...
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The shop-scheduling problem with two jobs and m machines is considered under the condition that the machine order is fixed in advance for the first job and nonfixed for the second job. The problems of makespan and mean flow time minimization are proved to be NP-hard if operation preemption is forbidden. In the case of preemption allowance for any given regular criterion the O(n*) algorithm is proposed. Here, n* is the maximum number of operations per job.
In this paper we consider the problem of minimizing a general quadratic function over the mixed integer points in an ellipsoid. This problem is strongly NP-hard, NP-hard to approximate within a constant factor, and op...
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In this paper we consider the problem of minimizing a general quadratic function over the mixed integer points in an ellipsoid. This problem is strongly NP-hard, NP-hard to approximate within a constant factor, and optimal solutions can be irrational. In our main result we show that an arbitrarily good solution can be found in polynomialtime, if we fix the number of integer variables. This algorithm provides a natural extension to the mixed integer setting, of the polynomial solvability of the trust region problem proven by Ye, Karmarkar, Vavasis, and Zippel. As a result, our findings pave the way for designing efficient trust region methods for mixed integer nonlinear optimization problems. The techniques that we introduce are of independent interest and can be used in other mixed integer nonlinear optimization problems. As an example, we consider the problem of minimizing a general quadratic function over the mixed integer points in a polyhedron. For this problem, we show that a solution satisfying weak bounds with respect to optimality can be computed in polynomialtime, provided that the number of integer variables is fixed. It is well known that finding a solution satisfying stronger bounds cannot be done in polynomialtime, unless P = NP.
In a partial inverse matroid problem, given a matroid M = (S, I), a real valued weight function w on S, and an independent set I-0 is an element of I, the goal is to modify the weight w as small as possible to a new w...
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In a partial inverse matroid problem, given a matroid M = (S, I), a real valued weight function w on S, and an independent set I-0 is an element of I, the goal is to modify the weight w as small as possible to a new weight (w) over bar such that there exists a (w) over bar -maximum base containing I-0. In this paper, we study a constraint version of the partial inverse matroid problem in which the weight can only be decreased. A polynomial time algorithm is presented under I-infinity-norm. (C) 2016 Elsevier B.V. All rights reserved.
We propose a randomized polynomial time algorithm for computing non-trivial zeros of quadratic forms in 4 or more variables over F-q(t), where F-q is a finite field of odd characteristic. The algorithm is based on a s...
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We propose a randomized polynomial time algorithm for computing non-trivial zeros of quadratic forms in 4 or more variables over F-q(t), where F-q is a finite field of odd characteristic. The algorithm is based on a suitable splitting of the form into two forms and finding a common value they both represent. We make use of an effective formula for the number of fixed degree irreducible polynomials in a given residue class. We apply our algorithms for computing a Witt decomposition of a quadratic form, for computing an explicit isometry between quadratic forms and finding zero divisors in quaternion algebras over quadratic extensions of F-q(t). (C) 2018 Elsevier Inc. All rights reserved.
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