In this paper we establish a dichotomy theorem for the complexity of homomorphisms to fixed locally semicomplete digraphs. It is also shown that the same dichotomy holds for list homomorphisms. The polynomial algorith...
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In this paper we establish a dichotomy theorem for the complexity of homomorphisms to fixed locally semicomplete digraphs. It is also shown that the same dichotomy holds for list homomorphisms. The polynomial algorithms follow from a different, shorter proof of a result by Gutjahr, Welzl and Woeginger. (c) 2010 Elsevier B.V. All rights reserved.
It is required to find an optimal order of constructing the edges of a network so as to minimize the sum of the weighted connection times of relevant pairs of vertices. Construction can be performed anytime anywhere i...
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It is required to find an optimal order of constructing the edges of a network so as to minimize the sum of the weighted connection times of relevant pairs of vertices. Construction can be performed anytime anywhere in the network, with a fixed overall construction speed. The problem is strongly NP-hard even on stars. We present polynomial algorithms for the problem on trees with a fixed number of leaves, and on general networks with a fixed number of relevant pairs. (C) 2021 Elsevier B.V. All rights reserved.
The Eulerian Editing problem asks, given a graph G and an integer k, whether G can be modified into an Eulerian graph using at most k edge additions and edge deletions. We show that this problem is polynomial-time sol...
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The Eulerian Editing problem asks, given a graph G and an integer k, whether G can be modified into an Eulerian graph using at most k edge additions and edge deletions. We show that this problem is polynomial-time solvable for both undirected and directed graphs. We generalize these results for problems with degree parity constraints and degree balance constraints, respectively. We also consider the variants where vertex deletions are permitted. Combined with known results, this leads to full complexity classifications for both undirected and directed graphs and for every subset of the three graph operations. (C) 2015 Elsevier Inc. All rights reserved.
In this paper, we present an efficient implementation of the O(mn+n(2) log n) time algorithm originally proposed by Nagamochi and Ibaraki (1992) for computing the minimum capacity cut of an undirected network. To enha...
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In this paper, we present an efficient implementation of the O(mn+n(2) log n) time algorithm originally proposed by Nagamochi and Ibaraki (1992) for computing the minimum capacity cut of an undirected network. To enhance computation, various ideas are added so that it can contract as many edges as possible in each iteration, To evaluate the performance of the resulting implementation, we conducted extensive computational experiments, and compared the results with that of Padberg and Rinaldi's algorithm (1990), which is currently known as one of the practically fastest programs for this problem. The results indicate that our program is considerably faster than Padberg and Rinaldi's program, and its running time is not significantly affected by the types of the networks being solved.
In this paper we consider problems of the following type: Let E = {e(1), e(2),..., e(n)} be a finite set and F be a family of subsets of E. For each element e(i) in E, c(i) is a given capacity and w(i) is the cost of ...
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In this paper we consider problems of the following type: Let E = {e(1), e(2),..., e(n)} be a finite set and F be a family of subsets of E. For each element e(i) in E, c(i) is a given capacity and w(i) is the cost of increasing capacity c(i) by one unit. It is assumed that we can expand the capacity of each element in E so that the capacity of family F can be expanded to a level r. For each r, let f (r) be the efficient function with respect to the capacity r of family F, and f (r) be the cost function for expanding the capacity of family F to r. The goal is to find the optimum capacity value r* and the corresponding expansion strategy so that the pure efficency function f (r*) - f (r*) is the largest. Firstly, we show that this problem can be solved efficiently by figuring out a series of bottleneck capacity expansion problem defined by paper (Yang and Chen, Acta Math Sci 22: 207 - 212, 2002) if f (r) is a piecewise linear function. Then we consider two variations and prove that these problems can be solved in polynomial time under some conditions. Finally the optimum capacity for maximum flow expansion problem is discussed. We tackle it by constructing an auxiliary network and transforming the problem into a maximum cost circulation problem on the auxiliary network.
No-wait re-entrant robotic flowshops are widely used in the electronic industry, such as PCB and semiconductor manufacturing. In such an industry, cyclic production policy is often used due to large lot size and simpl...
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No-wait re-entrant robotic flowshops are widely used in the electronic industry, such as PCB and semiconductor manufacturing. In such an industry, cyclic production policy is often used due to large lot size and simplicity of implementation. This paper addresses cyclic scheduling of a no-wait re-entrant robotic flowshop with multiple robots for material handling. We formulate the problem and propose a polynomial algorithm to find the minimum number of robots for all feasible cycle times. Consequently, the minimum cycle time for any given number of robots can be obtained with the proposed algorithm. The algorithm runs in O(N(5)) time in the worst case, where N is the number of machines in the robotic flowshop. (C) 2011 Elsevier B.V. All rights reserved.
Stable flows generalize the well-known concept of stable matchings to markets in which transactions may involve several agents, forwarding flow from one to another. An instance of the problem consists of a capacitated...
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Stable flows generalize the well-known concept of stable matchings to markets in which transactions may involve several agents, forwarding flow from one to another. An instance of the problem consists of a capacitated directed network in which vertices express their preferences over their incident edges. A network flow is stable if there is no group of vertices that all could benefit from rerouting the flow along a walk. Fleiner (algorithms 7:1-14, 2014) established that a stable flow always exists by reducing it to the stable allocation problem. We present an augmenting path algorithm for computing a stable flow, the first algorithm that achieves polynomial running time for this problem without using stable allocations as a black-box subroutine. We further consider the problem of finding a stable flow such that the flow value on every edge is within a given interval. For this problem, we present an elegant graph transformation and based on this, we devise a simple and fast algorithm, which also can be used to find a solution to the stable marriage problem with forced and forbidden edges. Finally, we study the stable multicommodity flow model introduced by Kiraly and Pap (algorithms 6:161-168, 2013). The original model is highly involved and allows for commodity-dependent preference lists at the vertices and commodity-specific edge capacities. We present several graph-based reductions that show equivalence to a significantly simpler model. We further show that it is NP-complete to decide whether an integral solution exists.
A hypergraph H = (V, E) is a subtree hypergraph if there is a tree T on V such that each hyperedge of E induces a subtree of T. Since the number of edges of a subtree hypergraph can be exponential in n = vertical bar ...
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A hypergraph H = (V, E) is a subtree hypergraph if there is a tree T on V such that each hyperedge of E induces a subtree of T. Since the number of edges of a subtree hypergraph can be exponential in n = vertical bar V vertical bar, one can not always expect to be able to find a minimum size transversal in time polynomial in n. In this paper, we show that if it is possible to decide if a set of vertices W subset of V is a transversal in time S(n) (where n = vertical bar V vertical bar), then it is possible to find a minimum size transversal in O(n(3)S(n)). This result provides a polynomial algorithm for the Source Location Problem: a set of (k, l)-sources for a digraph D = (V, A) is a subset S of V such that for any V is an element of V there are k arc-disjoint paths that each join a vertex of S to It and I arc-disjoint paths that each join v to S. The Source Location Problem is to find a minimum size set of (k, l)-sources. We show that this is a case of finding a transversal of a subtree hypergraph, and that in this case S(n) is polynomial. (c) 2007 Wiley Periodicals, Inc.
We consider the single-machine sequencing model with stochastic processing times and the problem of minimizing the number of stochastically tardy jobs. In general, this problem is NP-hard. Recently, however, van den A...
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We consider the single-machine sequencing model with stochastic processing times and the problem of minimizing the number of stochastically tardy jobs. In general, this problem is NP-hard. Recently, however, van den Akker and Hoogeveen found some special cases that could be solved in polynomial time. We generalize their findings by providing a polynomial time solution for any stochastically ordered processing times.
Recently, Pablo Saez (2009) [1] has developed a quadratic algorithm for a 2-cyclic robotic scheduling problem. In this note we uncover that the algorithm handles a special version of the problem only and fails to solv...
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Recently, Pablo Saez (2009) [1] has developed a quadratic algorithm for a 2-cyclic robotic scheduling problem. In this note we uncover that the algorithm handles a special version of the problem only and fails to solve the general 2-cyclic robotic scheduling problem. (C) 2009 Elsevier B.V. All rights reserved.
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