60,324 research outputs found

    A Dual Ascent Procedure for Large Scale Uncapacitated Network Design

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    The fixed-charge network design problem arises in a variety of problem contexts including transportation, communication, and production scheduling.We develop a family of dual ascent algorithms for this problem. This approach generalizes known ascent procedures for solving shortest path, plant location,Steiner network and directed spanning tree problems. Our computational results for several classes of test problems with up to 500 integer and 1.98 million continuous variables and constraints shows that the dual ascent procedure and an associated drop-add heuristic generates solutions that, in almost all cases, are guaranteed to be within 1 to 3 percent of optimality. Moreover, the procedure requires no more than 150 seconds on an IBM 3083 computer. The test problems correspond to dense and sparse networks,including some models arising in freight transport

    Computing shortest paths in 2D and 3D memristive networks

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    Global optimisation problems in networks often require shortest path length computations to determine the most efficient route. The simplest and most common problem with a shortest path solution is perhaps that of a traditional labyrinth or maze with a single entrance and exit. Many techniques and algorithms have been derived to solve mazes, which often tend to be computationally demanding, especially as the size of maze and number of paths increase. In addition, they are not suitable for performing multiple shortest path computations in mazes with multiple entrance and exit points. Mazes have been proposed to be solved using memristive networks and in this paper we extend the idea to show how networks of memristive elements can be utilised to solve multiple shortest paths in a single network. We also show simulations using memristive circuit elements that demonstrate shortest path computations in both 2D and 3D networks, which could have potential applications in various fields

    Semi-classical Dynamical Triangulations

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    For non-critical string theory the partition function reduces to an integral over moduli space after integrating over matter fields. The moduli integrand is known analytically for genus one surfaces. The formalism of dynamical triangulations provides us with a regularization of non-critical string theory and we show that even for very small triangulations it reproduces very well the continuum integrand when the central charge cc of the matter fields is large negative, thus providing a striking example of how the quantum fluctuations of geometry disappear when cc \to -\infty.Comment: 11 pages, 5 figure

    Improved Algorithms for Decremental Single-Source Reachability on Directed Graphs

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    Recently we presented the first algorithm for maintaining the set of nodes reachable from a source node in a directed graph that is modified by edge deletions with o(mn)o(mn) total update time, where mm is the number of edges and nn is the number of nodes in the graph [Henzinger et al. STOC 2014]. The algorithm is a combination of several different algorithms, each for a different mm vs. nn trade-off. For the case of m=Θ(n1.5)m = \Theta(n^{1.5}) the running time is O(n2.47)O(n^{2.47}), just barely below mn=Θ(n2.5)mn = \Theta(n^{2.5}). In this paper we simplify the previous algorithm using new algorithmic ideas and achieve an improved running time of O~(min(m7/6n2/3,m3/4n5/4+o(1),m2/3n4/3+o(1)+m3/7n12/7+o(1)))\tilde O(\min(m^{7/6} n^{2/3}, m^{3/4} n^{5/4 + o(1)}, m^{2/3} n^{4/3+o(1)} + m^{3/7} n^{12/7+o(1)})). This gives, e.g., O(n2.36)O(n^{2.36}) for the notorious case m=Θ(n1.5)m = \Theta(n^{1.5}). We obtain the same upper bounds for the problem of maintaining the strongly connected components of a directed graph undergoing edge deletions. Our algorithms are correct with high probabililty against an oblivious adversary.Comment: This paper was presented at the International Colloquium on Automata, Languages and Programming (ICALP) 2015. A full version combining the findings of this paper and its predecessor [Henzinger et al. STOC 2014] is available at arXiv:1504.0795

    Polynomial cases of the tarification problem

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    We consider the problem of determining a set of optimal tariffs for an agent in a network, who owns a subset of the arcs of the network, and who wishes to maximize his revenues on this subset from a set of clients that make use of the network.The general variant of this problem is NP-hard, already with a single client. This paper introduces several new polynomially solvable special cases. An important case is the following.For multiple clients, if the number of tariff arcs is bounded from above, we can solve the problem by a polynomial number of linear programs (each of which is of polynomial size). Furthermore, we show that the parametric tarification problem and the single arc fixed charge tarification problem can be solved in polynomial time.Economics ;
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