An FPTAS for Quickest Multicommodity Flows with Inflow-Dependent Transit Times
نویسندگان
چکیده
منابع مشابه
An FPTAS for Quickest Multicommodity Flows with Inflow-Dependent Transit Times1
Given a network with capacities and transit times on the arcs, the quickest flow problem asks for a “flow over time” that satisfies given demands within minimal time. In the setting of flows over time, flow on arcs may vary over time and the transit time of an arc is the time it takes for flow to travel through this arc. In most real-world applications (such as, e.g., road traffic, communicatio...
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For the earliest arrival flow problem one is given a network G = (V,A) with capacities u(a) and transit times τ(a) on its arcs a ∈ A, together with a source and a sink vertex s, t ∈ V . The objective is to send flow from s to t that moves through the network over time, such that for each point in time θ ∈ [0, T ) the maximum possible amount of flow reaches t. If, for each θ ∈ [0, T ) this flow ...
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We study flows over time in networks with transit times on the arcs. Transit times describe how long it takes to traverse an arc. A flow over time specifies for each arc a time-dependent flow rate that must always be bounded by the arc’s capacity. Only recently, Melkonian introduced an alternative model where so-called bridge capacities bound the total amount of flow traveling along an arc, at ...
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For k ≥ 1, the k-commodity flow problem is, we are given k pairs of vertices in a graph G, and we ask whether there exist k flows in the graph, where • the ith flow is between the ith pair of vertices, and has total value one; and • for each edge e, the sum of absolute values of the flows along e is at most one. We prove that for all k there exists n(k) such that if G is connected, and contract...
متن کاملInteger Multicommodity Flows with Reduced
Given a supply graph G = (V; E), a demand graph H = (T; D), edge capacities c : E 7 ! II N and requests r : D 7 ! II N, we consider the problem of nding integer multiiows subject to c; r. Korach and Penn constructed approximate integer multiiows for planar graphs, but no results were known for the general case. Via derandomization we present a polynomial-time approximation algorithm. There are ...
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ژورنال
عنوان ژورنال: Algorithmica
سال: 2007
ISSN: 0178-4617,1432-0541
DOI: 10.1007/s00453-006-0196-3