Designing Multi-Commodity Flow Trees
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Multi-commodity location-routing: Flow intercepting formulation and branch-and-cut algorithm
Research on the location-routing problem (LRP) is very active, producing a good number of effective exact and approximated solution approaches. It is noteworthy that most of the contributions present in the literature address the single-commodity LRP, whereas the multi-commodity case has been scarcely investigated. Yet, this issue assumes an important role in many LRP applications, particularly...
متن کاملDesigning Multi-Commodity Flow Trees
The traditional multi-commodity flow problem assumes a given flow network in which multiple commodities are to be maximally routed in response to given demands. This paper considers the multi-commodity flow network-desigu problem: given a set of multi-commodity flow demands, find a network subject to certain constraints such that the commodities can be maximally routed. This paper focuses on th...
متن کاملOn constant multi-commodity flow-cut gaps for directed minor-free graphs
The multi-commodity flow-cut gap is a fundamental parameter that affects the performance of several divide & conquer algorithms, and has been extensively studied for various classes of undirected graphs. It has been shown by Linial, London and Rabinovich [15] and by Aumann and Rabani [3] that for general n-vertex graphs it is bounded by Oplog nq and the GuptaNewman-Rabinovich-Sinclair conjectur...
متن کامل7.1 Multicut
P∈Pi P∋e fi,P ≤ ce ∀e fi,P ≥ 0 Dual 1 solves the max-sum multi-commodity flow problem: ce represents the capacity of an edge, and fi,P is the amount of flow directed from si to ti along the path P . The LP tries to maximize the total amount of commodity flow. Lemma 17.1.1 Multicut is always larger than the corresponding max-sum multi-commodity flow. Lemma 17.1.2 Multicut is at most O(logK) time...
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We prove that, for every integer k ≥ 1, every shortest-path metric on a graph of pathwidth k embeds into a distribution over random trees with distortion at most c = c(k), independent of the graph size. A well-known conjecture of Gupta, Newman, Rabinovich, and Sinclair [GNRS04] states that for every minor-closed family of graphs F , there is a constant c(F) such that the multi-commodity max-flo...
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