A Constant-factor Approximation Algorithm for Unsplittable Flow on Paths
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TL;DR: A constant-factor approximation algorithm for the unsplittable flow problem on a path which improves on the previous best known approximation factor of O(log n), and introduces several novel algorithmic techniques, which might be of independent interest.
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Abstract: In the unsplittable flow problem on a path, we are given a capacitated path $P$ and $n$ tasks, each task having a demand, a profit, and start and end vertices. The goal is to compute a maximum profit set of tasks such that, for each edge $e$ of $P$, the total demand of selected tasks that use $e$ does not exceed the capacity of $e$. This is a well-studied problem that has been described under alternative names, such as resource allocation, bandwidth allocation, resource constrained scheduling, temporal knapsack, and interval packing. We present a polynomial time constant-factor approximation algorithm for this problem. This improves on the previous best known approximation ratio of $O(\log n)$. The approximation ratio of our algorithm is $7+\epsilon$ for any $\epsilon>0$. We introduce several novel algorithmic techniques, which might be of independent interest: a framework which reduces the problem to instances with a bounded range of capacities, and a new geometrically inspired dynamic program which solv...
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Citations
A logarithmic approximation for unsplittable flow on line graphs
Nikhil Bansal,Zachary Friggstad,Rohit Khandekar,Mohammad R. Salavatipour +3 more
- 04 Jan 2009
TL;DR: The key idea is to exploit certain structural properties of the problem to show that instances that are bad for the LP can in fact be handled using dynamic programming.
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TL;DR: This paper proposes Dedicated Protection for Virtual Network Embedding (DRONE), a suite of solutions to the 1 + 1-ProViNE problem, which includes an integer linear programming formulation for optimal solution (OPT-DRONE) and a heuristic (FAST-DRONES) to tackle the computational complexity of the optimal solution.
64
A QPTAS for maximum weight independent set of polygons with polylogarithmically many vertices
Anna Adamaszek,Andreas Wiese +1 more
- 05 Jan 2014
TL;DR: In this paper, a (1 + e)-approximation algorithm for the maximum weight independent set of polygons problem is presented, assuming that each polygon in the input has at most a polylogarithmic number of vertices.
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A Mazing 2+ε Approximation for Unsplittable Flow on a Path
TL;DR: A polynomial-time approximation scheme (PTAS) for δ-large tasks, for any constant δ > 0, key to this result is a complex geometrically inspired dynamic program, which matches the best known approximation ratio for the considerably easier special case of uniform edge capacities.
A (5/3 + ε)-approximation for unsplittable flow on a path: placing small tasks into boxes
Fabrizio Grandoni,Tobias Mömke,Andreas Wiese,Hang Zhou +3 more
- 20 Jun 2018
TL;DR: This paper presents a polynomial-time algorithm that obtains roughly all profit from the optimal large tasks plus one third of the profit of the optimal small tasks, and introduces a horizontal slicing lemma which yields a novel geometric interpretation of certain solutions.
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