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Bruhn, Henning; Černý, Jakub; Hall, Alexander; Kolman, Petr; Sgall, Jiřį́

doi:10.4086/toc.2008.v004a001

Cited by 6 publications

References 32 publications

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Connecting the Dots: Molecular Machinery for Distributed Robotics

Brun

Reishus

2009

DNA Computing

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Nature is considered one promising area to search for inspiration in designing robotic systems. Some work in swarm robotics has tried to build systems that resemble distributed biological systems and inherit biology's fault tolerance, scalability, dependability, and robustness. Such systems, as well as ones in the areas of active self-assembly and amorphous computing, typically use relatively simple components with limited computation, memory, and computational power to accomplish complex tasks, such as forming paths in the presence of obstacles. We demonstrate that such tasks can be accomplished in the well-studied tile assembly model, a model of molecular self-assembly that is strictly simpler than other biologically-inspired models. Our systems use a small number of distinct components to find minimal-length paths in time linear in the length of the path while inheriting scalability and fault tolerance of the underlying natural process of self-assembly.

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Connecting the Dots: Molecular Machinery for Distributed Robotics

Brun

Reishus

2009

DNA Computing

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A Method for Obtaining the Maximum (δ,η)-Balanced Flow in a Network

Kishimoto

2011

Lecture Notes in Computer Science

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Towards Duality of Multicommodity Multiroute Cuts and Flows: Multilevel Ball-Growing

Kolman

Scheideler

2013

Theory Comput Syst

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An elementary h-route flow, for an integer h ≥ 1, is a set of h edge-disjoint paths between a source and a sink, each path carrying a unit of flow, and an h-route flow is a non-negative linear combination of elementary h-route flows. An h-route cut is a set of edges whose removal decreases the maximum h-route flow between a given source-sink pair (or between every source-sink pair in the multicommodity setting) to zero. The main result of this paper is an approximate duality theorem for multicommodity h-route cuts and flows, for h ≤ 3: The size of a minimum h-route cut is at least f /h and at most O(log 4 k · f ) where f is the size of the maximum h-route flow and k is the number of commodities. The main step towards the proof of this duality is the design and analysis of a polynomial-time approximation algorithm for the minimum h-route cut problem for h = 3 that has an approximation ratio of O(log 4 k). Previously, polylogarithmic approximation was known only for h-route cuts for h ≤ 2. A key ingredient of our algorithm is a novel rounding technique that we call multilevel ball-growing. Though the proof of the duality relies on this algorithm, it is not a straightforward corollary of it as in the case of classical multicommodity flows and cuts. Similar results are shown also for the sparsest multiroute cut problem.

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Cited by 6 publications

References 32 publications

Connecting the Dots: Molecular Machinery for Distributed Robotics

Connecting the Dots: Molecular Machinery for Distributed Robotics

A Method for Obtaining the Maximum (δ,η)-Balanced Flow in a Network

Towards Duality of Multicommodity Multiroute Cuts and Flows: Multilevel Ball-Growing

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