Data structures and algorithms for disjoint set union problems

Galil, Zvi; Italiano, Giuseppe F.

doi:10.1145/116873.116878

Cited by 142 publications

(83 citation statements)

References 54 publications

(19 reference statements)

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“…The actual coding operations are also deferred until the encoded block is read. Thus, the star component becomes equivalent to a disjoint-set forest structure [18], where our (deferred) coding operation is equivalent to the path compression, see Figure 5. Note that reading a block will occur not only at the final decoding of a star component, but also on uploading to another peer, thus also initiating a path compression.…”

Section: Decodingmentioning

confidence: 99%

Paircoding: Improving File Sharing Using Sparse Network Codes

Ortolf

Schindelhauer

Vater

2009

2009 Fourth International Conference on Internet and Web Applications and Services

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BitTorrent and Practical Network Coding are efficient methods for sharing files in a peer-to-peer network. Both face the problem to distribute a given file using peers with different and dynamic bandwidth and only temporal availability. For this, BitTorrent partitions the files and uses the upload and download of each peer. In addition to this, Practical Network Coding uses a random linear combination of the parts. The original file can be decoded by a matrix operation as soon as enough linear combinations have been gathered at a peer.It is known that Practical Network Coding optimizes the network flow in any peer-to-peer network, yet suffers from the cost of read/write disk operations for encoding and decoding. In this respect, BitTorrent is very efficient, yet falls behind because it has to face the coupon collector problem when distributing parts.We present Paircoding as an alternative which is regarding filesharing at least as good as BitTorrent and shares nearly the same computational disk access complexity with BitTorrent. In some scenarios Paircoding outperforms BitTorrent regarding network flow and performs as well as Practical Network Coding. Paircoding distributes only a linear combination of two parts which alleviates the coupon collector problem of BitTorrent without the computational overhead of Practical Network Coding.For analytical proofs of these statements we formalize filesharing in a peer-to-peer network in a round model and introduce a computational model which allows to compare the efficiency of the filesharing algorithms in a distributed environment. Since BitTorrent tries to overcome the coupon collector problem with various policies we face a family of BitTorrent systems. We show that for each BitTorrent policy there is a Paircoding policy which is at least as good regarding filesharing quality.

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Section: Decodingmentioning

confidence: 99%

Paircoding: Improving File Sharing Using Sparse Network Codes

Ortolf

Schindelhauer

Vater

2009

2009 Fourth International Conference on Internet and Web Applications and Services

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“…The classical union-find (also referred to as disjoint-set-union) algorithm was introduced by Tarjan in the seventies [TvL84]. A classic survey on the topic is [GI91]. The algorithm solves the problem of maintaining a collection of disjoint sets under the operation of union.…”

Section: The Union-find Algorithmmentioning

confidence: 99%

Quasi-Linear-Time Algorithms by Generalisation of Union-Find in CHR

Frühwirth

2008

Lecture Notes in Computer Science

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Abstract. The union-find algorithm can be seen as solving simple equations between variables or constants. With a few lines of code change, we generalise its implementation in CHR from equality to arbitrary binary relations. By choosing the appropriate relations, we can derive fast incremental algorithms for solving certain propositional logic (SAT) problems and polynomial equations in two variables. In general, we prove that when the relations are bijective functions, our generalisation yields a correct algorithm. We also show that bijectivity is a necessary condition for correctness if the relations include the identity function.The rules of our generic algorithm have additional properties that make them suitable for incorporation into constraint solvers: from classical union-find, they inherit a compact solved form and quasi-linear time and space complexity. By nature of CHR, they are anytime and online algorithms. They solve and simplify the constraints in the problem, and can test them for entailment, even when the constraints arrive incrementally.

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“…Once all of the pixels have been added, the MSERs can be found as the components that satisfy the maximal stability criterion mentioned above. Since the typical disjoint-set data structure is not persistent [3], it is impossibly to recover the connected components that existed after a subset of the pixels had been added. Thus, at the termination of the algorithm, nothing is known about the MSERs other than a single pixel within the region and a boundary threshold, since all of the information characterizing the connected components has been lost.…”

Section: Maximally Stable Extremal Regionsmentioning

confidence: 99%

N-tree Disjoint-Set Forests for Maximally Stable Extremal Regions

Murphy-Chutorian

Trivedi

2006

Procedings of the British Machine Vision Conference 2006

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In this paper we introduce the NDS-Forest data structure, which can be used for the calculation and representation of Maximally Stable Extremal Regions in real-time video. In contrast to the standard MSER algorithm, the NDSForest stores information about the extremal regions as they are formed, making it unnecessary to regrow the regions from seed pixels. Using the NDSForest structure, we describe a system that uses MSERs in an automobile for face registration, segmentation, and pose estimation of the driver.

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Data structures and algorithms for disjoint set union problems

Cited by 142 publications

References 54 publications

Paircoding: Improving File Sharing Using Sparse Network Codes

Paircoding: Improving File Sharing Using Sparse Network Codes

Quasi-Linear-Time Algorithms by Generalisation of Union-Find in CHR

N-tree Disjoint-Set Forests for Maximally Stable Extremal Regions

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