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A Randomized LinearTime Algorithm to Find Minimum Spanning Trees
, 1994
"... We present a randomized lineartime algorithm to find a minimum spanning tree in a connected graph with edge weights. The algorithm uses random sampling in combination with a recently discovered lineartime algorithm for verifying a minimum spanning tree. Our computational model is a unitcost ra ..."
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Cited by 118 (6 self)
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We present a randomized lineartime algorithm to find a minimum spanning tree in a connected graph with edge weights. The algorithm uses random sampling in combination with a recently discovered lineartime algorithm for verifying a minimum spanning tree. Our computational model is a unitcost randomaccess machine with the restriction that the only operations allowed on edge weights are binary comparisons.
A LinearWork Parallel Algorithm for Finding Minimum Spanning Trees
, 1994
"... We give the first linearwork parallel algorithm for finding a minimum spanning tree. It is a randomized algorithm, and requires O(2log \Lambda n log n) expected time. It is a modification of the sequential lineartime algorithm of Klein and Tarjan. ..."
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Cited by 14 (0 self)
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We give the first linearwork parallel algorithm for finding a minimum spanning tree. It is a randomized algorithm, and requires O(2log \Lambda n log n) expected time. It is a modification of the sequential lineartime algorithm of Klein and Tarjan.
Motorcycle Graphs and Straight Skeletons
, 2002
"... We present a new algorithm to compute a motorcycle graph. It runs in O(n p n log n) time when n is the size of the input. We give a new characterization of the straight skeleton of a polygon possibly with holes. ..."
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Cited by 13 (1 self)
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We present a new algorithm to compute a motorcycle graph. It runs in O(n p n log n) time when n is the size of the input. We give a new characterization of the straight skeleton of a polygon possibly with holes.
MST Construction in O(log log n) Communication Rounds
 In Proceedings of the 15 th ACM symposium on Parallel Algorithms and Architectures (SPAA
, 2003
"... We consider a simple model for overlay networks, where all n processes are connected to all other processes, and each message contains at most O(log n) bits. For this model, we present a distributed algorithm that constructs a minimumweight spanning tree in O(log log n) communication rounds, where i ..."
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Cited by 9 (1 self)
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We consider a simple model for overlay networks, where all n processes are connected to all other processes, and each message contains at most O(log n) bits. For this model, we present a distributed algorithm that constructs a minimumweight spanning tree in O(log log n) communication rounds, where in each round any process can send a message to each other process. This result is the first to break the Ω(log n) parallel time complexity barrier with small message sizes. 1.
Tetra: Evaluation of Serial Program Performance on FineGrain Parallel Processors
 University of Wisconsin
, 1993
"... Tetra is a tool for evaluating serial program performance under the resource and control constraints of finegrain parallel processors. Tetra's primary advantage to the architect is its ability to quickly generate performance metrics for yet to be designed architectures. All the user needs to s ..."
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Cited by 6 (0 self)
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Tetra is a tool for evaluating serial program performance under the resource and control constraints of finegrain parallel processors. Tetra's primary advantage to the architect is its ability to quickly generate performance metrics for yet to be designed architectures. All the user needs to specify is the capabilities of the architecture (e.g., number of functional units, issue model, etc.), rather than its implementation. Tetra first extracts a canonical form of the program from a serial instruction trace. It then applies control and resource constraint scheduling to produce an execution graph. The control and resource constraint scheduling is directed by a processor model specification supplied to the program. Once scheduled, Tetra provides a number of ways to analyze the program's performance under the specified processor model. These include parallelism profiles, storage demand profiles, data sharing distributions, data lifetime analysis, and control distance (branch, loop, and ...
Combinatorial Optimization: Mutual Relations among Graph Algorithms
 WSEAS Transactions on Mathematics
, 2008
"... Abstract: The Theory of Graphs is a wonderful, practical discipline. Informatics has played a big part in its development, and these two fields are strongly interconnected. This can, perhaps, mainly be seen in the design of computer algorithms. On the one hand, there are many methods which can be u ..."
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Cited by 3 (1 self)
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Abstract: The Theory of Graphs is a wonderful, practical discipline. Informatics has played a big part in its development, and these two fields are strongly interconnected. This can, perhaps, mainly be seen in the design of computer algorithms. On the one hand, there are many methods which can be used for solving the same problem, while on the other hand, using effective modifications of one algorithm, we can devise methods of solving various other tasks. To educate students in the area close connected with Graph Theory and Computer Science, called as Combinatorial or Discrete Optimization, it is important to make them familiar with certain algorithms in contexts to be able to get deeper into each problem and entirely understand it. In the paper we present just a few ideas that have proved successful in teaching and learning this quite young part of mathematics.
Improved Symmetric Lists
, 2004
"... We introduce a new data structure called symlist based on an idea of Tarjan [17]. A symlist is a doubly linked list without any directional information encoded into its cells. In a symlist the two pointers in each cell have no fixed meaning like previous or next in standard lists. ..."
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Cited by 2 (2 self)
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We introduce a new data structure called symlist based on an idea of Tarjan [17]. A symlist is a doubly linked list without any directional information encoded into its cells. In a symlist the two pointers in each cell have no fixed meaning like previous or next in standard lists.
Improved Distributed Steiner Forest Construction Extended Abstract
"... We present new distributed algorithms for constructing a Steiner Forest in the congest model. Our deterministic algorithm finds, for any given constant ε> 0, a (2 + ε)approximation in Õ(sk +√min {st, n}) rounds, where s is the shortest path diameter, t is the number of terminals, k is the numbe ..."
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We present new distributed algorithms for constructing a Steiner Forest in the congest model. Our deterministic algorithm finds, for any given constant ε> 0, a (2 + ε)approximation in Õ(sk +√min {st, n}) rounds, where s is the shortest path diameter, t is the number of terminals, k is the number of terminal components in the input, and n is the number of nodes. Our randomized algorithm finds, with high probability, an O(logn)approximation in time Õ(k + min {s,√n} + D), where D is the unweighted diameter of the network. We also prove a matching lower bound of Ω̃(k+min {s,√n}+D) on the running time of any distributed approximation algorithm for the Steiner Forest problem. Previous algorithms were randomized, and obtained either an O(logn)approximation in Õ(sk) time, or an O(1/ε)approximation in Õ((√n+ t)1+ε +D) time. 1.