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Finding Triconnected Components By Local Replacement
, 1993
"... . We present a parallel algorithm for finding triconnected components on a CRCW PRAM. The time complexity of our algorithm is O(log n) and the processortime product is O((m + n) log log n) where n is the number of vertices, and m is the number of edges of the input graph. Our algorithm, like other ..."
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Cited by 29 (6 self)
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. We present a parallel algorithm for finding triconnected components on a CRCW PRAM. The time complexity of our algorithm is O(log n) and the processortime product is O((m + n) log log n) where n is the number of vertices, and m is the number of edges of the input graph. Our algorithm, like other parallel algorithms for this problem, is based on open ear decomposition but it employs a new technique, local replacement, to improve the complexity. Only the need to use the subroutines for connected components and integer sorting, for which no optimal parallel algorithm that runs in O(log n) time is known, prevents our algorithm from achieving optimality. 1. Introduction. A connected graph G = (V; E) is kvertex connected if it has at least (k + 1) vertices and removal of any (k \Gamma 1) vertices leaves the graph connected. Designing efficient algorithms for determining the connectivity of graphs has been a subject of great interest in the last two decades. Applications of graph connect...
A Quantitative Comparison of Scheduling Algorithms for InputQueued Switches
 Computer Networks and ISDN Systems
, 1997
"... This paper quantitatively evaluates several alternative approaches to the scheduling of cells in a highbandwidth inputqueued ATM switch. In particular, we compare the performance of three algorithms described previously: FIFO queueing, parallel iterative matching (PIM), maximum matching and two new ..."
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Cited by 29 (4 self)
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This paper quantitatively evaluates several alternative approaches to the scheduling of cells in a highbandwidth inputqueued ATM switch. In particular, we compare the performance of three algorithms described previously: FIFO queueing, parallel iterative matching (PIM), maximum matching and two new algorithms: iterative roundrobin matching with slip (SLIP) and leastrecently used (LRU). For the synthetic workloads we consider, including uniform and bursty traffic, SLIP performs almost identically to the other algorithms. Cases for which PIM and SLIP perform poorly are presented, indicating that care should be taken when using these algorithms. But, we show that the implementation complexity of SLIP is an order of magnitude less than for PIM, making it feasible to implement a 32x32 switch scheduler for SLIP on a single chip. 1 Introduction The past few years has seen increasing interest in arbitrary topology cellbased local area networks, such as ATM [5]. In these networks, hosts a...
A Quantitative Comparison of Iterative Scheduling Algorithms for InputQueued Switches
 COMPUTER NETWORKS AND ISDN SYSTEMS
, 1998
"... In this paper we quantitatively evaluate three iterative algorithms for scheduling cells in a highbandwidth inputqueued ATM switch. In particular, we compare the performance of an algorithm described previously  parallel iterative matching (PIM)  with two new algorithms: iterative roundrob ..."
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Cited by 12 (0 self)
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In this paper we quantitatively evaluate three iterative algorithms for scheduling cells in a highbandwidth inputqueued ATM switch. In particular, we compare the performance of an algorithm described previously  parallel iterative matching (PIM)  with two new algorithms: iterative roundrobin matching with slip (iSLIP) and iterative leastrecently used (iLRU). We also compare each algorithm against FIFO inputqueueing and perfect outputqueueing. For the synthetic workloads we consider, including uniform and bursty traffic, iSLIP performs almost identically to the other algorithms. Cases for which PIM and iSLIP perform poorly are presented, indicating that care should be taken when using these algorithms. But, we show that the implementation complexity of iSLIP is an order of magnitude less than for PIM, making it feasible to implement a 32 x 32 switch scheduler for iSLIP on a single chip.
OutputSensitive Reporting of Disjoint Paths
, 1996
"... A kpath query on a graph consists of computing k vertexdisjoint paths between two given vertices of the graph, whenever they exist. In this paper, we study the problem of performing kpath queries, with k < 3, in a graph G with n vertices. We denote with the total length of the paths reported. For ..."
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Cited by 11 (2 self)
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A kpath query on a graph consists of computing k vertexdisjoint paths between two given vertices of the graph, whenever they exist. In this paper, we study the problem of performing kpath queries, with k < 3, in a graph G with n vertices. We denote with the total length of the paths reported. For k < 3, we present an optimal data structure for G that uses O(n) space and executes kpath queries in outputsensitive O() time. For triconnected planar graphs, our results make use of a new combinatorial structure that plays the same role as bipolar (st) orientations for biconnected planar graphs. This combinatorial structure also yields an alternative construction of convex grid drawings of triconnected planar graphs.
On Sum Coloring of Graphs
, 2000
"... The sum coloring problem asks to find a vertex coloring of a given graph G, using natural numbers, such that the total sum of the colors of vertices is minimized amongst all proper vertex colorings of G. This minimum total sum is the chromatic sum of the graph, \Sigma(G), and a coloring which achiev ..."
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Cited by 8 (0 self)
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The sum coloring problem asks to find a vertex coloring of a given graph G, using natural numbers, such that the total sum of the colors of vertices is minimized amongst all proper vertex colorings of G. This minimum total sum is the chromatic sum of the graph, \Sigma(G), and a coloring which achieves this total sum is called an optimum coloring. There are some graphs for which the optimum coloring needs more colors than indicated by the chromatic number. The minimum number of colors needed in any optimum coloring of a graph is called the strength of the graph, which we denote by s(G). Trivially (G) s(G). In this thesis we present various results about the sum coloring problem. We prove the NPHardness of finding the vertex strength for graphs with \Delta = 6 and also give some logarithmic upper bounds for the vertex strength of graphs with small chromatic number. We also prove that the sum coloring problem is NPcomplete for split graphs. Polynomial time algorithms are presented for the sum coloring of ksplit graphs, P 4 reducible graphs, chain bipartite graphs, and cobipartite graphs. We can