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37
Colouring Paths in Directed Symmetric Trees with Applications to WDM Routing
, 1997
"... . Let T be a symmetric directed tree, i.e., an undirected tree with each edge viewed as two opposite arcs. We prove that the minimum number of colours needed to colour the set of all directed paths in T , so that no two paths of the same colour use the same arc of T , is equal to the maximum number ..."
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Cited by 16 (1 self)
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. Let T be a symmetric directed tree, i.e., an undirected tree with each edge viewed as two opposite arcs. We prove that the minimum number of colours needed to colour the set of all directed paths in T , so that no two paths of the same colour use the same arc of T , is equal to the maximum number
Colouring Directed Paths in Symmetric Trees, with an Application to Optical Networks
 IN PROCEEDINGS OF ICALP 97
, 1997
"... Let T be a symmetric directed tree, i.e., an undirected tree with each edge viewed as two opposite arcs. We prove that the minimum number of colours needed to colour the set of all directed paths in T so that no two paths of the same colour use the same arc of T is equal to the maximum number of pat ..."
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Cited by 1 (1 self)
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Let T be a symmetric directed tree, i.e., an undirected tree with each edge viewed as two opposite arcs. We prove that the minimum number of colours needed to colour the set of all directed paths in T so that no two paths of the same colour use the same arc of T is equal to the maximum number
Island hopping and path colouring, with applications to WDM network design
 Proc. of ACMSIAM SODA
"... Two benefits of optical communication are (a) the possibility of using a single fiber optic cable to carry multiple signals simultaneously if each signal uses light of a distinct wavelength, and (b) the decreased latency for signals that avoid expensive opticalelectricoptical (OEO) conversions. Th ..."
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Cited by 3 (1 self)
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the number of hops required when routing the demands subject to the constraint that at most c fibers are connected to each other at each node. For c = 2, we show an O(log 1−ǫ n)approximation hardness result that complements the O(log n)approximation algorithm due to Anshelevich and Zhang. For directed
The PermutationPath Coloring Problem on Trees
, 2000
"... The paper deals with the problem of routing a set of communication requests representing a permutation of the nodes of an alloptical tree shaped network employing the wavelength division multiplexing (or WDM) technology. In such networks, information between nodes is transmitted as light on fibe ..."
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in order to minimize the number of wavelengths needed to perform all communications in only one round. Such a routing problem can be modeled as a permutationpath coloring problem on trees. An instance of the permutationpath coloring problem on trees is given by a directed symmetric tree graph T on n
Protecting multicast sessions in WDM optical mesh networks
 Journal of Lightwave Technology
, 2003
"... Abstract—Recent advances in wavelengthdivisionmultiplexing (WDM) technology are expected to facilitate bandwidthintensive multicast applications. However, a single fiber (bundle) cut on such a network can disrupt the transmission of information to several destination nodes on a “light tree”based ..."
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Cited by 17 (2 self)
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Abstract—Recent advances in wavelengthdivisionmultiplexing (WDM) technology are expected to facilitate bandwidthintensive multicast applications. However, a single fiber (bundle) cut on such a network can disrupt the transmission of information to several destination nodes on a “light tree
Efficient Bandwidth Allocation in Directed Optical Fibre Trees
"... We present improved bounds for efficient bandwidth allocation in a WDM optical network whose topology is that of a directed tree of fibreoptic links. The problem of bandwidth allocation is modelled as a colouring problem, where each path in a set of communication paths must be assigned a colour (re ..."
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We present improved bounds for efficient bandwidth allocation in a WDM optical network whose topology is that of a directed tree of fibreoptic links. The problem of bandwidth allocation is modelled as a colouring problem, where each path in a set of communication paths must be assigned a colour
AlltoAll Routing and Coloring in Weighted Trees of Rings
 IN PROCEEDINGS OF ELEVEN ANNUAL ACM SYMPOSIUM ON PARALLEL ALGORITHMS AND ARCHITECTURES
, 1999
"... A tree of rings is an undirected graph obtained from the union of rings, which intersect two by two in at most one node, such that any two nodes are connected by exactly two edgedisjoint paths. In this paper, we consider symmetric directed trees of rings with weighted nodes. A routing for a weighte ..."
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Cited by 7 (0 self)
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A tree of rings is an undirected graph obtained from the union of rings, which intersect two by two in at most one node, such that any two nodes are connected by exactly two edgedisjoint paths. In this paper, we consider symmetric directed trees of rings with weighted nodes. A routing for a
Limited Wavelength Conversion in AllOptical Tree Networks (Extended Abstract)
, 1998
"... Let T be a symmetric directed tree, i.e., a tree with each edge viewed as two opposite directed links. We consider the problem of routing arbitrary sets of connection requests in T . In alloptical communication tree networks with WDM (wavelengthdivision multiplexing) this is equivalent to color ..."
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Cited by 10 (3 self)
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Let T be a symmetric directed tree, i.e., a tree with each edge viewed as two opposite directed links. We consider the problem of routing arbitrary sets of connection requests in T . In alloptical communication tree networks with WDM (wavelengthdivision multiplexing) this is equivalent to color
New Techniques for Geographic Routing
, 2006
"... As wireless sensor networks continue to grow in size, we are faced with the prospect of emerging wireless networks with hundreds or thousands of nodes. Geographic routing algorithms are a promising alternative to tradition ad hoc routing algorithms in this new domain for pointtopoint routing, but ..."
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As wireless sensor networks continue to grow in size, we are faced with the prospect of emerging wireless networks with hundreds or thousands of nodes. Geographic routing algorithms are a promising alternative to tradition ad hoc routing algorithms in this new domain for pointtopoint routing
PAPER Path Coloring on Binary Caterpillars
"... SUMMARY The path coloring problem is to assign the minimum number of colors to a given set P of directed paths on a given symmetric digraph D so that no two paths sharing an arc have the same color. The problem has applications to ecient assignment of wavelengths to communications on WDM optical ne ..."
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SUMMARY The path coloring problem is to assign the minimum number of colors to a given set P of directed paths on a given symmetric digraph D so that no two paths sharing an arc have the same color. The problem has applications to ecient assignment of wavelengths to communications on WDM optical
Results 1  10
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37