Distributed Nodes Organization Algorithm for Channel Access in a Multihop Dynamic Radio Network
IEEE Transactions on Computers
Computer networks
Labelling graphs with a condition at distance 2
SIAM Journal on Discrete Mathematics
Labeling Chordal Graphs: Distance Two Condition
SIAM Journal on Discrete Mathematics
Code assignment for hidden terminal interference avoidance in multihop packet radio networks
IEEE/ACM Transactions on Networking (TON)
The $L(2,1)$-Labeling Problem on Graphs
SIAM Journal on Discrete Mathematics
Assigning codes in wireless networks: bounds and scaling properties
Wireless Networks
Efficient use of radio spectrum in wireless networks with channel separation between close stations
DIALM '00 Proceedings of the 4th international workshop on Discrete algorithms and methods for mobile computing and communications
Journal of Parallel and Distributed Computing
Graph labeling and radio channel assignment
Journal of Graph Theory
Optimal Channel Assignments for Lattices with Conditions at Distance Two
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Workshop 12 - Volume 13
L(2, 1)-labeling of strong products of cycles
Information Processing Letters
New bounds for the L(h, k) number of regular grids
International Journal of Mobile Network Design and Innovation
Optimal frequency assignments of cycles and powers of cycles
International Journal of Mobile Network Design and Innovation
Graph labellings with variable weights, a survey
Discrete Applied Mathematics
L(2,1)-labeling of strong products of cycles
Information Processing Letters
Channel assignment for interference avoidance in honeycomb wireless networks
Journal of Parallel and Distributed Computing
L(h,1,1)-Labeling of outerplanar graphs
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
Generalized powers of graphs and their algorithmic use
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
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Given an integer\sigma 1 , a vector(\delta_1, \delta_2, \ldots, \delta_{\sigma-1})of nonnegative integers, and an undirected graphG=(V,E) , anL(\delta_1, \delta_2, \ldots,\delta_{\sigma-1}){\hbox{-}}\rm coloringofGis a functionffrom the vertex setVto a set of nonnegative integers such that| f(u) -f(v) | \ge \delta_i , ifd(u,v) = i, \ 1 \le i \le \sigma-1 , whered(u,v)is the distance (i.e., the minimum number of edges) between the verticesuandv . An optimalL(\delta_1, \delta_2, \ldots,\delta_{\sigma-1}){\hbox{-}}\rm coloringforGis one using the smallest range\lambdaof integers over all such colorings. This problem has relevant application in channel assignment for interference avoidance in wireless networks, where channels (i.e., colors) assigned to interfering stations (i.e., vertices) at distanceimust be at least\delta_iapart, while the same channel can be reused in vertices whose distance is at least\sigma . In particular, two versions of the coloring problem驴 L(2,1,1)andL(\delta_1, 1, \ldots,1) 驴are considered. Since these versions of the problem areNP{\hbox{-}}\rm hardfor general graphs, efficient algorithms for finding optimal colorings are provided for specific graphs modeling realistic wireless networks, including rings, bidimensional grids, and cellular grids.