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34
A clientdriven approach for channel management in wireless LANs
 In IEEE Infocom
, 2006
"... Abstract — We propose an efficient clientbased approach for channel management (channel assignment and load balancing) in 802.11based WLANs that lead to better usage of the wireless spectrum. This approach is based on a “conflict set coloring ” formulation that jointly performs load balancing alon ..."
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Cited by 58 (3 self)
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Abstract — We propose an efficient clientbased approach for channel management (channel assignment and load balancing) in 802.11based WLANs that lead to better usage of the wireless spectrum. This approach is based on a “conflict set coloring ” formulation that jointly performs load balancing along with channel assignment. Such a formulation has a number of advantages. First, it explicitly captures interference effects at clients. Next, it intrinsically exposes opportunities for better channel reuse. Finally, algorithms based on this formulation do not depend on specific physical RF models and hence can be applied efficiently to a widerange of inbuilding as well as outdoor scenarios. We have performed extensive packetlevel simulations and measurements on a deployed wireless testbed of 70 APs to validate the performance of our proposed algorithms. We show that in addition to single network scenarios, the conflict set coloring formulation is well suited for channel assignment where multiple wireless networks share and contend for spectrum in the same physical space. Our results over a wide range of both simulated topologies and inbuilding testbed experiments indicate that our approach improves application level performance at the clients by upto three times (and atleast 50%) in comparison to current bestknown techniques. I.
On ConflictFree Coloring of Points and Simple Regions in the Plane
"... In this paper, we study coloring problems related to frequency assignment problems in cellular networks. In abstract setting, the problems are of the following two types: CFcoloring of regions: Given a finite family of n regions of some fixed type (such as discs, pseudodiscs, axisparallel rec ..."
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Cited by 37 (8 self)
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In this paper, we study coloring problems related to frequency assignment problems in cellular networks. In abstract setting, the problems are of the following two types: CFcoloring of regions: Given a finite family of n regions of some fixed type (such as discs, pseudodiscs, axisparallel rectangles, etc.), what is the minimum integer k, such that one can assign a color to each region of using a total of at most k colors, such that the resulting coloring has the following property: For each point p b#S b there is at least one region b # S that contains p in its interior, whose color is unique among all regions in that contain p in their interior (in this case we say that p is being `served' by that color). We refer to such a coloring as a conflictfree coloring of (CFcoloring in short).
Coverage preserving redundancy elimination in sensor networks
 in Proceedings of IEEE International Conference on Sensor and Ad hoc Communications and Networks (SECON’04
, 2004
"... Abstract — In this paper we study the problem of detecting and eliminating redundancy in a sensor network with a view to improving energy efficiency, while preserving the network’s coverage. We also examine the impact of redundancy elimination on the related problem of coverageboundary detection. W ..."
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Cited by 14 (1 self)
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Abstract — In this paper we study the problem of detecting and eliminating redundancy in a sensor network with a view to improving energy efficiency, while preserving the network’s coverage. We also examine the impact of redundancy elimination on the related problem of coverageboundary detection. We reduce both problems to the computation of Voronoi diagrams, prove and achieve lower bounds on the solution of these problems, and present efficient distributed algorithms for computing and maintaining solutions in cases of sensor failures or insertion of new sensors. We prove the correctness and termination properties of our distributed algorithms, and analytically characterize the time complexity and the traffic generated by our algorithms. Our simulations show that the traffic generated per sensor insertion or removal (failure) experiences a dramatic decrease with increase in sensor density, (up to 300 % when the number of sensors deployed in the same 1000 × 1000m 2 area increases from 150 to 800), and with increase in radio transmission range (up to 200 % when the sensor’s transmission range increases from 70m to 200m). I.
Monadic Secondorder Logic for Parameterized Verification
 in: Proc. 19th Symp. on Parallelism in Algorithms and Architectures (SPAA
, 1994
"... Given a set of points P ⊆ R 2, a conflictfree coloring of P is an assignment of colors to points of P, such that each nonempty axisparallel rectangle T in the plane contains a point whose color is distinct from all other points in P ∩ T. This notion has been the subject of recent interest, and is ..."
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Cited by 13 (0 self)
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Given a set of points P ⊆ R 2, a conflictfree coloring of P is an assignment of colors to points of P, such that each nonempty axisparallel rectangle T in the plane contains a point whose color is distinct from all other points in P ∩ T. This notion has been the subject of recent interest, and is motivated by frequency assignment in wireless cellular networks: one naturally would like to minimize the number of frequencies (colors) assigned to bases stations (points), such that within any range (for instance, rectangle), there is no interference. We show that any set of n points in R 2 can be conflictfree colored with Õ(n.382+ɛ) colors in expected polynomial time, for any arbitrarily small ɛ> 0. This improves upon the previously known bound of O ( p n log log n/log n).
Conflictfree colorings of shallow discs
 In Proc. 22nd Annual ACM Symposium on Computational Geometry (SoCG
, 2006
"... We prove that any collection of n discs in which each one intersects at most k others, can be colored with at most O(log 3 k) colors so that for each point p in the union of all discs there is at least one disc in the collection containing p whose color differs from that of all other members of the ..."
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Cited by 12 (3 self)
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We prove that any collection of n discs in which each one intersects at most k others, can be colored with at most O(log 3 k) colors so that for each point p in the union of all discs there is at least one disc in the collection containing p whose color differs from that of all other members of the collection that contain p. This is motivated by a problem on frequency assignments in cellular networks, and improves the best previously known upper bound of O(log n) when k is much smaller than n. 1
ConflictFree Coloring for Intervals: from Offline to Online (Extended Abstract)
, 2006
"... This paper studies deterministic algorithms for a frequency assignment problem in cellular networks. A cellular network consists of fixedposition base stations and moving agents. Each base station operates at a fixed frequency, and this allows an agent tuned at this frequency to communicate with th ..."
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Cited by 11 (5 self)
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This paper studies deterministic algorithms for a frequency assignment problem in cellular networks. A cellular network consists of fixedposition base stations and moving agents. Each base station operates at a fixed frequency, and this allows an agent tuned at this frequency to communicate with the base station. Each agent has a specific range of communication (described as a geometric shape, e.g., a disc) that may contain one or several base stations. To avoid interference, the goal is to assign frequencies to base stations such that for any range, there exists a base station in the range with a frequency that is not reused by some other base station in the range. The base station with this unique (in the range) frequency serves the aforementioned range. Since using many frequencies is expensive, the optimization goal is to use as few frequencies as possible. The problem can be modeled as a special coloring problem for hypergraphs. Base stations are the vertices, ranges are the hyperedges, and colors (frequencies) must be assigned to vertices following the conflictfree property: In every hyperedge there is a color that occurs exactly once. We concentrate on the special case where the n base stations lie on the real line and ranges are the n(n + 1)/2 nonempty subsets of consecutive points. This problem is called conflictfree coloring for intervals. We introduce a hierarchy of four models for the above problem: (i) the static model, where the complete hypergraph is given and all vertices are colored simultaneously, (ii) the dynamic offline model, where the vertices appear in some order and the conflictfree prop
How to play a coloring game against a colorblind adversary
 In Proc. 22nd Annual ACM Symposium on Computational Geometry (SoCG 2006
, 2006
"... We study the problem of conflictfree (CF) coloring of a set of points in the plane, in an online fashion, with respect to halfplanes, nearlyequal axisparallel rectangles, and congruent disks. As a warmup exercise, the online CF coloring of points on the line with respect to intervals is also con ..."
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Cited by 11 (3 self)
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We study the problem of conflictfree (CF) coloring of a set of points in the plane, in an online fashion, with respect to halfplanes, nearlyequal axisparallel rectangles, and congruent disks. As a warmup exercise, the online CF coloring of points on the line with respect to intervals is also considered. We present randomized algorithms in the oblivious adversary model, where the adversary does not see the colors used. For the problems considered, the algorithms always produce valid CF colorings, and use O(log n) colors with high probability (these bounds are optimal in the worst case). Our randomized online algorithms are considerably simpler than previous algorithms for this problem and use fewer colors. We also present a deterministic algorithm for the CF coloring of points in the plane with respect to nearlyequal axisparallel rectangles, using O(polylog(n)) colors. This is the first efficient deterministic online CF coloring algorithm for this problem. 1
ConflictFree Colorings of Rectangles Ranges
 In Proc. 23rd International Symposium on Theoretical Aspects of Computer Science (STACS 2006
, 2006
"... Abstract. Given the range space (P, R), where P is a set of n points in IR 2 and R is the family of subsets of P induced by all axisparallel rectangles, the conflictfree coloring problem asks for a coloring of P with the minimum number of colors such that (P, R) is conflictfree. We study the foll ..."
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Cited by 11 (1 self)
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Abstract. Given the range space (P, R), where P is a set of n points in IR 2 and R is the family of subsets of P induced by all axisparallel rectangles, the conflictfree coloring problem asks for a coloring of P with the minimum number of colors such that (P, R) is conflictfree. We study the following question: Given P, is it possible to add a small set of points Q such that (P ∪ Q, R) can be colored with fewer colors than (P, R)? Our main result is the following: given P, and any ǫ ≥ 0, one can always add a set Q of O(n 1−ǫ) points such that P ∪ Q can be conflictfree colored using Õ(n3 8 (1+ǫ) ) 1 colors. Moreover, the set Q and the conflictfree coloring can be computed in polynomial time, with high probability. Our result is obtained by introducing a general probabilistic recoloring technique, which we call quasiconflictfree coloring, and which may be of independent interest. A further application of this technique is also given. 1
Online conflictfree coloring for intervals
 SIAM Journal on Computing
, 2006
"... Abstract. We consider an online version of the conflictfree coloring of a set of points on the line, where each newly inserted point must be assigned a color upon insertion, and at all times the coloring has to be conflictfree, in the sense that in every interval I there is a color that appears ex ..."
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Cited by 11 (6 self)
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Abstract. We consider an online version of the conflictfree coloring of a set of points on the line, where each newly inserted point must be assigned a color upon insertion, and at all times the coloring has to be conflictfree, in the sense that in every interval I there is a color that appears exactly once in I. We present deterministic and randomized algorithms for achieving this goal, and analyze their performance, that is, the maximum number of colors that they need to use, as a function of the number n of inserted points. We first show that a natural and simple (deterministic) approach may perform rather poorly, requiring Ω ( √ n) colors in the worst case. We then derive two efficient variants of this simple algorithm. The first is deterministic and uses O(log 2 n) colors, and the second is randomized and uses O(log n) colors with high probability. We also show that the O(log 2 n) bound on the number of colors used by our deterministic algorithm is tight on the worst case. We also analyze the performance of the simplest proposed algorithm when the points are inserted in a random order, and present an incomplete analysis that indicates that, with high probability, it uses only O(log n) colors. Finally, we show that in the extension of this problem to two dimensions, where the relevant ranges are disks, n colors may be required in the worst case.
Online Conflictfree Colorings for Hypergraphs
, 2007
"... We provide a framework for online conflictfree coloring (CFcoloring) of any hypergraph. We use this framework to obtain an efficient randomized online algorithm for CFcoloring any kdegenerate hypergraph. Our algorithm uses O(k log n) colors with high probability and this bound is asymptotically ..."
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Cited by 8 (3 self)
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We provide a framework for online conflictfree coloring (CFcoloring) of any hypergraph. We use this framework to obtain an efficient randomized online algorithm for CFcoloring any kdegenerate hypergraph. Our algorithm uses O(k log n) colors with high probability and this bound is asymptotically optimal for any constant k. Moreover, our algorithm uses O(k log k log n) random bits with high probability. As a corollary, we obtain asymptotically optimal randomized algorithms for online CFcoloring some hypergraphs that arise in geometry. Our algorithm uses exponentially fewer random bits compared to previous results. We introduce deterministic online CFcoloring algorithms for points on the line with respect to intervals and for points on the plane with respect to halfplanes (or unit discs) that use Θ(log n) colors and recolor O(n) points in total.