Results 1  10
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15
Wireless scheduling with power control
 In Proc. 17th European Symposium on Algorithms (ESA
, 2009
"... We consider the scheduling of arbitrary wireless links in the physical model of interference to minimize the time for satisfying all requests. We study here the combined problem of scheduling and power control, where we seek both an assignment of power settings and a partition of the links so that e ..."
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Cited by 44 (3 self)
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We consider the scheduling of arbitrary wireless links in the physical model of interference to minimize the time for satisfying all requests. We study here the combined problem of scheduling and power control, where we seek both an assignment of power settings and a partition of the links so that each set satisfies the signaltointerferenceplusnoise (SINR) constraints. We give an algorithm that attains an approximation ratio of O(log n · log log Λ), where Λ is the ratio between the longest and the shortest linklength. Under the natural assumption that lengths are represented in binary, this gives the first polylog(n)approximation. The algorithm has the desirable property of using an oblivious power assignment, where the power assigned to a sender depends only on the length of the link. We show this dependence on Λ to be unavoidable, giving a construction for which any oblivious power assignment results in a Ω(log log Λ)approximation. We also give a simple online algorithm that yields a O(log Λ)approximation, by a reduction to the coloring of unitdisc graphs. In addition, we obtain improved approximation for a bidirectional variant of the scheduling problem, give partial answers to questions about the utility of graphs for modeling physical interference, and generalize the setting from the standard 2dimensional Euclidean plane to doubling metrics. 1
Approximation algorithms for secondary spectrum auctions
 In Proc. 23rd Symp. Parallelism in Algorithms and Architectures (SPAA
, 2011
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Secondary spectrum auctions for symmetric and submodular bidders
 In Proc. 13th Conf. Electronic Commerce (EC
, 2012
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How well can PrimalDual and LocalRatio algorithms perform?
, 2007
"... We define an algorithmic paradigm, the stack model, that captures many primaldual and localratio algorithms for approximating covering and packing problems. The stack model is defined syntactically and without any complexity limitations and hence our approximation bounds are independent of the P v ..."
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Cited by 12 (4 self)
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We define an algorithmic paradigm, the stack model, that captures many primaldual and localratio algorithms for approximating covering and packing problems. The stack model is defined syntactically and without any complexity limitations and hence our approximation bounds are independent of the P vs NP question. We provide tools to bound the performance of primal dual and local ratio algorithms and supply a (log n + 1)/2 inapproximability result for set cover, a 4/3 inapproximability for min steiner tree, and a 0.913 inapproximability for interval scheduling on two machines.
The Power of NonUniform Wireless Power
, 2012
"... We study a fundamental measure for wireless interference in the SINR model when power control is available. This measure characterizes the effectiveness of using oblivious power — when the power used by a transmitter only depends on the distance to the receiver — as a mechanism for improving wireles ..."
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Cited by 7 (0 self)
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We study a fundamental measure for wireless interference in the SINR model when power control is available. This measure characterizes the effectiveness of using oblivious power — when the power used by a transmitter only depends on the distance to the receiver — as a mechanism for improving wireless capacity. We prove optimal bounds for this measure, implying a number of algorithmic applications. An algorithm is provided that achieves — due to existing lower bounds — capacity that is asymptotically best possible using oblivious power assignments. Improved approximation algorithms are provided for a number of problems for oblivious power and for power control, including distributed scheduling, secondary spectrum auctions, wireless connectivity, and dynamic packet scheduling.
On TreeConstrained Matchings and Generalizations
, 2011
"... We consider the following TreeConstrained Bipartite Matching problem: Given two rooted trees T1 = (V1, E1), T2 = (V2, E2) and a weight function w: V1 × V2 ↦ → R+, find a maximum weight matching M between nodes of the two trees, such that none of the matched nodes is an ancestor of another matched ..."
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Cited by 5 (2 self)
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We consider the following TreeConstrained Bipartite Matching problem: Given two rooted trees T1 = (V1, E1), T2 = (V2, E2) and a weight function w: V1 × V2 ↦ → R+, find a maximum weight matching M between nodes of the two trees, such that none of the matched nodes is an ancestor of another matched node in either of the trees. This generalization of the classical bipartite matching problem appears, for example, in the computational analysis of live cell video data. We show that the problem is APXhard and thus, unless P = N P, disprove a previous claim that it is solvable in polynomial time. Furthermore, we give a 2approximation algorithm based on a combination of the local ratio technique and a careful use of the structure of basic feasible solutions of a natural LPrelaxation, which we also show to have an integrality gap of 2 − o(1). In the second part of the paper, we consider a natural generalization of the problem, where trees are replaced by partially ordered sets (posets). We show that the local ratio technique gives a 2kρapproximation for the kdimensional matching generalization of the problem, in which the maximum number of incomparable elements below (or above) any given element in each poset is bounded by ρ. We finally give an almost matching integrality gap example, and an inapproximability result showing that the dependence on ρ is most likely unavoidable.
Densest kSubgraph Approximation on Intersection Graphs
"... Abstract. We study approximation solutions for the densest ksubgraph problem (DSk) on several classes of intersection graphs. We adopt the concept of σquasi elimination orders, introduced by Akcoglu et al. [1], generalizing the perfect elimination orders for chordal graphs, and develop a simple O ..."
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Cited by 4 (0 self)
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Abstract. We study approximation solutions for the densest ksubgraph problem (DSk) on several classes of intersection graphs. We adopt the concept of σquasi elimination orders, introduced by Akcoglu et al. [1], generalizing the perfect elimination orders for chordal graphs, and develop a simple O(σ)approximation technique for graphs admitting such a vertex order. This concept allows us to derive constant factor approximation algorithms for DSk on many intersection graph classes, such as chordal graphs, circulararc graphs, clawfree graphs, line graphs of ℓhypergraphs, disk graphs, and the intersection graphs of fat geometric objects. We also present a PTAS for DSk on unit disk graphs using the shifting technique. 1
Online independent set beyond the worstcase: Secretaries, prophets and periods
 In Proc. 41st Intl. Coll. Automata, Languages and Programming (ICALP
, 2014
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On Sum Coloring and Sum MultiColoring for Restricted Families of Graphs
"... We consider the sum coloring (chromatic sum) and sum multicoloring problems for restricted families of graphs. In particular, we consider the graph classes of proper intersection graphs of axisparallel rectangles, proper interval graphs, and unit disk graphs. All the above mentioned graph classes ..."
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We consider the sum coloring (chromatic sum) and sum multicoloring problems for restricted families of graphs. In particular, we consider the graph classes of proper intersection graphs of axisparallel rectangles, proper interval graphs, and unit disk graphs. All the above mentioned graph classes belong to a more general graph class of (k + 1)clawfree graphs (respectively, for k = 4,2, 5). We prove that sum coloring is NPhard for penny graphs and unit square graphs which implies NPhardness for unit disk graphs and proper intersection graphs of axisparallel rectangles. We show a 2approximation algorithm for unit square graphs, with the assumption that the geometric representation of the graph is given. For sum multicoloring, we confirm that the greedy firstfit coloring, after ordering vertices by their demands, achieves a kapproximation for the preemptive version of sum multicoloring on (k + 1)clawfree graphs. Finally, we study priority algorithms as a model for greedy algorithms for the sum coloring and sum multicoloring problems. We show various inapproximation results under several natural input representations.
Distributed Algorithms for Coloring Interval Graphs?
"... Abstract. We explore the question how well we can color graphs in distributed models, especially in graph classes for which ∆+ 1colorings provide no approximation guarantees. We particularly focus on interval graphs. In the LOCAL model, we give an algorithm that computes a constant factor approxima ..."
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Abstract. We explore the question how well we can color graphs in distributed models, especially in graph classes for which ∆+ 1colorings provide no approximation guarantees. We particularly focus on interval graphs. In the LOCAL model, we give an algorithm that computes a constant factor approximation to the coloring problem on interval graphs in O(log ∗ n) rounds, which is best possible. The result holds also for the CONGEST model when the representation of the nodes as intervals is given. We then consider restricted beep models, where communication is restricted to the aggregate acknowledgment of whether a node’s attempted coloring succeeds. We apply an algorithm designed for the SINR model and give a simplified proof of a O(logn)approximation. We show a nearly matching Ω(logn / log logn)approximation lower bound in that model. 1