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44
Scheduling Algorithms for Multihop Radio Networks
 IEEE/ACM Transactions on Networking
, 1993
"... Abstructqew algorithms for transmission scheduling in multihop broadcast radio networks are presented. Both link scheduling and broadcast scheduling are considered. In each instance, scheduling algorithms are given that improve upon existing algorithms both theoretically and experimentally. Theore ..."
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Cited by 173 (1 self)
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Abstructqew algorithms for transmission scheduling in multihop broadcast radio networks are presented. Both link scheduling and broadcast scheduling are considered. In each instance, scheduling algorithms are given that improve upon existing algorithms both theoretically and experimentally. Theoretically, it is shown that tree networks can be scheduled optimally, and that arbitrary networks can be scheduled so that the schedule is bounded by a length that is proportional to a function of the network thickness times the optimum. Previous algorithms could guarantee only that the schedules were bounded by a length no worse than the maximum node degree times optimum. Since the thickness is typically several orders of magnitude less than the maximum node degree, the algorithms presented here represent a considerable theoretical improvement. Experimentally, a realistic model of a radio network is given and the performance of the new algorithms is studied. These results show that, for both types of scheduling, the new algorithms (experimentally) perform consistently better than earlier methods.
Implicit Representation of Graphs
 SIAM Journal On Discrete Mathematics
, 1992
"... How to represent a graph in memory is a fundamental data structuring question. In the usual representations of an nvertex graph, the names of the vertices (i.e. integers from 1 to n) betray nothing about the graph itself. Indeed, the names (or labels) on the n vertices are just log n bit place h ..."
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Cited by 71 (0 self)
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How to represent a graph in memory is a fundamental data structuring question. In the usual representations of an nvertex graph, the names of the vertices (i.e. integers from 1 to n) betray nothing about the graph itself. Indeed, the names (or labels) on the n vertices are just log n bit place holders to allow data on the edges to encode the structure of the graph. In our scenario, there is no such waste. By assigning O(log n) bit labels to the vertices, we completely encode the structure of the graph, so that given the labels of two vertices we can test if they are adjacent in time linear in the size of the labels. Furthermore, given an arbitrary original labeling of the vertices, we can find structure coding labels (as above) that are no more than a small constant factor larger than the original labels. These notions are intimately related to vertex induced universal graphs of polynomial size. For example, we can label planar graphs with structure coding labels of size ! 4 log n, which implies the existence of a graph with n 4 vertices that contains all nvertex planar graphs as vertex induced subgraphs.
Planar Orientations with Low OutDegree and Compaction of Adjacency Matrices
 Theoretical Computer Science
, 1991
"... We consider the problem of orienting the edges of a planar graph in such a way that the outdegree of each vertex is minimized. If, for each vertex v, the outdegree is at most d, then we say that such an orientation is dbounded. We prove the following results: ffl Each planar graph has a 5bounde ..."
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Cited by 33 (4 self)
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We consider the problem of orienting the edges of a planar graph in such a way that the outdegree of each vertex is minimized. If, for each vertex v, the outdegree is at most d, then we say that such an orientation is dbounded. We prove the following results: ffl Each planar graph has a 5bounded acyclic orientation, which can be constructed in linear time. ffl Each planar graph has a 3bounded orientation, which can be constructed in linear time. ffl A 6bounded acyclic orientation, and a 3bounded orientation, of each planar graph can each be constructed in parallel time O(log n log n) on an EREW PRAM, using O(n= log n log n) processors. As an application of these results, we present a data structure such that each entry in the adjacency matrix of a planar graph can be looked up in constant time. The data structure uses linear storage, and can be constructed in linear time. Department of Mathematics and Computer Science, University of California, Riverside, CA 92521. On...
A BranchandCut Algorithm for Capacitated Network Design Problems
 MATHEMATICAL PROGRAMMING
, 1998
"... We present a branchandcut algorithm to solve capacitated network design problems. Given a capacitated network and pointtopoint traffic demands, the objective is to install more capacity on the edges of the network and route traffic simultaneously, so that the overall cost is minimized. We study ..."
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Cited by 30 (2 self)
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We present a branchandcut algorithm to solve capacitated network design problems. Given a capacitated network and pointtopoint traffic demands, the objective is to install more capacity on the edges of the network and route traffic simultaneously, so that the overall cost is minimized. We study a mixedinteger programming formulation of the problem and identify some new facet defining inequalities. These inequalities, together with other known combinatorial and mixedinteger rounding inequalities, are used as cutting planes. To choose the branching variable, we use a new rule called "knapsack branching". We also report on our computational experience using reallife data.
Arboricity and Bipartite Subgraph Listing Algorithms
, 1994
"... In graphs of bounded arboricity, the total complexity of all maximal complete bipartite subgraphs is O(n). We describe a linear time algorithm to list such subgraphs. The arboricity bound is necessary: for any constant k and any n there exists an nvertex graph with O(n) edges and (n/ log n) k ..."
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Cited by 29 (2 self)
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In graphs of bounded arboricity, the total complexity of all maximal complete bipartite subgraphs is O(n). We describe a linear time algorithm to list such subgraphs. The arboricity bound is necessary: for any constant k and any n there exists an nvertex graph with O(n) edges and (n/ log n) k maximal complete bipartite subgraphs K k,# . # Work supported in part by NSF grant CCR9258355. 1 Introduction A number of graph algorithms depend on finding all subgraphs of a certain type in a larger graph. For instance, in interval or chordal graphs, a decomposition into maximal cliques is key; such a decomposition can be constructed in linear time [4, 17]. Optimal triangulation construction [3] and certain planar graph computations [8] require a listing of all triangles. Related subgraph isomorphism problems also occur in a wide variety of practical applications [2, 5, 12, 9, 13, 14, 19]. For planar graphs, or more generally for graphs of bounded arboricity, the problem of listing c...
The Cycle Space of an Infinite Graph
 COMB., PROBAB. COMPUT
, 2004
"... Finite graph homology may seem trivial, but for infinite graphs things become interesting. We present a new approach that builds the cycle space of a graph not on its finite cycles but on its topological circles, the homeomorphic images of the unit circle in the space formed by the graph togethe ..."
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Cited by 26 (9 self)
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Finite graph homology may seem trivial, but for infinite graphs things become interesting. We present a new approach that builds the cycle space of a graph not on its finite cycles but on its topological circles, the homeomorphic images of the unit circle in the space formed by the graph together with its ends. Our approach
Fully Dynamic Output Bounded Single Source Shortest Path Problem (Extended Abstract)
 In ACMSIAM Symposium on Discrete Algorithms
"... ) Abstract We consider the problem of maintaining the distances and the shortest paths from a single source in either a directed or an undirected graph with positive real edge weights, handling insertions, deletions and cost updates of edges. We propose fully dynamic algorithms with optimal space ..."
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Cited by 24 (4 self)
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) Abstract We consider the problem of maintaining the distances and the shortest paths from a single source in either a directed or an undirected graph with positive real edge weights, handling insertions, deletions and cost updates of edges. We propose fully dynamic algorithms with optimal space requirements and query time. The cost of update operations depends on the class of the considered graph and on the number of vertices that, due to an edge modification, either change their distance from the source or change their parent in the shortest path tree. In the case of graphs with bounded genus (including planar graphs), bounded degree graphs, bounded treewidth graphs and finearplanar graphs with bounded fi, the update procedures require O(log n) amortized time per vertex update, while for general graphs with n vertices and m edges they require O( p m log n) amortized time per vertex update. The solution is based on a dynamization of Dijkstra's algorithm [6] and requires simple ...
Compact Routing for Graphs Excluding a Fixed Minor (Extended Abstract)
, 2005
"... This paper concerns compact routing schemes with arbitrary node names. We present a compact nameindependent routing scheme for unweighted networks with n nodes excluding a fixed minor. For any fixed minor, the scheme, constructible in polynomial time, has constant stretch factor and requires routin ..."
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Cited by 20 (10 self)
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This paper concerns compact routing schemes with arbitrary node names. We present a compact nameindependent routing scheme for unweighted networks with n nodes excluding a fixed minor. For any fixed minor, the scheme, constructible in polynomial time, has constant stretch factor and requires routing tables with polylogarithmic number of bits at each node. For shortestpath labeled routing scheme in planar graphs, we prove an Ω(n ɛ) space lower bound for some constant ɛ>0. This lower bound holds even for bounded degree triangulations, and is optimal for polynomially weighted planar graphs (ɛ =1/2).
On Achieving Optimized Capacity Utilization in Application Overlay Networks with Multiple Competing Sessions
 Sessions, 16th annual ACM symposium on parallelism in algorithms and architectures (SPAA ’04
, 2004
"... In this paper, we examine the problem of largevolume data dissemination via overlay networks. A natural way to maximize the throughput of an overlay multicast session is to split the traffic and feed them into multiple trees. While in singletree solutions, bandwidth of leaf nodes may remain larg ..."
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Cited by 18 (3 self)
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In this paper, we examine the problem of largevolume data dissemination via overlay networks. A natural way to maximize the throughput of an overlay multicast session is to split the traffic and feed them into multiple trees. While in singletree solutions, bandwidth of leaf nodes may remain largely underutilized, multitree solutions increase the chances for a node to contribute its bandwidth by being a relaying node in at least one of the trees. We study the following problems: (1) What is the maximum capacity multitree solutions can exploit from overlay networks? (2) When multiple sessions compete within the same network, what is the relationship of two contradictory goals: achieving fairness and maximizing overall throughput? (3) What is the impact of IP routing in achieving at constraining the optimal performance of overlay multicast? We extend the multicommodity flow model to the case of overlay data dissemination, where each commodity is associated with an overlay session, rather than the traditional sourcedestination pair. We first prove that the problem is solvable in polynomial time, then propose an #approximation algorithm, assuming that each commodity can be split in arbitrary ways. The solution to this problem establishes the theoretical upper bound of overall throughput that any multitree solution could reach. We then study the same problem with the restriction that each commodity can only be split and fed into a limited number of trees. A randomized rounding algorithm and an online treeconstruction algorithm are presented. All these algorithms are evaluated by extensive simulations.