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Bora Uçar - One of the best experts on this subject based on the ideXlab platform.

  • Comments on the hierarchically structured bin packing problem
    Information Processing Letters, 2015
    Co-Authors: Thomas Lambert, Loris Marchal, Bora Uçar
    Abstract:

    We study the hierarchically structured bin packing problem. In this problem, the items to be packed into bins are at the leaves of a tree. The objective of the packing is to minimize the total number of bins into which the descendants of an Internal Node are packed, summed over all Internal Nodes. We investigate an existing algorithm and make a correction to the analysis of its approximation ratio. Further results regarding the structure of an optimal solution and a strengthened inapproximability result are given.

  • Comments on the hierarchically structured bin packing problem
    Information Processing Letters, 2015
    Co-Authors: Thomas Lambert, Loris Marchal, Bora Uçar
    Abstract:

    We study the hierarchically structured bin packing problem. In this problem, the items to be packed into bins are at the leaves of a tree. The objective of the packing is to minimize the total number of bins into which the descendants of an Internal Node are packed, summed over all Internal Nodes. We investigate an existing algorithm and make a correction to the analysis of its approximation ratio. Further results regarding the structure of an optimal solution and a strengthened inapproximability result are given. No APTAS for hierarchically structured bin packing problem with non-uniform weights.A condition for a known heuristic to have 3/2 approximation guarantee.Best post-order is not always best.

Thomas Lambert - One of the best experts on this subject based on the ideXlab platform.

  • Comments on the hierarchically structured bin packing problem
    Information Processing Letters, 2015
    Co-Authors: Thomas Lambert, Loris Marchal, Bora Uçar
    Abstract:

    We study the hierarchically structured bin packing problem. In this problem, the items to be packed into bins are at the leaves of a tree. The objective of the packing is to minimize the total number of bins into which the descendants of an Internal Node are packed, summed over all Internal Nodes. We investigate an existing algorithm and make a correction to the analysis of its approximation ratio. Further results regarding the structure of an optimal solution and a strengthened inapproximability result are given.

  • Comments on the hierarchically structured bin packing problem
    Information Processing Letters, 2015
    Co-Authors: Thomas Lambert, Loris Marchal, Bora Uçar
    Abstract:

    We study the hierarchically structured bin packing problem. In this problem, the items to be packed into bins are at the leaves of a tree. The objective of the packing is to minimize the total number of bins into which the descendants of an Internal Node are packed, summed over all Internal Nodes. We investigate an existing algorithm and make a correction to the analysis of its approximation ratio. Further results regarding the structure of an optimal solution and a strengthened inapproximability result are given. No APTAS for hierarchically structured bin packing problem with non-uniform weights.A condition for a known heuristic to have 3/2 approximation guarantee.Best post-order is not always best.

Ivan Stojmenovic - One of the best experts on this subject based on the ideXlab platform.

  • Internal Node and Shortcut Based Routing with Guaranteed Delivery in Wireless Networks
    Cluster Computing, 2002
    Co-Authors: Susanta Datta, Ivan Stojmenovic, Jie Wu
    Abstract:

    Several localized position based routing algorithms for wireless networks were described recently. In greedy routing algorithm (that has close performance to the shortest path algorithm, if successful), sender or Node S currently holding the message m forwards m to one of its neighbors that is the closest to destination. The algorithm fails if S does not have any neighbor that is closer to destination than S . FACE algorithm guarantees the delivery of m if the network, modeled by unit graph, is connected. GFG algorithm combines greedy and FACE algorithms. Greedy algorithm is applied as long as possible, until delivery or a failure. In case of failure, the algorithm switches to FACE algorithm until a Node closer to destination than last failure Node is found, at which point greedy algorithm is applied again. Past traffic does not need to be memorized at Nodes. In this paper we further improve the performance of GFG algorithm, by reducing its average hop count. First we improve the FACE algorithm by adding a sooner-back procedure for earlier escape from FACE mode. Then we perform a shortcut procedure at each forwarding Node S . Node S uses the local information available to calculate as many hops as possible and forwards the packet to the last known hop directly instead of forwarding it to the next hop. The second improvement is based on the concept of dominating sets. Each Node in the network is classified as Internal or not, based on geographic position of its neighboring Nodes. The network of Internal Nodes defines a connected dominating set, i.e., and each Node must be either Internal or directly connected to an Internal Node. In addition, Internal Nodes are connected. We apply several existing definitions of Internal Nodes, namely the concepts of intermediate, inter-gateway and gateway Nodes. We propose to run GFG routing, enhanced by shortcut procedure, on the dominating set, except possibly the first and last hops. The performance of proposed algorithms is measured by comparing its average hop count with hop count of the basic GFG algorithm and the benchmark shortest path algorithm, and very significant improvements were obtained for low degree graphs. More precisely, we obtained localized routing algorithm that guarantees delivery and has very low excess in terms of hop count compared to the shortest path algorithm. The experimental data show that the length of additional path (in excess of shortest path length) can be reduced to about half of that of existing GFG algorithm.

  • Internal Node and shortcut based routing with guaranteed delivery in wireless networks
    International Conference on Distributed Computing Systems, 2001
    Co-Authors: Souptik Datta, Ivan Stojmenovic
    Abstract:

    Several distributed routing algorithms for wireless networks were described recently, based on location information of Nodes available via Global Positioning System (GPS). In a greedy routing algorithm, the sender or Node S currently holding the message m forwards m to one of its neighbors that is the closest to the destination. The algorithm fails if S does not have any neighbor that is closer to destination than S. The FACE algorithm guarantees the delivery of m if the network, modeled by unit graph, is connected. The GFG algorithm combines greedy and FACE algorithms. We further improve the performance of the GFG algorithm, by reducing its average hop count. First we improve the FACE algorithm by adding a sooner-back procedure for earlier escape from FACE mode. Then we perform a shortcut procedure at each forwarding Node S. Node S uses the local information available to calculate as many hops as possible and forwards the packet to the last known hop directly instead of forwarding it to the next hop. The second improvement is based on the concept of dominating sets. The network of Internal Nodes defines a connected dominating set, and each Node must be either Internal or directly connected to an Internal Node. We apply several existing definitions of Internal Nodes, namely the concepts of intermediate, inter-gateway and gateway Nodes. We propose to run GFG routing, enhanced by shortcut procedure, on the dominating set, except possibly the first and last hops. We obtained localized routing algorithm that guarantees delivery and has very low excess in terms of hop count compared to the shortest path algorithm. Experimental data show that the length of additional path can be reduced to about half that of existing GFG algorithm.

  • RNG and Internal Node based broadcasting algorithms for wireless one-to-one networks
    ACM SIGMOBILE Mobile Computing and Communications Review, 2001
    Co-Authors: Mahtab Seddigh, Julio Solano Gonzalez, Ivan Stojmenovic
    Abstract:

    In a multihop wireless network, each Node has a transmission radius and is able to send a message to one of its neighbors (one-to-one) or all of its neighbors (one-to-all) that are located within the radius. In a broadcasting task, a source Node needs to send the same message to all the Nodes in the network. In this paper, we propose to reduce the communication overhead of broadcasting algorithm for one-to-one model by applying the concepts of planar graphs such as RNG (relative neighborhood graphs) and connected dominating sets determined by Internal Nodes. Regular message exchanges between neighbors, which include location updates or signal strengths, suffice to maintain these structures, and they therefore do not impose additional communication overhead. In Internal Node based broadcasting, messages are forwarded on the edges that connect two Internal Nodes, and on edges that connect each non-Internal Node with its closest Internal Node. A neighbor elimination scheme is added to the Internal Node concept, to improve its performance. Similarly, only edges in a planar subgraph may be used for retransmissions. The reduction in communication overhead for broadcasting task, with respect to existing methods, is measured experimentally. The number of retransmissions is reduced to about 50% for sparse networks and to about 5% for dense networks, and the overhead with respect to ideal solution is up to 20% (for 100 Nodes).

  • ICDCS Workshops - Internal Node and shortcut based routing with guaranteed delivery in wireless networks
    Proceedings 21st International Conference on Distributed Computing Systems Workshops, 1
    Co-Authors: Souptik Datta, Ivan Stojmenovic
    Abstract:

    Several distributed routing algorithms for wireless networks were described recently, based on location information of Nodes available via Global Positioning System (GPS). In a greedy routing algorithm, the sender or Node S currently holding the message m forwards m to one of its neighbors that is the closest to the destination. The algorithm fails if S does not have any neighbor that is closer to destination than S. The FACE algorithm guarantees the delivery of m if the network, modeled by unit graph, is connected. The GFG algorithm combines greedy and FACE algorithms. We further improve the performance of the GFG algorithm, by reducing its average hop count. First we improve the FACE algorithm by adding a sooner-back procedure for earlier escape from FACE mode. Then we perform a shortcut procedure at each forwarding Node S. Node S uses the local information available to calculate as many hops as possible and forwards the packet to the last known hop directly instead of forwarding it to the next hop. The second improvement is based on the concept of dominating sets. The network of Internal Nodes defines a connected dominating set, and each Node must be either Internal or directly connected to an Internal Node. We apply several existing definitions of Internal Nodes, namely the concepts of intermediate, inter-gateway and gateway Nodes. We propose to run GFG routing, enhanced by shortcut procedure, on the dominating set, except possibly the first and last hops. We obtained localized routing algorithm that guarantees delivery and has very low excess in terms of hop count compared to the shortest path algorithm. Experimental data show that the length of additional path can be reduced to about half that of existing GFG algorithm.

  • HICSS - Internal Nodes based broadcasting in wireless networks
    Proceedings of the 34th Annual Hawaii International Conference on System Sciences, 1
    Co-Authors: Ivan Stojmenovic, Mahtab Seddigh, J. Zunic
    Abstract:

    In a multi-hop wireless network, each Node has a transmission radius and is able to send a message to one or all of its neighbors that are located within the radius. In a broadcasting task, a source Node sends the same message to all the Nodes in the network. Some existing solutions apply re-broadcasting from each cluster-head or border Node in a clustered structure. We propose to reduce the communication overhead of the broadcasting algorithm by applying the concept of Internal Nodes. The maintenance of Internal Nodes requires much less communication overhead than the maintenance of the cluster structure of the Nodes. In one-to-all broadcasting, only the Internal Nodes forward the message, while in the one-to-one case, messages are forwarded on the edges that connect two Internal Nodes and on edges that connect each non-Internal Node with its closest Internal Node. Existing notions of Internal Nodes are improved by using Node degrees instead of their IDs in Internal Node decisions. Highest Node degrees are also proposed for reducing the number of cluster-heads and border Nodes in a clustering algorithm. Further savings are obtained if GPS and the concept of planar subgraphs are used for one-to-one networks. In case of one-to-all model, no re-broadcasting is needed if all neighbors have already received the message. The important features of the proposed algorithms are their reliability, significant savings in the re-broadcasting, and their localized and parameterless behavior. The reduction in the communication overhead for the broadcasting task, with respect to existing methods, is measured experimentally.

Loris Marchal - One of the best experts on this subject based on the ideXlab platform.

  • Comments on the hierarchically structured bin packing problem
    Information Processing Letters, 2015
    Co-Authors: Thomas Lambert, Loris Marchal, Bora Uçar
    Abstract:

    We study the hierarchically structured bin packing problem. In this problem, the items to be packed into bins are at the leaves of a tree. The objective of the packing is to minimize the total number of bins into which the descendants of an Internal Node are packed, summed over all Internal Nodes. We investigate an existing algorithm and make a correction to the analysis of its approximation ratio. Further results regarding the structure of an optimal solution and a strengthened inapproximability result are given.

  • Comments on the hierarchically structured bin packing problem
    Information Processing Letters, 2015
    Co-Authors: Thomas Lambert, Loris Marchal, Bora Uçar
    Abstract:

    We study the hierarchically structured bin packing problem. In this problem, the items to be packed into bins are at the leaves of a tree. The objective of the packing is to minimize the total number of bins into which the descendants of an Internal Node are packed, summed over all Internal Nodes. We investigate an existing algorithm and make a correction to the analysis of its approximation ratio. Further results regarding the structure of an optimal solution and a strengthened inapproximability result are given. No APTAS for hierarchically structured bin packing problem with non-uniform weights.A condition for a known heuristic to have 3/2 approximation guarantee.Best post-order is not always best.

Jie Wu - One of the best experts on this subject based on the ideXlab platform.

  • Internal Node and Shortcut Based Routing with Guaranteed Delivery in Wireless Networks
    Cluster Computing, 2002
    Co-Authors: Susanta Datta, Ivan Stojmenovic, Jie Wu
    Abstract:

    Several localized position based routing algorithms for wireless networks were described recently. In greedy routing algorithm (that has close performance to the shortest path algorithm, if successful), sender or Node S currently holding the message m forwards m to one of its neighbors that is the closest to destination. The algorithm fails if S does not have any neighbor that is closer to destination than S . FACE algorithm guarantees the delivery of m if the network, modeled by unit graph, is connected. GFG algorithm combines greedy and FACE algorithms. Greedy algorithm is applied as long as possible, until delivery or a failure. In case of failure, the algorithm switches to FACE algorithm until a Node closer to destination than last failure Node is found, at which point greedy algorithm is applied again. Past traffic does not need to be memorized at Nodes. In this paper we further improve the performance of GFG algorithm, by reducing its average hop count. First we improve the FACE algorithm by adding a sooner-back procedure for earlier escape from FACE mode. Then we perform a shortcut procedure at each forwarding Node S . Node S uses the local information available to calculate as many hops as possible and forwards the packet to the last known hop directly instead of forwarding it to the next hop. The second improvement is based on the concept of dominating sets. Each Node in the network is classified as Internal or not, based on geographic position of its neighboring Nodes. The network of Internal Nodes defines a connected dominating set, i.e., and each Node must be either Internal or directly connected to an Internal Node. In addition, Internal Nodes are connected. We apply several existing definitions of Internal Nodes, namely the concepts of intermediate, inter-gateway and gateway Nodes. We propose to run GFG routing, enhanced by shortcut procedure, on the dominating set, except possibly the first and last hops. The performance of proposed algorithms is measured by comparing its average hop count with hop count of the basic GFG algorithm and the benchmark shortest path algorithm, and very significant improvements were obtained for low degree graphs. More precisely, we obtained localized routing algorithm that guarantees delivery and has very low excess in terms of hop count compared to the shortest path algorithm. The experimental data show that the length of additional path (in excess of shortest path length) can be reduced to about half of that of existing GFG algorithm.