Harri Haanpää

Balanced Multipath Source Routing

We consider the problem of balancing the traffic load ideally over a wireless multihop network. In previous work, a systematic approach to this task was undertaken, starting with an approximate optimisation method that guarantees a provable congestion performance bound, and then designing a distributed implementation by modifying the DSR protocol. In this paper, the performance of the resulting Balanced Multipath Source Routing ( BMSR ) protocol is validated in a number of simulated networking scenarios. In particular, we study the effect of irregular network structure on the performance of the protocol, and compare it to the performance of DSR and an idealised shortest-path routing algorithm in setups with several source-destination pairs. For all network scenarios we consider, BMSR outperforms DSR significantly. BMSR is also shown to be more robust than the shortest-path algorithm, in that it can distribute the traffic load more evenly in cases where shortest-path routing is impeded by radio interference between proximate paths.

Distributed computation of maximum lifetime spanning subgraphs in sensor networks

We present a simple and efficient distributed method for determining the transmission power assignment that maximises the lifetime of a data-gathering wireless sensor network with stationary nodes and static power assignments. Our algorithm determines the transmission power level inducing the maximum-lifetime spanning subgraph of a network by means of a distributed breadth-first search for minmax-power communication paths, i.e. paths that connect a given reference node to each of the other nodes so that the maximum transmission power required on any link of the path is minimised. The performance of the resulting Maximum Lifetime Spanner (MLS) protocol is validated in a number of simulated networking scenarios. In particular, we study the performance of the protocol in terms of the number of required control messages, and compare it to the performance of a recently proposed Distributed Min-Max Tree (DMMT) algorithm. For all network scenarios we consider, MLS outperforms DMMT significantly. We also discuss bringing down the message complexity of our algorithm by initialising it with the Relative Neighbourhood Graph (RNG) of a transmission graph rather than the full graph, and present an efficient distributed method for reducing a given transmission graph to its RNG.

Load balancing by distributed optimisation in ad hoc networks

We approach the problem of load balancing for wireless multi-hop networks by distributed optimisation. We implement an approximation algorithm for minimising the maximum network congestion as a modification to the DSR routing protocol. The algorithm is based on shortest-path computations that are integrated into the DSR route discovery and maintenance process. The resulting Balanced Multipath Source Routing (BMSR) protocol does not need to disseminate global information throughout the network. Our simulations with the ns2 simulator show a gain of 14% to 69% in the throughput, depending on the setup, compared to DSR for a high network load.

Distributed algorithms for lifetime maximization in sensor networks via Min---Max spanning subgraphs

We consider the problem of static transmission-power assignment for lifetime maximization of a wireless sensor network with stationary nodes operating in a data-gathering scenario. Using a graph-theoretic approach, we propose two distributed algorithms, MLS and BSpan, that construct spanning trees with minimum maximum (minmax) edge cost. MLS is based on computation of minmax-cost paths from a reference node, while BSpan performs a binary search over the range of power levels and exploits the wireless broadcast advantage. We also present a simple distributed method for pruning a graph to its Relative Neighborhood Graph, which reduces the worst-case message complexity of MLS under natural assumptions on the path-loss. In our network simulations both MLS and BSpan significantly outperform the recently proposed Distributed Min–Max Tree algorithm in terms of number of messages required.

Distributed Sleep Scheduling in Wireless Sensor Networks via Fractional Domatic Partitioning

We consider setting up sleep scheduling in sensor networks. We formulate the problem as an instance of the fractional domatic partition problem and obtain a distributed approximation algorithm by applying linear programming approximation techniques. Our algorithm is an application of the Garg-Konemann (GK) scheme that requires solving an instance of the minimum weight dominating set (MWDS) problem as a subroutine. Our two main contributions are a distributed implementation of the GK scheme for the sleep-scheduling problem and a novel asynchronous distributed algorithm for approximating MWDS based on a primal-dual analysis of Chvatals set-cover algorithm. We evaluate our algorithm with ns2 simulations.

On the coexistence of conference matrices and near resolvable 2-(2 k + 1, k , k - 1) designs

We show that a near resolvable 2-(2k + 1, k, k - 1) design exists if and only if a conference matrix of order 2k + 2 does. A known result on conference matrices then allows us to conclude that a near resolvable 2-(2k + 1, k, k - 1) design with even k can only exist if 2k + 1 is the sum of two squares. In particular, neither a near resolvable 2-(21, 10, 9) design nor does a near resolvable 2-(33, 16, 15) design exist. For k ≤ 14, we also enumerate the near resolvable 2-(2k + 1, k, k - 1) designs and the corresponding conference matrices.

The near resolvable 2-(13, 4, 3) designs and thirteen-player whist tournaments

Abstract.A ν-player whist tournament is a schedule of games, where in each round the ν players are partitioned into games of four players each with at most one player left over. In each game two of the players play as partners against the other two. All pairs of players must play in the same game exactly three times during the tournament; of those three times, they are to play as partners exactly once. Whist tournaments for ν players are known to exist for all ν ≡ 0,1 (mod 4). The special cases of directed whist tournaments and triplewhist tournaments are known to exist for all sufficiently large ν, but for small ν several open cases remain. In this paper we introduce a correspondence between near resolvable 2-(ν, k, λ designs and a particular class of codes. The near resolvable 2-(13, 4, 3) designs are classified by classifying the corresponding codes with an orderly algorithm. Finally, the thirteen-player whist tournaments are enumerated starting from the near resolvable 2-(13, 4, 3) designs.

Classification of whist tournaments with up to 12 players

A v-player whist tournament Wh(v) is a schedule of games, each involving two players opposing two others. Every round, the players are partitioned into games, with at most one player left over. Each player partners every other player exactly once and opposes every other player exactly twice during the tournament. Directed whist tournaments DWh(v), and triplewhist tournaments TWh(v), are Wh(v) with certain additional requirements. In this work the nonisomorphic Wh(v), DWh(v), and TWh(v) are enumerated for v ≤ 12. We find an apparently new Wh(9) and establish that there exists no DWh(12)--and thereby no (12, 4, 1 )-RPMD--nor a TWh(12).

Distributed network utility maximization in wireless networks with a bounded number of paths

We consider the fair multicommodity flow problem in multihop wireless networks. We optimize the flow between a number of source-destination pairs to achieve a fair allocation of network resources while satisfying node capacity constraints. To account for the limitations of wireless devices, we use a path-based formulation and allow only a bounded number of paths between each source-destination pair. We develop a dual decomposition based distributed algorithm for solving the problem, show the optimality of a stationary solution, and compare the performance of the algorithm with a centralized branch-and-bound method.

Lifetime maximization in wireless sensor networks by distributed binary search

We consider the problem of determining the transmission power assignment that maximizes the lifetime of a data-gathering wireless sensor network with stationary nodes and static transmission power levels. We present a simple and efficient distributed algorithm for this task that works by establishing the minimum power level at which the network stays connected. The algorithm is based on a binary search over the range of feasible transmission power levels and does not require prior knowledge of network topology. We study the performance of the resulting BSpan protocol by network simulations and compare the number of control messages required by BSpan to two other recently proposed methods, the Distributed Min-Max Tree (DMMT) and Maximum Lifetime Spanner (MLS) algorithms. We find that BSpan outperforms both DMMT and MLS significantly.