Hideyuki Uehara

Source location problems considering vertex-connectivity and edge-connectivity simultaneously

Let G = (V, E) be an undirected multigraph, where V and E are a set of vertices and a set of edges, respectively. Let k and l be fixed nonnegative integers. This paper considers location problems of finding a minimum-size vertex-subset S ⊆ V such that for each vertex x ∈ V the vertex-connectivity between S and x is greater than or equal to k and the edge-connectivity between S and x is greater than or equal to l. For the problem with edge-connectivity requirements, that is, k = 0, an O(L(|V|, |E|, l)) time algorithm is already known, where L(|V|, |E|, l) is the time to find all h-edge-connected components for h = 1, 2, … , l and O(L(|V|, |E|, l)) = O(|E| + |V|2 + |V|min{|E|, l|V|}min{l, |V|}) is known. In this paper, we show that the problem with k ≥ 3 is NP-hard even for l = 0. We then present an O(L(|V|, |E|, l)) time algorithm for 0 ≤ k ≤ 2 and l ≥ 0. Moreover, we prove that the problem parameterized by the size of S is fixed-parameter tractable (FPT) for k = 3 and l ≥ 0.

2-Dimension Ham Sandwich Theorem for Partitioning into Three Convex Pieces

Let m ≥ 2, n ≥ 2 and q ≥ 2 be positive integers. Let S r and S b be two disjoint sets of points in the plane such that no three points of S r ∪ S b are collinear, |S r | = nq, and |S b | = mq. This paper shows that Kaneko and Kano’s conjecture is true, i.e., S r ∪ S b can be partitioned into q subsets P 1,P 2,...,P q satisfying that: (i) conv(P i ) ∩ conv(P j ) = ∅ for all 1 ≤ i < j ≤ q; (ii) |P i ∩ S r |= n and |P i ∩ S b | = m for all 1 ≤ i ≤ q. This is a generalization of 2-dimension Ham Sandwich Theorem.

Location Problems Based on Node-Connectivity and Edge-Connectivity between Nodes and Node-Subsets

Let G = (V, E) be an undirected multi-graph where V and E are a set of nodes and a set of edges, respectively. Let k and l be fixed nonnegative integers. This paper considers location problems of finding a minimum size of node-subset S ⊆ V such that node-connectivity between S and x is greater than or equal to k and edge-connectivity between S and x is greater than or equal to l for every x ∈ V . This problem has important applications for multi-media network control and design. For a problem of considering only edge-connectivity, i.e., k = 0, an O(L(|V|, |E|, l)) = O(|E| + |V|2 + |V|min{|E|, l|V|}min{l, |V|}) time algorithm was already known, where L(|V|, |E|, l) is a time to find all h-edge-connected components for h = 1, 2, ..., l. This paper presents an O(L(|V|, |E|, l)) time algorithm for 0 ≤ k ≤ 2 and l ≥ 0. It also shows that if k ≥ 3, the problem is NP-hard even for l = 0. Moreover, it shows that if the size of S is regarded as a parameter, the parameterized problem for k = 3 and l ≤ 1 is FPT (fixed parameter tractable).

Effect of hop counts on power division ratio in multi-hop power transfer via magnetic resonance

In this paper, we discuss the effect of the number of hops on the power division in wireless power transfer via magnetic resonance based on the electric circuit theory. First, a power division ratio (PDR) of single-hop power transfer to multiple receivers is addressed by using an equivalent circuit. The PDR of each receiver is shown to be inversely proportional to load resistances. Secondly, the PDR of multi-hop power transfer to multiple receivers is discussed focusing on the parity of the number of hops. Under the condition that a transmitter and intermediate couplers are arranged on an equal distance, it is needed to switch the control strategy of adjusting load resistance according to the parity of the number of hops on multi-hop power transfer to multiple receivers.

An optical synchronous M‐ary FSK/CDMA system using an interference canceler

In this paper, a cancellation technique using a reference signal which does not contain the components of the desired signal is proposed for optical synchronous M-ary FSK/CDMA. As spreading codes, the modified prime sequence codes which can increase the number of users are employed. Interference cancellation is done by using the correlation property of the modified prime sequence codes. A reference signal is constructed by using one of the modified prime sequence codes that do not have data components of the desired signal, and cancellation is performed by subtracting the reference signal from the received signal of the desired user. In the theoretical analysis, the Poisson effect in the input–output characteristic of the photodetector is considered, and the upper bound on the bit error rate (BER) is derived. The performance is compared to the optical synchronous M-ary PPM/CDMA system with an interference canceler in which a reference signal does not contain the data components of the desired signal. It is found that an optical synchronous M-ary FSK/CDMA system with an interference canceler has better BER performance than optical synchronous M-ary PPM/CDMA systems with an interference canceler under the condition of the same chip rate and number of symbols M, and achieves higher bit rate. Also, when the chip rate and bit rate are constant, it is found that optical synchronous M-ary FSK/CDMA system with an interference canceler can increase the number of simultaneous users.

Efficient Clustering Scheme Considering Non-uniform Correlation Distribution for Ubiquitous Sensor Networks

We propose a novel clustering scheme considering non-uniform correlation distribution derived by experimental environment property. Firstly, we investigate the entropy property of actual environment, and then show that its spatial correlation is not uniformly distributed. Based on this result, we present the clustering strategy which provides the efficient data aggregation. Through the simulation under the non-uniform correlation distribution, we show the advantage of the proposed scheme in terms of the energy consumption property per node and the network lifetime.

NP-Completeness of Stage Illumination Problems

The stage illumination problem presented by Urrutia in 1992 is one of illumination problems, which uses floodlights for illuminating a stage. The problem asks whether or not it is possible to rotate given floodlights around their apexes so as to obtain a final configuration such that a given stage is completely illuminated. The problem for finding a polynomial time algorithm for this problem or proving NP-hardness of this problem was open. This paper shows that it is NP-complete even with some restrictions.

Intermittent transmission method based on aggregation model for clustering scheme

In wireless sensor networks, reducing the energy consumption of the whole network is one of the most important research themes. In this paper, we first define a data aggregation model that defines the relationship between the increased amount of entropy and the number of sensor nodes. We also develop an intermittent transmission method, which is mainly assumed clustered sensor networks. Each sensor node transits their data with a probability that is set based on the aggregation model and the number of nodes within the cluster. From simulation using real sensing data, we reveal the intermittent transmission method is effective for energy-saving.

Directional monitoring MAC protocol using smart antennas in wireless multi-hop networks

Recently, many studies in wireless ad hoc networks assume the use of smart antennas which can electronically control their beam pattern. Communications using smart antennas can be expected to improve spatial utilization efficiency and to extend communication distance. However, there are some unique problems caused by the use of the smart antennas. In this paper, we focus on the directional hidden terminal and the deafness problems. We propose a directional monitoring scheme and a switching backoff scheme for overcoming these problems. The directional monitoring scheme can solve the directional hidden terminal problem by monitoring the direction toward the destination after sending a data packet. The switching backoff scheme can reduce deafness loss time by keeping backoff-interval as long as the terminal is deaf. Comparing the proposed scheme with conventional schemes by computer simulations, the results show that the proposed scheme can mitigate the effect of these problems and it achieves higher throughput.

Route Selection Metrics in Wireless Mobile Ad Hoc Networks

In this study, we present a way to choose route selection metric while discovering a new route in ad hoc mobile networks. We have used link expiration time and busy rate to calculate the route cost. The route cost is compared to a threshold value to decide whether the traffic of the route is high or low. If it is high then the system chooses busy rate as a route selection metric to avoid traffic congestion and if it is low the link expiration time is used to select the longlasting route. We have examined the characteristics of the routing protocol by computer simulation and found that it over performs the conventional protocols.