For a graph G=(V,E), finding a set of disjoint edges that do not share any vertices is called a matching problem, and finding the maximum matching is a fundamental problem in the theory of distributed graph algorithms. Although local algorithms for the approximate maximum matching problem have been widely studied, exact algorithms have not been much studied. In fact, no exact maximum matching algorithm that is faster than the trivial upper bound of O(n2) rounds is known for general instances. In this paper, we propose a randomized $O(s_{max}^{3/2})$-round algorithm in the CONGEST model, where smax is the size of maximum matching. This is the first exact maximum matching algorithm in o(n2) rounds for general instances in the CONGEST model. The key technical ingredient of our result is a distributed algorithms of finding an augmenting path in O(smax) rounds, which is based on a novel technique of constructing a sparse certificate of augmenting paths, which is a subgraph of the input graph preserving at least one augmenting path. To establish a highly parallel construction of sparse certificates, we also propose a new characterization of sparse certificates, which might also be of independent interest.

A polarization switchable slot-coupled microstrip antenna using PIN diodes is proposed and studied. The microstrip feed line installed behind the ground plane is divided into two branches and each tip of the branches is connected to the ground plane through a PIN diode. One of the diodes is oriented from the tip to the ground plane and the other is oriented from the ground to the tip so that a slot in the ground can be selected to feed the patch by switching the dc bias between positive and negative. This selection contributes to switch the polarization between horizontal and vertical. In this paper, the authors investigate the polarization switching antenna theoretically and experimentally and confirmed sufficient differencce of antenna gain between horizontal and vertical polarization.

The maximal independent set (MIS) problem is one of the most fundamental problems in the field of distributed computing. This paper focuses on the MIS problem with unreliable communication between processes in the system. We propose a relaxed notion of MIS, named almost MIS (ALMIS), and show that the loosely-stabilizing algorithm proposed in our previous work can achieve exponentially long holding time with logarithmic convergence time and space complexity regarding ALMIS, which cannot be achieved at the same time regarding MIS in our previous work.

In the rendezvous problem, two computing entities (called agents) located at different vertices in a graph have to meet at the same vertex. In this paper, we consider the synchronous neighborhood rendezvous problem, where the agents are initially located at two adjacent vertices. While this problem can be trivially solved in O(Δ) rounds (Δ is the maximum degree of the graph), it is highly challenging to reveal whether that problem can be solved in o(Δ) rounds, even assuming the rich computational capability of agents. The only known result is that the time complexity of O($O(sqrt{n})$) rounds is achievable if the graph is complete and agents are probabilistic, asymmetric, and can use whiteboards placed at vertices. Our main contribution is to clarify the situation (with respect to computational models and graph classes) admitting such a sublinear-time rendezvous algorithm. More precisely, we present two algorithms achieving fast rendezvous additionally assuming bounded minimum degree, unique vertex identifier, accessibility to neighborhood IDs, and randomization. The first algorithm runs within $ ilde{O}(sqrt{nDelta/delta} + n/delta)$ rounds for graphs of the minimum degree larger than $sqrt{n}$, where n is the number of vertices in the graph, and δ is the minimum degree of the graph. The second algorithm assumes that the largest vertex ID is O(n), and achieves $ ilde{O}left( rac{n}{sqrt{delta}} ight)$-round time complexity without using whiteboards. These algorithms attain o(Δ)-round complexity in the case of $delta = {omega}(sqrt{n} log n)$ and δ=ω(n2/3log4/3n) respectively. We also prove that four unconventional assumptions of our algorithm, bounded minimum degree, accessibility to neighborhood IDs, initial distance one, and randomization are all inherently necessary for attaining fast rendezvous. That is, one can obtain the Ω(n)-round lower bound if either one of them is removed.