Junichiro Fukuyama

NP-completeness of the Planar Separator Problems

For a given graph G, the Separator Problem asks whether a vertex or edge set of small cardinality (or weight) exists whose removal partitions G into two disjoint graphs of approximately equal sizes. Called the Vertex Separator Problem when the removed set is a vertex set, and the Edge Separator Problem when it is an edge set, both problems are NP-complete for general unweighted graphs [6]. Despite the significance of planar graphs, it has not been known whether the Planar Separator Problem, which considers a planar graph and a threshold as an input, is NP-complete or not. In this paper, we prove that the Vertex Separator Problem is in fact NP-complete when G is a vertex weighted planar graph. The Edge Separator Problem will be shown NP-complete when G is a vertex and edge weighted planar graph. In addition, we consider how to treat the constant � 2 R

Context-driven disruption tolerant networking for vehicular applications

In this paper, we describe how a context-driven disruption tolerant network may be utilized for vehicular applications. The key concept involves utilizing contextual information pertaining to space and time settings of applications to drive networking functions. As a result, the performance characteristics may be better attuned to the time-scale of relevant vehicular applications. We discuss the protocol highlights and present a compact grid-based method for performance evaluation of such systems. Novel metrics such as information freshness demonstrate the discrete nature of information dissemination. Additionally, we observe that asymptotic evaluation of metrics such as packet delivery ratio do not provide a realistic picture of application performance. As a consequence, the time-scale of interest for the applications becomes crucial.

Transmit Only: An Ultra Low Overhead MAC Protocol for Dense Wireless Systems

The number of small wireless devices is rapidly increasing, making the radio channel efficiency in limited geographic areas (individual rooms or buildings) an important metric for MAC protocols. Many of these emerging devices have use-cases that are difficult to satisfy with current hardware solutions and channel access methods; for instance device mobility, small energy reserves, and requirements for low cost and small form factors. However, for most of these applications, such as health care monitoring or sensing, feedback to the radio device is unnecessary and unidirectional communication techniques are not only sufficient, but can also be advantageous. We propose an efficient, reliable technique for unidirectional communication, called Transmit Only (TO), that satisfies these requirements while maintaining packet throughput guarantees and reducing energy consumption. In this paper we will demonstrate the feasibility and performance of this kind of highly asymmetric, transmit-only protocol through theoretical, simulated, and experimental results.

A probabilistic protocol for multihop routing in VANETs

Vehicular ad hoc networks (VANETs) allow communications over sequences of vehicles with radio devices. There are many possible applications over a VANET such as traffic jam warning, collision warning, parking lot reservations, camera picture feed, and so forth. There have been quite a few results in the area seeking for a fast and reliable communication protocol due to their potential. VANETs, however, are pointed out as difficult for numerical optimizations due to frequent changes in their topologies. As a result, heuristic methods such as GPSR have been mainly used for routing packets over multihop communications. In this paper, we present an algorithm to precompute the probability that communication is possible between specified source and destination in a VANET, under certain mathematical assumption. The proposed new protocol for multihop communication refers to a lookup table containing the precomputed data to decide a good packet forwarder quickly. We create a simulation testbed that seems challenging for all the existing multihop routing protocols for VANETs, in which we test ours. We seemuch improved performances over GPSR after the algorithm is refined for some practical issues.

An Online Algorithm for the Postman Problem with a Small Penalty

The Postman Problem is defined in the following manner: Given a connected graph G and a start point s ∈ V (G), we call a path J in G a postman tour if J starts and ends at s and contains every edge in E(G). We want to find a shortest postman tour in G. Thus, we minimize the number |J| - |E(G)|, called the penalty of J for G. In this paper, we consider two online versions of The Postman Problem, in which the postman is initially placed at a start point and allowed to move on edges. The postman is given information on the incident edges and/or the adjacent vertices of the current vertex v. The first model is called The Labyrinth Model, where the postman only knows the existence of the incident edges from v. Thus, he/she does not know the other endpoint w of an edge from v, even if it is already visited. The second one is The Corridor Model, where the postman can see the other endpoint w from v. This means that if w is already visited, he/she knows the existence of w before traversing the edge (v,w). We devised an algorithm for The Corridor Model whose penalty is bounded by 2|V (G)|-2. It performs better than the algorithm described in [8], in the case when the other visited endpoint of an edge from a current vertex is known to the postman. In addition, we obtained lower bounds of a penalty for The Corridor and Labyrinth Models. They are (4|V (G)|-5)/3 and (5|V (G)|-3)/4, respectively. Our online algorithm uses a linear time algorithm for the offline Postman Problem with a penalty at most |V|-1. Thus, the minimum penalty does not exceed |V|-1 for every connected graph G. This is the first known upper bound of a penalty of an offline postman tour, and matches the obvious lower bound exactly.

Variable length sequencing with two lengths

Certain tasks, like accessing pages on the World Wide Web, require duration that varies over time. This poses the following Variable Length Sequencing Problem, or VLSP-L. Let [i, j) denote {i, i+1, ..., j- 1}. The problem is given by a set of jobs J and the time-dependent length function λ : J ×[0, n) → L. A sequencing function σ :J →[0, n) assigns to each job j a time interval Τσ(j) when this job is executed; if σ(j) = t then Τσ(j) = [t, t+λ(j, t)). The sequencing is valid if these time intervals are disjoint. Our objective is to minimize the makespan, i. e. the maximum ending of an assign time interval. Recently it was shown VLSP-[0, n) is NP-hard and that VLSP-{1, 2} can be solved efficiently. For a more general case of VLSP-{1, k} an 2 - 1/k approximation was shown. This paper shows that for k ≥ 3 VLSP-{1, k} is MAX-SNP hard, and that we can approximate it with ratio 2 - 4/(k + 3).