Tsunehiko Kameda

Leader election problem on networks in which processor identity numbers are not distinct

In the networks considered in this paper, processors do not have distinct identity numbers. On such a network, we discuss the leader election problem and the problem of counting the number of processors having the same identity number. As the communication mode, we consider port-to-port, broadcast-to-port, port-to-mail box, and broadcast-to-mailbox. For each of the above communication modes, we present: an algorithm for counting the number of processors with the same identity number; an algorithm for solving the leader election problem; and a graph theoretical characterization of the solvable class for the leader election problem.

Computing on anonymous networks. II. Decision and membership problems

For pt I see ibid. In anonymous networks, the processors do not have identity numbers. In Part I of this paper, we characterized the classes of networks on which some representative distributed computation problems are solvable under different conditions. A new graph property called symmetricity played a central role in our analysis of anonymous networks. In Part II, we turn our attention to the computational complexity issues. We first discuss the complexity of determining the symmetricity of a given graph, and then that of testing membership in each of the 16 classes of anonymous networks defined in Part I. It turns out that, depending on the class, the complexity varies from P-time to NP-complete or co-NP-complete.

Bushiness and a tight worst-case upper bound on the search number of a simple polygon

Abstract We show that 1 + ⌊ log 3 (2 b + 1)⌋ is a tight worst-case upper bound on the minimum number of searchers having 360° visibility needed to search a simple polygon with bushiness b .

Optimal coteries for rings and related networks

SummaryLet a distributed system be represented by a graphG=(V, E), whereV is the set of nodes andE is the set of communication links. A coterie is defined as a family,C, of subsets ofV such that any pair of subsets inC has at least one node in common and no subset inC contains any other subset inC. Assuming that each nodevi∈V (resp. linkej∈E) is operational with probabilitypi (resp.rj), the availability of a coterie is defined as the probability that the operational nodes and links ofG connect all nodes in at least one subset in the coterie. Although it is computationally intractable to find an optimal coterie that maximizes availability for general graphG, we show in this paper that, ifG is a ring, either a singleton coterie or a 3-majority coterie is optimal. Therefore, for any ring, an optimal coterie can be computed in polynomial time. This result is extended to the more general graphs, in which each biconnected component is either an edge or a ring.

Online polygon search by a seven-state boundary 1-searcher

Polygon search is the problem of finding mobile intruders who move unpredictably in a polygonal region. In this paper, we consider a special case of this problem, called boundary search, where the searcher is allowed to move only along the boundary of the polygon. We concentrate on a single searcher with one flashlight (called a 1-searcher), but it is known that a single boundary 1-searcher has the same searching power as a single boundary searcher with 360/spl deg/ vision. Our main result is that the movement of the searcher can be controlled by a finite-state machine having only seven states. This automaton has no built-in information about the input polygon and, for any given polygon P, if P can be searched by a boundary searcher at all, then this automaton will successfully search P, no matter where on the boundary of P it is initially placed. All information about P is acquired by the automaton online, as it searches P. We also show that if P can be searched by a boundary searcher, then our automaton searches it by circling its boundary less than three times.

Harmonic block windows scheduling through harmonic windows scheduling

In Harmonic windows scheduling (HWS), a data file is divided into N pages and the pages are scheduled in c channels in such a way that each page i appears at least once in some channel in every window of size i. The optimal HWS problem aims to maximize N. Let κ be the largest integer satisfying Hκ ≤ c, where Hn is the nth harmonic number. Then κ is an upper bound on N, if the HWS framework is used. Thus an optimal HWS schedule wastes “bandwidth” at least c–Hκ. Harmonic block windows scheduling (HBWS) generalizes HWS by grouping b consecutive pages into a superpage. Let N be the total number of pages scheduled. The ratio N/b is directly proportional to the maximum initial waiting time in Media-on-Demand applications. We propose a method that starts with a HWS schedule and modifies it to generate a HBWS schedule that achieves a higher ratio N/b. For up to five channels, we demonstrate that we can always achieve N/b >κ. We also prove that as we increase b, N/b approaches the theoretical upper bound.

A Linear Time Algorithm for Computing Minmax Regret 1-Median on a Tree

In a model of facility location problem, the uncertainty in the weight of a vertex is represented by an interval of weights, and minimizing the maximum “regret” is the goal. The most efficient previously known algorithm for finding the minmax regret 1-median on trees with positive vertex weights takes O(nlogn) time. We improve it to O(n), solving the open problem posed by Brodal et al. in [3].

A Linear Time Algorithm for Computing Minmax Regret 1-Median on a Tree Network

In a model of facility location problem, the uncertainty in the weight of a vertex is represented by an interval of weights, and the objective is to minimize the maximum “regret.” The most efficient algorithm previously known for finding the minmax regret 1-median in a tree network with nonnegative vertex weights takes O(nlogn) time. We improve it to O(n), settling the open problem posed by Brodal et al. (Oper. Res. Lett. 36:14–18, 2008).

Modeling K-coteries by well-covered graphs

The concept of k-coterie is useful for achieving k-mutual exclusion in distributed systems. A graph is said to be well covered if any of its maximal independent sets is also maximum. We first show that a graph G is well covered with independence number k if and only if G represents the incidence relation among quorums forming a k-coterie. We then discuss the problem of constructing k-coteries having some desirable properties. We also characterize the well-covered graphs with independence number 2.

Generalized Fibonacci broadcasting an efficient VOD scheme with user bandwidth limit

Broadcasting is attractive in delivering popular videos in video-on-demand service, because the server broadcast bandwidth is independent of the number of users. However, the required server bandwidth does depend on how much bandwidth each user can use, as well as on the users initial waiting time. This paper addresses the issue of limiting the user bandwidth, and proposes a new broadcasting scheme, named Generalized Fibonacci Broadcasting (GFB). In terms of many performance graphs, we show that, for any given combination of the server bandwidth and user bandwidth, GFB can achieve the least waiting time among all the currently known fixed-delay broadcasting schemes. Furthermore, it is very easy to implement GFB. We also demonstrate that there is a trade-off between the user waiting time and the buffer requirement at the user.