Parallelization of the P-complete problem is known to be difficult. In this paper, we consider the parallelizability of a stack breadth-first search (stack BFS) problem, which is proved to be P-complete. We first propose the longest path length (LPL) as a measure for the P-completeness of the stack BFS. Next, using this measure, we propose an efficient parallel algorithm for the stack BFS. Assuming the size and LPL of an input graph are n and l, respectively, the complexity of the algorithm indicates that the stack BFS is in the class NCk+1 if l = O(logk n), where k is a positive integer. In addition, the algorithm is cost optimal if l=O(nε), where 0 < ε < 1.

In the present paper, we consider fully asynchronous parallelism in membrane computing, and propose two asynchronous P systems for the satisfiability (SAT) and Hamiltonian cycle problem. We first propose an asynchronous P system that solves SAT with n variables and m clauses, and show that the proposed P system computes SAT in O(mn2n) sequential steps or O(mn) parallel steps using O(mn) kinds of objects. We next propose an asynchronous P system that solves the Hamiltonian cycle problem with n nodes, and show that the proposed P system computes the problem in O(n!) sequential steps or O(n2) parallel steps using O(n2) kinds of objects.

This paper proposes a signal-to-interference power ratio (SIR) measurement method that employs the transmission gap of a data channel (TGDC) interval for precise link adaptation, in order to eliminate the influence of severe multipath interference (MPI) from a shared packet channel and to decrease further the instantaneous variations in interference components for high-speed packet transmission in the forward link using adaptive data modulation associated with the multipath interference canceller (MPIC). Computer simulation results elucidate that the required received signal energy per chip-to-background noise power spectrum density ratio (Ec/N0) based on the SIR measurement employing TGDC at the throughput of 4.2 Mbps is decreased by approximately 2.0 dB compared to the conventional method without TGDC using chip-based interference power measurement for the number of paths L = 1, and by approximately 1.5 dB compared to the conventional method using symbol-based interference power measurement for L = 2, respectively. Therefore, we show that the adaptive data modulation with the SIR measurement exploiting the TGDC interval achieves almost the maximum (i.e., almost ideal selection) throughput, without changing the SIR measurement method according to the propagation conditions such as the number of multipaths.

In this paper, we present two parallel algorithms for computing the all nearest neighbors of an n n binary image on the Bulk-Synchronous Parallel(BSP) model. The BSP model is an asynchronous parallel computing model, where its communication features are abstracted by two parameters L and g: L denotes synchronization periodicity and g denotes a reciprocal of communication bandwidth. We propose two parallel algorithms for the all nearest neighbor problems based on two distance metrics. The first algorithm is for Lp distance, and the second algorithm is for weighted distance. Both two algorithms run in O(n2/p + L) computation time and in O(g(n/p) + L) communication time using p (1 p n) processors and in O(n2/p + (d+L)(log(p/n)/log(d+1))) computation time and in O(g(n/p) + (gd+L)(log(p/n)/log(d+1))) communication time using p (n< p n2) processors on the BSP model, for any integer d(1 dp/n).

P-complete problems seem to have no parallel algorithm which runs in polylogarithmic time using a polynomial number of processors. A P-complete problem is in the class EP (Efficient and Polynomially fast) if and only if there exists a cost optimal algorithm to solve it in T(n) = O(t(n)ε) (ε < 1) using P(n) processors such that T(n) P(n) = O(t(n)), where t(n) is the time complexity of the fastest sequential algorithm which solves the problem. The goal of our research is to find EP parallel algorithms for some P-complete problems. In this paper first we consider the convex layers problem. We give an algorithm for computing the convex layers of a set S of n points in the plane. Let k be the number of the convex layers of S. When 1 k nε/2 (0 ε < 1) our algorithm runs in O((n log n)/p) time using p processors, where 1 p n1-ε/2, and it is cost optimal. Next, we consider the envelope layers problem of a set S of n line segments in the plane. Let k be the number of the envelope layers of S. When 1 k nε/2 (0 ε < 1), we propose an algorithm for computing the envelope layers of S in O((n α(n) log3 n)/p) time using p processors, where 1 p n1-ε/2, and α(n) is the functional inverse of Ackermann's function which grows extremely slowly. The computational model we use in this paper is the CREW-PRAM. Our first algorithm, for the convex layers problem, belongs to EP, and the second one, for the envelope layers problem, belongs to the class EP if a small factor of log n is ignored.

The medial axis transform (MAT) is an image representation scheme. For a binary image, the MAT is defined as a set of upright maximal squares which consist of pixels of value l entirely. The MAT plays an important role in image understanding. This paper presents a parallel algorithm for computing the MAT of an n n binary image. We show that the algorithm can be performed in O(log n) time using n2/log n processors on the EREW PRAM and in O(log log n) time using n2/log log n processors on the common CRCW PRAM. We also show that the algorithm can be performed in O(n2/p2 + n) time on a p p mesh and in O(n2/p2 + (n log p)/p) time on a p2 processor hypercube (for 1 p n). The algorithm is cost optimal on the PRAMs, on the mesh (for 1 p n) and on the hypercube (for 1 p n/log n).

In this paper, we present deterministic parallel algorithms for the convex hull of sorted points and their application to a related problem. The algorithms are proposed for the coarse grained multicomputer (CGM) model. We first propose a cost optimal parallel algorithm for computing the problem with a constant number of communication rounds for n/p p2, where n is the size of an input and p is the number of processors. Next we propose a cost optimal algorithm, which is more complicated, for n/p pε, where 0 < ε < 2. From the above two results, we can compute the convex hull of sorted points with O(n/p) computation time and a constant number of communication rounds for n/p pε, where ε > 0. Finally we show an application of our convex hull algorithms. We solve the convex layers for d lines in O((n log n)/p) computation time with a constant number of communication rounds. The algorithm is also cost optimal for the problem.