The feedback vertex set (FVS) problem is to find the set of vertices of minimum cardinality whose removal renders the graph acyclic. The FVS problem has applications in several areas such as combinatorial circuit desi...The feedback vertex set (FVS) problem is to find the set of vertices of minimum cardinality whose removal renders the graph acyclic. The FVS problem has applications in several areas such as combinatorial circuit design, synchronous systems, computer systems, and very-large-scale integration (VLSI) circuits. The FVS problem is known to be NP-hard for simple graphs, but polynomi-al-time algorithms have been found for special classes of graphs. The intersection graph of a collection of arcs on a circle is called a circular-arc graph. A normal Helly circular-arc graph is a proper subclass of the set of circular-arc graphs. In this paper, we present an algorithm that takes time to solve the FVS problem in a normal Helly circular-arc graph with n vertices and m edges.展开更多
Given a simple graph G with n vertices and m edges, the spanning tree problem is to find a spanning tree for a given graph G. This problem has many applications, such as electric power systems, computer network design...Given a simple graph G with n vertices and m edges, the spanning tree problem is to find a spanning tree for a given graph G. This problem has many applications, such as electric power systems, computer network design and circuit analysis. For a simple graph, the spanning tree problem can be solved in O(log n) time with O(m+n) processors on the CRCW PRAM. In general, it is known that more efficient parallel algorithms can be developed by restricting classes of graphs. In this paper, we shall propose a parallel algorithm which runs O(log n) time with O(n/log n) processors on the EREW PRAM for constructing on proper circle trapezoid graphs.展开更多
Given a simple graph G with n vertices, m edges and k connected components. The spanning forest problem is to find a spanning tree for each connected component of G. This problem has applications to the electrical pow...Given a simple graph G with n vertices, m edges and k connected components. The spanning forest problem is to find a spanning tree for each connected component of G. This problem has applications to the electrical power demand problem, computer network design, circuit analysis, etc. In this paper, we present an?time parallel algorithm with processors for constructing a spanning forest on proper circle graph G on EREW PRAM.展开更多
The vertex connectivity k(G) of a graph G is the minimum number of nodes whose deletion disconnects it. Graph connectivity is one of the most fundamental problems in graph theory. In this paper, we designed an O(n2) t...The vertex connectivity k(G) of a graph G is the minimum number of nodes whose deletion disconnects it. Graph connectivity is one of the most fundamental problems in graph theory. In this paper, we designed an O(n2) time algorithm to solve connectivity problem on circular trapezoid graphs.展开更多
文摘The feedback vertex set (FVS) problem is to find the set of vertices of minimum cardinality whose removal renders the graph acyclic. The FVS problem has applications in several areas such as combinatorial circuit design, synchronous systems, computer systems, and very-large-scale integration (VLSI) circuits. The FVS problem is known to be NP-hard for simple graphs, but polynomi-al-time algorithms have been found for special classes of graphs. The intersection graph of a collection of arcs on a circle is called a circular-arc graph. A normal Helly circular-arc graph is a proper subclass of the set of circular-arc graphs. In this paper, we present an algorithm that takes time to solve the FVS problem in a normal Helly circular-arc graph with n vertices and m edges.
文摘Given a simple graph G with n vertices and m edges, the spanning tree problem is to find a spanning tree for a given graph G. This problem has many applications, such as electric power systems, computer network design and circuit analysis. For a simple graph, the spanning tree problem can be solved in O(log n) time with O(m+n) processors on the CRCW PRAM. In general, it is known that more efficient parallel algorithms can be developed by restricting classes of graphs. In this paper, we shall propose a parallel algorithm which runs O(log n) time with O(n/log n) processors on the EREW PRAM for constructing on proper circle trapezoid graphs.
文摘Given a simple graph G with n vertices, m edges and k connected components. The spanning forest problem is to find a spanning tree for each connected component of G. This problem has applications to the electrical power demand problem, computer network design, circuit analysis, etc. In this paper, we present an?time parallel algorithm with processors for constructing a spanning forest on proper circle graph G on EREW PRAM.
文摘The vertex connectivity k(G) of a graph G is the minimum number of nodes whose deletion disconnects it. Graph connectivity is one of the most fundamental problems in graph theory. In this paper, we designed an O(n2) time algorithm to solve connectivity problem on circular trapezoid graphs.
