This paper first presents a unified approach to design efficient algorithms for the weighted domination problem and its three variants, i.e., the weighted independent, connected, and total domination problems, on inte...
详细信息
This paper first presents a unified approach to design efficient algorithms for the weighted domination problem and its three variants, i.e., the weighted independent, connected, and total domination problems, on interval graphs. Given an interval model with endpoints sorted, these algorithms run in time O(n) or O(n log log n) where n is the number of vertices. The results are then extended to solve the same problems on circular-arc graphs in O(n+m) time where m is the number of edges of the input graph.
This report proposes a theory of multi-relations, which are similar to normal mathematical relations, except for the fact that each tuple has a given multiplicity. it is shown that most of the set-oriented operations ...
详细信息
This report proposes a theory of multi-relations, which are similar to normal mathematical relations, except for the fact that each tuple has a given multiplicity. it is shown that most of the set-oriented operations on relations, such as union and intersection can be generalised tin the same way in which sets can be generalised to multisets. The typical relational operations of composition and transposition and the theory of 'lifting' can be generalised too. Several alternative representations are discussed, including ternary relations, and multisets of tuples. Multi-relations can be visualised as directed graphs where each edge is labeled with a number. Alternatively, the multiplicity could be visualised by giving the edge a certain thickness. The approach is helpful in situations where one is not satisfied with the knowledge that there is a certain connection ('uses','calls': etc.) between two units (components, modules, processes), but where one wants to have quantitative information on how many sub connections exist.
The dominating set problem in graphs asks for a minimum size subset of vertices with the following property: each vertex is required to be either in the dominating set, or adjacent to some vertex in the dominating set...
详细信息
The dominating set problem in graphs asks for a minimum size subset of vertices with the following property: each vertex is required to be either in the dominating set, or adjacent to some vertex in the dominating set. We focus on the related question of finding a connected dominating set of minimum size, where the graph induced by vertices in the dominating set is required to be connected as well. This problem arises in network testing, as well as in wireless communication. Two polynomial time algorithms that achieve approximation factors of 2H(Delta) + 2 and H(Delta) + 2 are presented, where Delta is the maximum degree and H is the harmonic function. This question also arises in relation to the traveling tourist problem, where one is looking for the shortest tour such that each vertex is either visited or has at least one of its neighbors visited. We also consider a generalization of the problem to the weighted case, and give an algorithm with an approximation factor of (c(n) + 1) ln n where c(n) ln k is the approximation factor for the node weighted Steiner tree problem (currently c(n) = 1.6103). We also consider the more general problem of finding a connected dominating set of a specified subset of vertices and provide a polynomial time algorithm with a (c + 1)H(Delta) + c - 1 approximation factor, where c is the Steiner approximation ratio for graphs (currently c = 1.644).
A vertex (edge) coloring phi : V --> {1, 2, ..., t} (phi' : E --> {1, 2, ..., t}) of a graph G = (V, E) is a vertex (edge) t-ranking if, for any two vertices (edges) of the same color, every path between the...
详细信息
A vertex (edge) coloring phi : V --> {1, 2, ..., t} (phi' : E --> {1, 2, ..., t}) of a graph G = (V, E) is a vertex (edge) t-ranking if, for any two vertices (edges) of the same color, every path between them contains a vertex (edge) of larger color. The vertex ranking number chi(r)(G) (edge ranking number chi(r)' (G)) is the smallest value of t such that G has a vertex (edge) t-ranking. In this paper we study the algorithmic complexity of the VERTEX RANKING and EDGE RANKING problems. It is shown that chi(r)(G) can be computed in polynomial time when restricted to graphs with treewidth at most k for any fixed k. We characterize the graphs where the vertex ranking number chi(r) and the chromatic number chi coincide on all induced subgraphs, show that chi(r)(G) = chi(G) implies chi(G) = omega(G) (largest clique size), and give a formula for chi(r)' (K-n).
Consider the problem of transporting a set of objects between the vertices of a simple graph by a vehicle that traverses the edges of the graph. The problem of finding a shortest tour for the vehicle to transport all ...
详细信息
Consider the problem of transporting a set of objects between the vertices of a simple graph by a vehicle that traverses the edges of the graph. The problem of finding a shortest tour for the vehicle to transport all objects from their initial vertices to their destination vertices is called the vehicle routing problem. The problem is multiple capacity if the vehicle can handle more than one objects at a time. The problem is preemptive if objects can be unloaded at the intermediate vertices. In this paper, we present an O(kn + n(2)) time algorithm for multiple capacity preemptive vehicle routing problem on paths, where k is the number of objects to be moved and n is the number of vertices in the path.
The minimum degree and minimum local fill algorithms are two bottom-up heuristics for reordering a sparse matrix prior to factorization. Minimum degree chooses a node of least degree to eliminate next;minimum local fi...
详细信息
The minimum degree and minimum local fill algorithms are two bottom-up heuristics for reordering a sparse matrix prior to factorization. Minimum degree chooses a node of least degree to eliminate next;minimum local fill chooses a n ode whose elimination creates the least fill. Contrary to popular belief, we find that minimum local fill produces significantly better orderings than minimum degree, albeit at a greatly increased runtime. We describe two simple modifications to this strategy that further improve ordering quality. We also describe a simple modification to minimum degree, which we term approximate minimum mean local fill, that reduces factorization work by roughly 25% with only a small increase in runtime.
We show that there is an O(n(2) log n) algorithm to compute the bandwidth of a chain graph. Here n is the number of vertices in the graph. (C) 1998 Elsevier Science B.V. All rights reserved.
We show that there is an O(n(2) log n) algorithm to compute the bandwidth of a chain graph. Here n is the number of vertices in the graph. (C) 1998 Elsevier Science B.V. All rights reserved.
We study the problem of maintaining the distances and the shortest paths from a source node in a directed graph with arbitrary arc weights, when weight updates of arcs are performed. We propose algorithms that work fo...
详细信息
We address the problem of verifying that a tree is connected using probe operations which check mutual connectivity between two (or more) leaves of the tree. We present optimal algorithms for determining minimal probe...
详细信息
We address the problem of verifying that a tree is connected using probe operations which check mutual connectivity between two (or more) leaves of the tree. We present optimal algorithms for determining minimal probe sets that detect all possible edge and vertex faults in arbitrary trees. Our results are of particular interest for the testing of interconnection substrates in VLSI multichip module packaging technologies. (C) 1998 John Wiley & Sons, Inc.
We introduce a new approach to planning in STRIPS-like domains based on constructing and analyzing a compact structure we call a planning graph. We describe a new planner, graphplan, that uses this paradigm. graphplan...
详细信息
We introduce a new approach to planning in STRIPS-like domains based on constructing and analyzing a compact structure we call a planning graph. We describe a new planner, graphplan, that uses this paradigm. graphplan always returns a shortest possible partial-order plan, or states that no valid plan exists. We provide empirical evidence in favor of this approach, showing that graphplan outperforms the total-order planner, Prodigy, and the partial-order planner, UCPOP, on a variety of interesting natural and artificial planning problems. We also give empirical evidence that the plans produced by graphplan are quite sensible. Since searches made by this approach are fundamentally different from the searches of other common planning methods, they provide a new perspective on the planning problem. (C) 1997 Elsevier Science B.V.
暂无评论