Connected Searching of Weighted Trees
نویسنده
چکیده
In this paper we consider the problem of connected edge searching of weighted trees. Barrière et al. claim in [Capture of an intruder by mobile agents, SPAA’02 (2002) 200-209] that there exists a polynomial-time algorithm for finding an optimal search strategy, that is, a strategy that minimizes the number of used searchers. However, due to some flaws in their algorithm, the problem turns out to be open. It is proven in this paper that the considered problem is strongly NP-complete even for node-weighted trees (the weight of each edge is 1) with one vertex of degree greater than 2. It is also shown that there exists a polynomial-time algorithm for finding an optimal connected search strategy for a given bounded degree tree with arbitrary weights on the edges and on the vertices. This is an FPT algorithm with respect to the maximum degree of a tree.
منابع مشابه
Approximate search strategies for weighted trees
The problems of (classical) searching and connected searching of weighted trees are known to be computationally hard. In this work we give a polynomial-time 3-approximation algorithm that finds a connected search strategy of a given weighted tree. This in particular yields constant factor approximation algorithms for the (non-connected) classical searching problems and for the weighted pathwidt...
متن کاملConnected and Internal Graph Searching
This paper is concerned with the graph searching game. The search number s(G) of a graph G is the smallest number of searchers required to “clear” G. A search strategy is monotone (m) if no recontamination ever occurs. It is connected (c) if the set of clear edges always forms a connected subgraph. It is internal (i) if the removal of searchers is not allowed. The difficulty of the “connected” ...
متن کاملOn Weighted Edge-Searching
In this document we address some complications regarding the weighted edge-searching problem. This variant of edge-searching extends the original problem by considering situations where multiple searchers may be required to clear a single edge or guard a single vertex. We show that previous work on this topic overlooked a fundamental problem that arises from the addition of weights. As a conseq...
متن کاملA method for analyzing the problem of determining the maximum common fragments of temporal directed tree, that do not change with time
In this study two actual types of problems are considered and solved: 1) determining the maximum common connected fragment of the T-tree (T-directed tree) which does not change with time; 2) determining all maximum common connected fragments of the T-tree (T-directed tree) which do not change with time. The choice of the primary study of temporal directed trees and trees is justified by the wid...
متن کاملOn Hop Roman Domination in Trees
Let $G=(V,E)$ be a graph. A subset $Ssubset V$ is a hop dominating setif every vertex outside $S$ is at distance two from a vertex of$S$. A hop dominating set $S$ which induces a connected subgraph is called a connected hop dominating set of $G$. Theconnected hop domination number of $G$, $ gamma_{ch}(G)$, is the minimum cardinality of a connected hopdominating set of $G$...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010