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The view of a node in a port-labeled network is an infinite tree encoding all walks in the network originating from this node. We prove that for any integers n ≥ D ≥ 1, there exists a port-labeled network with at most n nodes and diameter at most D which contains a pair of nodes whose (infinite) views are different, but whose views truncated to depth Ω(D… (More)

The rotor-router mechanism was introduced as a deterministic alternative to the random walk in undirected graphs. In this model, a set of k identical walkers is deployed in parallel, starting from a chosen subset of nodes, and moving around the graph in synchronous steps. During the process, each node maintains a cyclic ordering of its outgoing arcs, and… (More)

We study the problem of the amount of information required to draw a complete or a partial map of a graph with unlabeled nodes and arbitrarily labeled ports. A mobile agent, starting at any node of an unknown connected graph and walking in it, has to accomplish one of the following tasks: draw a complete map of the graph, i.e., find an isomorphic copy of it… (More)

In this paper we consider the edge ranking problem of weighted trees. We prove that a special instance of this problem, namely edge ranking of multitrees is NP-hard already for multi-trees with diameter at most 10. Note that the same problem but for trees is linearly solvable. We give an O(log n)-approximation polynomial time algorithm for edge ranking of… (More)

We consider a problem of searching an element in a partially ordered set (poset). The goal is to find a search strategy which minimizes the number of comparisons. Ben-Asher, Farchi and Newman considered a special case where the partial order has the maximum element and the Hasse diagram is a tree (tree-like posets) and they gave an O(n 4 log 3 n)-time… (More)

In this paper we consider the vertex ranking problem of weighted trees. We show that this problem is strongly NP-hard. We also give a polynomial-time reduction from the problem of vertex ranking of weighted trees to the vertex ranking of (simple) chordal graphs, which proves that the latter problem is NP-hard. In this way we solve an open problem of Aspvall… (More)

In this paper we deal with the problem of finding an optimal query execution plan in database systems. We improve the analysis of a polynomial-time approximation algorithm due to Makino et al. for designing query execution plans with almost optimal number of parallel steps. This algorithm is based on the concept of edge ranking of graphs. We use a new upper… (More)

It is proven that the connected pathwidth of any graph G is at most 2 · pw(G) + 1, where pw(G) is the pathwidth of G. The method is constructive, i.e. it yields an efficient algorithm that for a given path decomposition of width k computes a connected path decomposition of width at most 2k + 1. The running time of the algorithm is O(dk 2), where d is the… (More)

We consider the problem of leader election among mobile agents operating in an arbitrary network modeled as an undirected graph. Nodes of the network are unlabeled and all agents are identical. Hence the only way to elect a leader among agents is by exploiting asymmetries in their initial positions in the graph. Agents do not know the graph or their… (More)