Pawel Zylinski

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Consider the following survival problem:Given a set of k trajectories (paths) with maximum unit speed in a boundedregion over a (long) time interval [0,T], find another trajectory (if itexists) subject to the same maximum unit speed limit, that avoids (that is, stays at a safe distance of)each of the other trajectories over the entire time interval. We call(More)
Given an undirected, connected graph G with maximum degree , we introduce the concept of a [1, ]-factor k-packing in G, defined as a set of k edgedisjoint subgraphs of G such that every vertex of G has an incident edge in at least one subgraph. The problem of deciding whether a graph admits a [1, ]-factor kpacking is shown to be solvable in linear time for(More)
Given a set L of non-parallel lines in the plane and a nonempty subset L′ ⊆ L, a guarding tree for L′ is a tree contained in the union of the lines in L such that if a mobile guard (agent) runs on the edges of the tree, all lines in L′ are visited by the guard. Similarly, given a connected arrangement S of line segments in the plane and a nonempty subset S(More)
We consider the mixed graph coloring problem. A mixed graph GM = (V,E,A) is a graph with vertex set V and containing edges (set E) and arcs (set A). An edge joining vertices i and j is denoted by {i, j}, while an arc with tail p and head q is denoted by (p, q). A kcoloring of GM is a function φ : V → {1, 2, . . . , k} such that φ(i) 6= φ(j) for {i, j} ∈ E(More)
We revisit the problem of pursuit-evasion in a grid introduced by Sugihara and Suzuki in the lineof-sight vision model. Consider an arbitrary evader Z with the maximum speed of 1 who moves (in a continuous way) on the streets and avenues of an n × n grid Gn. The cunning evader is to be captured by a group of pursuers, possibly only one. The maximum speed of(More)