Gila Morgenstern

GUARDING ORTHOGONAL ART GALLERIES WITH SLIDING CAMERAS

A system for networking dispatch-type of communications. A plurality of radio cells are coupled to a centralized hub controller via the public switched telephone network. The radio cells are networked together via the hub controller using one or more telephone voice lines and a respective data line for providing communications between each radio cell and the hub controller. Data packets are transferred between the radio cells and the hub controller on the data lines to set up a path for the dispatch communications on the telephone voice lines. The hub controller carries out a trunking function of the telephone voice lines so that the number of voice lines are minimized, while yet preventing blocking of dispatch communications.

TYPENESS FOR ω-REGULAR AUTOMATA

We introduce and study three notions of typeness for automata on infinite words. For an acceptance-condition class γ (that is, γ is weak, Buchi, co-Buchi, Rabin, or Streett), deterministic γ-typeness asks for the existence of an equivalent γ-automaton on the same deterministic structure, nondeterministic γ-typeness asks for the existence of an equivalent γ-automaton on the same structure, and γ-powerset-typeness asks for the existence of an equivalent γ-automaton on the (deterministic) powerset structure – one obtained by applying the subset construction. The notions are helpful in studying the complexity and complication of translations between the various classes of automata. For example, we prove that deterministic Buchi automata are co-Buchi type; it follows that a translation from deterministic Buchi to deterministic co-Buchi automata, when exists, involves no blow up. On the other hand, we prove that nondeterministic Buchi automata are not co-Buchi type; it follows that a translation from a nondeterministic Buchi to nondeterministic co-Buchi automata, when exists, should be more complicated than just redefining the acceptance condition. As a third example, by proving that nondeterministic co-Buchi automata are Buchi-powerset type, we show that a translation of nondeterministic co-Buchi to deterministic Buchi automata, when exists, can be done applying the subset construction. We give a complete picture of typeness for the weak, Buchi, co-Buchi, Rabin, and Streett acceptance conditions, and discuss its usefulness.

Approximation algorithms for B 1 -EPG graphs

The edge intersection graphs of paths on a grid (or EPG graphs) are graphs whose vertices can be represented as simple paths on a rectangular grid such that two vertices are adjacent if and only if the corresponding paths share at least one edge of the grid. We consider the case of single-bend paths, namely, the class known as B1-EPG graphs. The motivation for studying these graphs comes from the context of circuit layout problems. It is known that recognizing B1-EPG graphs is NP-complete, nevertheless, optimization problems when given a set of paths in the grid are of considerable practical interest. In this paper, we show that the coloring problem and the maximum independent set problem are both NP-complete for B1-EPG graphs, even when the EPG representation is given. We then provide efficient 4-approximation algorithms for both of these problems, assuming the EPG representation is given. We conclude by noting that the maximum clique problem can be optimally solved in polynomial time for B1-EPG graphs, even when the EPG representation is not given.

Conflict-Free Coloring of points on a line with respect to a set of intervals

We present approximation algorithms for CF-coloring of points on a line with respect to a given set of intervals. For the restricted case where no two intervals have a common right endpoint, we present a 2-approximation algorithm, and, for the general case where intervals may share a right endpoint, we present a 4-approximation algorithm. The running time of both algorithms is O ( n log n ) .

MULTI COVER OF A POLYGON MINIMIZING THE SUM OF AREAS

We consider a geometric optimization problem that arises in sensor network design. Given a polygon P (possibly with holes) with n vertices, a set Y of m points representing sensors, and an integer k, 1 ≤ k ≤ m. The goal is to assign a sensing range, ri, to each of the sensors yi ∈ Y, such that each point p ∈ P is covered by at least k sensors, and the cost, , of the assignment is minimized, where α is a constant. In this paper, we assume that α = 2, that is, find a set of disks centered at points of Y, such that (i) each point in P is covered by at least k disks, and (ii) the sum of the areas of the disks is minimized. We present, for any constant k ≥ 1, a polynomial-time c1-approximation algorithm for this problem, where c1 = c1(k) is a constant. The discrete version, where one has to cover a given set of n points, X, by disks centered at points of Y, arises as a subproblem. We present a polynomial-time c2-approximation algorithm for this problem, where c2 = c2(k) is a constant.

Approximation Schemes for Covering and Packing

The local search framework for obtaining PTASs for NP-hard geometric optimization problems was introduced, independently, by Chan and Har-Peled [6] and Mustafa and Ray [17]. In this paper, we generalize the framework by extending its analysis to additional families of graphs, beyond the family of planar graphs. We then present several applications of the generalized framework, some of which are very different from those presented to date (using the original framework). These applications include PTASs for finding a maximum l-shallow set of a set of fat objects, for finding a maximum triangle matching in an l-shallow unit disk graph, and for vertex-guarding a (not-necessarily-simple) polygon under an appropriate shallowness assumption.

Optimal Cover of Points by Disks in a Simple Polygon

Let

Do directional antennas facilitate in reducing interferences

P

Settling the bound on the rectilinear link radius of a simple rectilinear polygon

be a simple polygon, and let

Symmetric Connectivity with Directional Antennas

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