597 research outputs found

    Considerations for the design of an onboard air traffic situation display

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    The basic concept of remoting information to the cockpit is used to design and develop a computerized airborne traffic situation display device that automatically selects and presents segments of a controller's scope to the aircraft pilot via a narrow band digital data link. These data are integrated with aircraft heading and navigation information to provide a display useful in congested air space. The display can include alphanumerical symbols, air route maps, and controller instructions

    Outerplanar crossing numbers of 3-row meshes, Halin graphs and complete p-partite graphs

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    An outerplanar (also called circular, convex, one-page) drawing of an n-vertex graph G is a drawing in which the vertices are placed on a circle and each edge is drawn using one straight-line segment. We derive exact results for the minimal number of crossings in any outerplanar drawings of the following classes of graphs: 3-row meshes, Halin graphs and complete p−partite graphs with equal size partite sets

    Covering Partial Cubes with Zones

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    A partial cube is a graph having an isometric embedding in a hypercube. Partial cubes are characterized by a natural equivalence relation on the edges, whose classes are called zones. The number of zones determines the minimal dimension of a hypercube in which the graph can be embedded. We consider the problem of covering the vertices of a partial cube with the minimum number of zones. The problem admits several special cases, among which are the problem of covering the cells of a line arrangement with a minimum number of lines, and the problem of finding a minimum-size fibre in a bipartite poset. For several such special cases, we give upper and lower bounds on the minimum size of a covering by zones. We also consider the computational complexity of those problems, and establish some hardness results

    Dynamic source routing for ad hoc networks using the global positioning system

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    Abstract-This paper proposes a new routing protocol for ad hoc networks built -around the source routing technique combined with the location (e.g., GPS coordinates) of nodes obtained by an energy and distance smart dissemination mechanism. The key new observation used is that the location information provides each node with a snapshot of the topology of the complete network from which a source route may be computed locally rather than through route discovery. The resulting protocol has reduced delay, and is more bandwidth and energy efficient, than both traditional (proactive and reactive) ad hoc routing protocols, as well as location based routing protocols

    Infinite motion and 2-distinguishability of graphs and groups

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    A group A acting faithfully on a set X is 2-distinguishable if there is a 2-coloring of X that is not preserved by any nonidentity element of A, equivalently, if there is a proper subset of X with trivial setwise stabilizer. The motion of an element a in A is the number of points of X that are moved by a, and the motion of the group A is the minimal motion of its nonidentity elements. When A is finite, the Motion Lemma says that if the motion of A is large enough (specifically at least 2 log_2 |A|), then the action is 2-distinguishable. For many situations where X has a combinatorial or algebraic structure, the Motion Lemma implies that the action of Aut(X) on X is 2-distinguishable in all but finitely many instances. We prove an infinitary version of the Motion Lemma for countably infinite permutation groups, which states that infinite motion is large enough to guarantee 2-distinguishability. From this we deduce a number of results, including the fact that every locally finite, connected graph whose automorphism group is countably infinite is 2-distinguishable. One cannot extend the Motion Lemma to uncountable permutation groups, but nonetheless we prove that (under the permutation topology) every closed permutation group with infinite motion has a dense subgroup which is 2-distinguishable. We conjecture an extension of the Motion Lemma which we expect holds for a restricted class of uncountable permutation groups, and we conclude with a list of open questions. The consequences of our results are drawn for orbit equivalence of infinite permutation groups

    The generalized 3-edge-connectivity of lexicographic product graphs

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    The generalized kk-edge-connectivity λk(G)\lambda_k(G) of a graph GG is a generalization of the concept of edge-connectivity. The lexicographic product of two graphs GG and HH, denoted by GHG\circ H, is an important graph product. In this paper, we mainly study the generalized 3-edge-connectivity of GHG \circ H, and get upper and lower bounds of λ3(GH)\lambda_3(G \circ H). Moreover, all bounds are sharp.Comment: 14 page

    Ramified rectilinear polygons: coordinatization by dendrons

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    Simple rectilinear polygons (i.e. rectilinear polygons without holes or cutpoints) can be regarded as finite rectangular cell complexes coordinatized by two finite dendrons. The intrinsic l1l_1-metric is thus inherited from the product of the two finite dendrons via an isometric embedding. The rectangular cell complexes that share this same embedding property are called ramified rectilinear polygons. The links of vertices in these cell complexes may be arbitrary bipartite graphs, in contrast to simple rectilinear polygons where the links of points are either 4-cycles or paths of length at most 3. Ramified rectilinear polygons are particular instances of rectangular complexes obtained from cube-free median graphs, or equivalently simply connected rectangular complexes with triangle-free links. The underlying graphs of finite ramified rectilinear polygons can be recognized among graphs in linear time by a Lexicographic Breadth-First-Search. Whereas the symmetry of a simple rectilinear polygon is very restricted (with automorphism group being a subgroup of the dihedral group D4D_4), ramified rectilinear polygons are universal: every finite group is the automorphism group of some ramified rectilinear polygon.Comment: 27 pages, 6 figure

    Regular graphs of large girth and arbitrary degree

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    For every integer d > 9, we construct infinite families {G_n}_n of d+1-regular graphs which have a large girth > log_d |G_n|, and for d large enough > 1,33 log_d |G_n|. These are Cayley graphs on PGL_2(q) for a special set of d+1 generators whose choice is related to the arithmetic of integral quaternions. These graphs are inspired by the Ramanujan graphs of Lubotzky-Philips-Sarnak and Margulis, with which they coincide when d is prime. When d is not equal to the power of an odd prime, this improves the previous construction of Imrich in 1984 where he obtained infinite families {I_n}_n of d+1-regular graphs, realized as Cayley graphs on SL_2(q), and which are displaying a girth > 0,48 log_d |I_n|. And when d is equal to a power of 2, this improves a construction by Morgenstern in 1994 where certain families {M_n}_n of 2^k+1-regular graphs were shown to have a girth > 2/3 log_d |M_n|.Comment: (15 pages) Accepted at Combinatorica. Title changed following referee's suggestion. Revised version after reviewing proces
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