On Minimum Circular Arrangement

Ganapathy, Murali K.; Lodha, Sachin

doi:10.1007/978-3-540-24749-4_35

Cited by 5 publications

(7 citation statements)

References 21 publications

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“…Beyond the graph drawing application, we expect that the presented method is also useful for generating initial solutions to heuristic methods for general N P-hard arrangement problems [3,11].…”

Section: Resultsmentioning

confidence: 99%

“…Bachmaier et al extend the traditional Sugiyama approach by a cyclic level assignment [1]. The lowest level is considered to be on top of the highest level; this modification renders some of the involved optimization problems N P-complete; for the combinatorial background of cyclic arrangements for directed graphs, see also [3,11]. The assignment of levels to nodes in such a cyclic setting is done with various heuristics.…”

Section: Introductionmentioning

confidence: 99%

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Drawing Directed Graphs Clockwise

Pich

2010

Graph Drawing

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We present a method for clockwise drawings of directed cyclic graphs. It is based on the eigenvalue decomposition of a skew-symmetric matrix associated with the graph and draws edges clockwise around the center instead of downwards, as in the traditional hierarchical drawing style. The method does not require preprocessing for cycle removal or layering, which often involves computationally hard problems. We describe an efficient algorithm which produces optimal solutions, and we present some application examples.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Drawing Directed Graphs Clockwise

Pich

2010

Graph Drawing

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“…Whenever LB (U ) plus the shortest path h * (U ) to the current state U is equal to or exceeds the upper bound UB, the respective state can be fathomed as it cannot improve the solution. We apply the simple lower bound argument introduced by Ganapathy and Lodha [12]. This bound, which is based on the relaxation of the consistent assignment of vehicles to periods, so that for each vehicle u separately outgoing and incoming shipments can be optimally ordered, is defined as follows:…”

Section: Dp-based Exact and Heuristic Solution Proceduresmentioning

confidence: 99%

“…Very few papers have treated the CAP up to now. Except for Liberatore , who innovated the problem and proved NP‐hardness, there are the papers by Naor and Schwartz ; Ganapathy and Lodha , who all provide different approximation algorithms for the CAP. From an application perspective, the CAP is mainly applied for sending data packages on multicast computer servers and for graph drawing .…”

Section: Introductionmentioning

confidence: 99%

Synchronization in hub terminals with the circular arrangement problem

Boysen

Emde

Stephan

et al. 2015

Naval Research Logistics

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Hub terminals are important entities in modern distribution networks and exist for any transportation device, that is, cross docks and parcel distribution centers for trucks, container ports for ships, railway yards for trains, and hub airports for aircraft. In any of these hubs, the mid-term planning task of synchronizing the transshipment of goods and passengers when servicing the transportation devices has to be solved, for which many different solution approaches specifically tailored to the respective application exist. We, however, take a unified view on synchronization in hubs and aim at a general building block. As a point of origin, a basic vertex ordering problem, the circular arrangement problem (CAP), is identified. We explain the relation between the CAP and hub processes, develop suited algorithms for solving the CAP, and extend the basic CAP by multiple additions, for example, arrival times, limited storage space, and multiple service points, make the problem adaptable to a wide range of hub terminals.

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“…This problem is reducible from the extensively studied NP-complete problem of Minimum Linear Arrangement [9]. Additional related circular arrangement problems and applications are mentioned in [6,14]. Another NP-hard problem is Circular Crossing Minimization [15], where the goal is to minimize the number of edge crossings in the layout.…”

Section: Node Placementmentioning

confidence: 99%

Improved Circular Layouts

Gansner

Koren

Graph Drawing

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Abstract. Circular graph layout is a drawing scheme where all nodes are placed on the perimeter of a circle. An inherent issue with circular layouts is that the rigid restriction on node placement often gives rise to long edges and an overall dense drawing. We suggest here three independent, complementary techniques for lowering the density and improving the readability of circular layouts. First, a new algorithm is given for placing the nodes on the circle such that edge lengths are reduced. Second, we enhance the circular drawing style by allowing some of the edges to be routed around the exterior of the circle. This is accomplished with an algorithm for optimally selecting such a set of externally routed edges. The third technique reduces density by coupling groups of edges as bundled splines that share part of their route. Together, these techniques are able to reduce clutter, density and crossings compared with existing methods.

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On Minimum Circular Arrangement

Cited by 5 publications

References 21 publications

Drawing Directed Graphs Clockwise

Drawing Directed Graphs Clockwise

Synchronization in hub terminals with the circular arrangement problem

Improved Circular Layouts

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