13217169
New Method for Constructing Isospectral Graphs
There exist several methods available to construct isospectral molecular graphs.l-1° Recently, M. RandiC and his co-workers proposed the ring enlargement process (vide infra) for constructing subspectral graphs.” This method can be also used to construct isospectral graphs; however, it may fail sometimes. For example, the isospectral pair 1, 2 can be enlarged to the isospectral graphs 3,4 shown in Figure 1, where the symbol ‘‘z” signifies an isospectral pair and “-” denotes the ring enlargement procedure. Eigenvalues of 3, 4 are divided into two parts, those in coincidence with that of 1 , 2 are listed on the left, and the remaining ones are put on the right. On the other hand, graph pairs 7, 8 and 9, 10 in Figure 2, yielded from isospectral pair 5, 6, are not isospectral. Noticing the difference of the spectrum of graphs XX, XX’ (by “XX, XX”’ we mean that they are generated from subgraph X in double size by the enlargement procedure, such as 7, 8 from 5; and 9, 10 from a), RandiC suggested that if XX, XX’ are bipartite, they should be isospectral, because all eigenvalues now occur in pairs and the difference between XX and XX’ disappears. Hence, he proposed a conjecture below. CONJECTURE: If graph X yields nonisomorphic bipartite enlargements XX, XX’, etc.; the derived graphs are not only superspectral to the parent graph X but are also mutually cospectral.
33033165
Embedding in Benzenoid Hydrocarbons
Using the embedding scheme and a rule we proposed previously, in this work we discuss common eigenvalues and their degeneracies in benzenoid molecular graphs.
2027823
Evolutionary Search for Faces from Line Drawings
Single 2D line drawing is a straightforward method to illustrate 3D objects. The faces of an object depicted by a line drawing give very useful information for the reconstruction of its 3D geometry. Two recently proposed methods for face identification from line drawings are based on two steps: finding a set of circuits that may be faces and searching for real faces from the set according to some criteria. The two steps, however, involve two combinatorial problems. The number of the circuits generated in the first step grows exponentially with the number of edges of a line drawing. These circuits are then used as the input to the second combinatorial search step. When dealing with objects having more faces, the combinatorial explosion prevents these methods from finding solutions within feasible time. This paper proposes a new method to tackle the face identification problem by a variable-length genetic algorithm with a novel heuristic and geometric constraints incorporated for local search. The hybrid GA solves the two combinatorial problems simultaneously. Experimental results show that our algorithm can find the faces of a line drawing having more than 30 faces much more efficiently. In addition, simulated annealing for solving the face identification problem is also implemented for comparison.
8844798
Learning not to share
Strong reasons exist for executing a large-scale discrete-event simulation on a cluster of processor nodes (each of which may be a shared-memory multiprocessor or a uniprocessor). This is the architecture of the largest scale parallel machines, and so the largest simulation problems can only be solved this way. It is a common architecture even in less esoteric settings, and is suitable for memory-bound simulations. This paper describes our approach to porting the SSF simulation kernel to this architecture, using the Message Passing Interface (MPI) system. The notable feature of this transformation is to support an efficient two-level synchronization and communication scheme that addresses cost discrepancies between shared-memory and distributed memory. In the initial implementation, we use a globally synchronous approach between distributed-memory nodes, and an asynchronous shared-memory approach within a SMP cluster. The SSF API reflects inherently shared-memory assumptions; we report therefore on our approach for porting an SSF kernel to a cluster of SMP nodes. Experimental results on two architectures are described, for a model of TCP/IP traffic flows over a hierarchical network. The performance on a distributed network of commodity SMPs connected through ethernet is seen to frequently exceed performance on a Sun shared-memory multiprocessor.
205905865
Chinese document layout analysis based on adaptive split-and-merge and qualitative spatial reasoning
The ultimate goal of automatic document processing is to understand the semantics of a document. Towards such an end, one of the primary enabling steps has been to first reason about the layout of the document by means of page segmentation and segment spatial reasoning or labeling. This, in turn, allows for the derivation of document logical organization. This paper describes a generic document segmentation and geometric relation labeling method with applications to Chinese document analysis. Unlike the previous document segmentation methods where text spacing, border lines, and/or a priori layout models based on template matching processing are performed, the present method begins with a hierarchy of partitioned image layers where inhomogeneous higher-level regions are recursively partitioned into lower-level rectangular subregions and at the same time lower-level smaller homogeneous regions are merged into larger homogeneous regions. Furthermore, the derived segment data structure readily enables efficient search for geometric relationships between identified document segments.
33569862
Survey of Double Vertex Graphs
Abstract. Let G be a (V,E) graph of order p≥2. The double vertex graphU2(G) is the graph whose vertex set consists of all 2-subsets of V such that two distinct vertices {x,y} and {u,v} are adjacent if and only if |{x,y}∩{u,v}|=1 and if x=u, then y and v are adjacent in G. For this class of graphs we discuss the regularity, eulerian, hamiltonian, and bipartite properties of these graphs. A generalization of this concept is n-tuple vertex graphs, defined in a manner similar to double vertex graphs. We also review several recent results for n-tuple vertex graphs.
656200
Robust distributed node localization with error management
Location knowledge of nodes in a network is essential for many tasks such as routing, cooperative sensing, or service delivery in ad hoc, mobile, or sensor networks. This paper introduces a novel iterative method ILS for node localization starting with a relatively small number of anchor nodes in a large network. At each iteration, nodes are localized using a least-squares based algorithm. The computation is lightweight, fast, and any-time. To prevent error from propagating and accumulating during the iteration, the error control mechanism of the algorithm uses an error registry to select nodes that participate in the localization, based on their relative contribution to the localization accuracy. Simulation results have shown that the active selection strategy significantly mitigates the effect of error propagation. The algorithm has been tested on a network of Berkeley Mica2 motes with ultrasound TOA ranging devices. We have compared the algorithm with more global methods such as MDS-MAP and SDP-based algorithm both in simulation and on real hardware. The iterative localization achieves comparable location accuracy in both cases, compared to the more global methods, and has the advantage of being fully decentralized.