A tight layout of the cube-connected cycles

Preparata and Vuillemin proposed the cubeconnected cycles (CCC) in 1981 [lS], and in the same paper, gave an asymptotically-optimal layout scheme for the CCC. We give a new layout scheme for the CCC which requires less than half of the area of th,e Preparata- Vuillemin layout. We also give a non-trivial lower bound on the layout area of the CCC. There is a constant factor of 2 between the new layout and the lower bound. We conjectur.e that the new layout is optimal (minimal).published_or_final_versio

A tight layout of the cube-connected cycles

Preparata and Vuillemin proposed the cubeconnected cycles (CCC) in 1981 [lS], and in the same paper, gave an asymptotically-optimal layout scheme for the CCC. We give a new layout scheme for the CCC which requires less than half of the area of th,e Preparata- Vuillemin layout. We also give a non-trivial lower bound on the layout area of the CCC. There is a constant factor of 2 between the new layout and the lower bound. We conjectur.e that the new layout is optimal (minimal).published_or_final_versio

Tighter layouts of the cube-connected cycles

Preparata and Vuillemin proposed the cube-connected cycles (CCC) and its compact layout in 1981 [17]. We give a new layout of the CCC which uses less than half the area of the Preparata-Vuillemin layout. We also give a lower bound on the layout area of the CCC. The area of the new layout deviates from this bound by a small constant factor. If we 'unfold' the cycles in the CCC, the resulting structure can be laid out in optimal area.published_or_final_versio

Ramified rectilinear polygons: coordinatization by dendrons

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 $l_1$-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 $D_4$), ramified rectilinear polygons are universal: every finite group is the automorphism group of some ramified rectilinear polygon.Comment: 27 pages, 6 figure

Near-Memory Address Translation

Memory and logic integration on the same chip is becoming increasingly cost effective, creating the opportunity to offload data-intensive functionality to processing units placed inside memory chips. The introduction of memory-side processing units (MPUs) into conventional systems faces virtual memory as the first big showstopper: without efficient hardware support for address translation MPUs have highly limited applicability. Unfortunately, conventional translation mechanisms fall short of providing fast translations as contemporary memories exceed the reach of TLBs, making expensive page walks common. In this paper, we are the first to show that the historically important flexibility to map any virtual page to any page frame is unnecessary in today's servers. We find that while limiting the associativity of the virtual-to-physical mapping incurs no penalty, it can break the translate-then-fetch serialization if combined with careful data placement in the MPU's memory, allowing for translation and data fetch to proceed independently and in parallel. We propose the Distributed Inverted Page Table (DIPTA), a near-memory structure in which the smallest memory partition keeps the translation information for its data share, ensuring that the translation completes together with the data fetch. DIPTA completely eliminates the performance overhead of translation, achieving speedups of up to 3.81x and 2.13x over conventional translation using 4KB and 1GB pages respectively.Comment: 15 pages, 9 figure

On crossing numbers of hypercubes and cube connected cycles

Recently the hypercube-like networks have received considerable attention in the field of parallel computing due to its high potential for system availability and parallel execution of algorithms. The crossing number ${\rm cr}(G)$ of a graph $G$ is defined as the least number of crossings of its edges when $G$ is drawn in a plane. Crossing numbers naturally appear in the fabrication of VLSI circuit and provide a good area lower bound argument in VLSI complexity theory. According to the survey paper of Harary et al., all that is known on the exact values of an n-dimensional hypercube ${\rm cr}(Q_n)$ is ${\rm cr}(Q_3)=0, {\rm cr}(Q_4)=8$ and ${\rm cr}(Q_5)\le 56.$ We prove the following tight bounds on ${\rm cr}(Q_n)$ and ${\rm cr}(CCC_n)$: $$\frac{4^n}{20} - (n+1)2^{n-2} < {\rm cr}(Q_n) < \frac{4^n}{6} -n^22^{n-3}$$ $$\frac{4^n}{20} - 3(n+1)2^{n-2} < {\rm cr}(CCC_n) < \frac{4^n}{6} + 3n^22^{n-3}.$$ Our lower bounds on ${\rm cr}(Q_n)$ and ${\rm cr}(CCC_n)$ give immediately alternative proofs that the area complexity of {\it hypercube} and $CCC$ computers realized on VLSI circuits is $A=\Omega (4^n)

Characterisation of a new VUV beamline at the Daresbury SRS using a dispersed fluorescence apparatus incorporating CCD detection

The design and performance of a new normal incidence monochromator at the Daresbury Synchrotron Radiation Source, optimised for experiments requiring high flux of vacuum-UV radiation, are described. The re-developed beamline 3.1, based on the Wadsworth design of monochromator, is the source of tunable vacuum-UV photons in the range 4 – 31 eV, providing over two orders of magnitude more flux than the vacuum-UV, Seya monochromator in its previous manifestation. The undispersed and dispersed fluorescence spectra resulting from photoexcitation of N$_2$, CO$_2$, CF$_4$ and C$_6$F$_6$ are presented. Emitting species observed were N$_2^+$ B$^2\Sigma_u^+$ - X$^2\Sigma_g^+$, CO$_2^+$ A$^2\Pi_u$ - X$^2\Pi_g$ and B$^2\Sigma_u^+$ - X$^2\Pi_g$, CF$_4$$^+$ C$^2$T$_2$ - X$^2$T$_1$ and C$^2$T$_2$ - A$^2$T$_2$, CF$_3$* $^2$A$^’_2$ - $^2$A$^”_2$, and C$_6$F$_6^+$ B$^2$A$_{2u}$ - X$^2$E$_{1g}$. A CCD multi-channel detector has significantly reduced the time period needed to record dispersed fluorescence spectra with a comparable signal-to-noise ratio

Parallel computation on sparse networks of processors

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