5,667 research outputs found
Maintaining Approximate Maximum Matching in an Incremental Bipartite Graph in Polylogarithmic Update Time
No full textA sparse subgraph G' of G is called a matching sparsifier if the size or weight of matching in G' is approximately equal to the size or weight of maximum matching in G. Recently, algorithms have been developed to find matching sparsifiers in a static bipartite graph. In this paper, we show that we can find matching sparsifier even in an incremental bipartite graph.
This observation leads to following results: 1. We design an algorithm that maintains a (1+epsilon) approximate matching in an incremental bipartite graph in O(log^2(n) / (epsilon^{4}) update time. 2. For weighted graphs, we design an algorithm that maintains (1+epsilon) approximate weighted matching in O((log(n)*log(n*N)) / (epsilon^4) update time where \maxweight is the maximum weight of any edge in the graph
Replication Data for: Toroidal versus Fano resonances in high Q planar THz metamaterials
No full textRadiative losses are crucial in optimizing the performance of metamaterial based devices across the electromagnetic spectrum. Introducing structural asymmetry in meta-atom design leads to the excitation of sharp Fano resonances with reduced radiative losses. However, at larger asymmetries, the Fano resonance becomes highly radiative which results in the broadening of the asymmetric line shaped resonances. Here, we experimentally demonstrate a scheme to couple mirrored asymmetric Fano resonators through interaction of anti-aligned magnetic dipoles which results in a strong toroidal resonance in two-dimensional planar metasurface. The quality (Q) factor and the figure of merit of the toroidal dipolar mode is significantly higher than the Fano resonance. Moreover, we discover that the exponential decay of the Q factor of toroidal resonance mode occurs at half the rate of that in the Fano resonance as the asymmetry of the system is enhanced which indicates significant tailoring and the suppression of the radiative loss channel in the toroidal configuration. The weakly-radiative toroidal resonance in planar metamaterials offers the potential for applications in terahertz and optical sensing, spectroscopy, narrow-band filtering and large modulation
Replication Data for: 150 Gbps THz Chipscale Topological Photonic Diplexer
No full textPhotonic diplexers are being widely investigated for high data transfer rates in on-chip communication. However, dividing the available spectrum into non-overlapping multicarrier frequency sub-bands has remained a challenge in designing frequency-selective time-invariant channels. Here, we report an on-chip topological diplexer exhibiting terahertz frequency band filtering through Klein tunnelling of topological edge modes. The silicon topological diplexer chip facilitates two high-speed channels with quadrature amplitude modulation (QAM) over a broad bandwidth of 12.5 GHz each. These channels operate at carrier frequencies of 305 GHz and 321.6 GHz, achieving a combined diplexer capacity of 150 Gbit/s. To ensure minimal interference between adjacent channels, a guard band is implemented. Topologically protected edge modes suppress the frequency selective fading of the broadband signals and hold promise for diverse integrated photonic applications spanning terahertz and telecommunication realms, including the design of lossless topological multiplexers, interconnects, antennas, and modulators for the sixth to X generation (6G to XG) wireless
Replication Data for: Terahertz Sensing with Optimized Q/Veff Metasurface Cavities
No full textConfinement of electromagnetic radiation in a subwavelength cavity is an important platform for strong light–matter interaction as it enables efficient design of photonic switches, modulators, and ultrasensitive sensors. Metallic metasurfaces consist of an array of planar cavities that allow easy access to confined electromagnetic modes on the surface. However, the radiative and nonradiative losses limit the quality factor (Q) of the resonantly confined mode. Therefore, metasurface designs with effectively low mode volume (Veff) cavities become extremely important for enhancing the photonic density of states. Here, a symmetric Lorentzian resonant metasurface with lower Veff is demonstrated as compared to asymmetric Fano resonators. Lower mode volume and optimized Q/Veff metasurfaces reveal enhanced sensitivity for ultrathin analyte overlayers deposited on metasurfaces signaling enhanced light–matter interaction. Such metasurfaces with tightly confined electromagnetic modes could find wide range of applications in the development of terahertz metadevices including ultrasensitive sensors, bandpass filters, and energy-efficient modulators
Investing in Tax Deferred Schemes
No full textManoj Gupta is an Assistant Professor in the Department of Finance. Real Estate and Decision Sciences. Barton School of Business at Wichita State University. Avanti P. Sethi is an Associate Professor and Chair in the Depanment of Finance, Real Estate and Decision Sciences, Barton School of Business at Wichita State University
Generic Single Edge Fault Tolerant Exact Distance Oracle
No full textGiven an undirected unweighted graph G and a source set S of |S| = sigma sources, we want to build a data structure which can process the following query Q(s,t,e): find the shortest distance from s to t avoiding an edge e, where s in S and t in V. When sigma=n, Demetrescu, Thorup, Chowdhury and Ramachandran (SIAM Journal of Computing, 2008) designed an algorithm with O~(n^2) space and O(1) query time. A natural open question is to generalize this result to any number of sources. Recently, Bil{ò} et. al. (STACS 2018) designed a data-structure of size O~(sigma^{1/2}n^{3/2}) with the query time of O(sqrt{n sigma}) for the above problem. We improve their result by designing a data-structure of size O~(sigma^{1/2} n^{3/2}) that can answer queries in O~(1) time.
In a related problem of finding fault tolerant subgraph, Parter and Peleg (ESA 2013) showed that if detours of replacement paths ending at a vertex t are disjoint, then the number of such paths is O(sqrt{n sigma}). This eventually gives a bound of O(n sqrt{n sigma}) = O(sigma^{1/2}n^{3/2}) for their problem. Disjointness of detours is a very crucial property used in the above result. We show a similar result for a subset of replacement path which may not be disjoint. This result is the crux of our paper and may be of independent interest
Multiple Source Dual Fault Tolerant BFS Trees
No full textLet G=(V,E) be a graph with n vertices and m edges, with a designated set of sigma sources S subseteq V. The fault tolerant subgraph for any graph problem maintains a sparse subgraph H=(V,E') of G with E' subseteq E, such that for any set F of k failures, the solution for the graph problem on G\F is maintained in its subgraph H\F. We address the problem of maintaining a fault tolerant subgraph for computing Breath First Search tree (BFS) of the graph from a single source s in V (referred as k FT-BFS) or multiple sources S subseteq V (referred as k FT-MBFS). We simply refer to them as FT-BFS (or FT-MBFS) for k=1, and dual FT-BFS (or dual FT-MBFS) for k=2.
The problem of k FT-BFS was first studied by Parter and Peleg [ESA13]. They designed an algorithm to compute FT-BFS subgraph of size O(n^{3/2}). Further, they showed how their algorithm can be easily extended to FT-MBFS requiring O(sigma^{1/2}n^{3/2}) space. They also presented matching lower bounds for these results. The result was later extended to solve dual FT-BFS by Parter [PODC15] requiring (n^{5/3}) space, again with matching lower bounds. However, their result was limited to only edge failures in undirected graphs and involved very complex analysis. Moreover, their solution doesn't seems to be directly extendible for dual FT-MBFS problem.
We present a similar algorithm to solve dual FT-BFS problem with a much simpler analysis. Moreover, our algorithm also works for vertex failures and directed graphs, and can be easily extended to handle dual FT-MBFS problem, matching the lower bound of O(sigma^{1/3}n^{5/3}) space described by Parter [PODC15]. The key difference in our approach is a much simpler classification of path interactions which formed the basis of the analysis by Parter [PODC15]
Replication Data for: 327 Gbps THz Silicon Photonic Interconnect with Sub-λ Bends
No full textMiniaturized photonic devices at the terahertz (THz) band are envisioned to bring significant enhancement to data transfer capacity and integration density for computing and future wireless communications. Broadband silicon waveguiding technology has continuously matured to advance low-loss platforms for integrated solutions. However, challenges are faced in realizing compact waveguiding platforms with different degrees of bends due to bend induced losses and mode distortion. Here, we demonstrate multiple bend incorporated photonic crystal waveguide platform for multi-carrier on-chip transmission. Our silicon interconnect device exhibits optimized bending radius to the free space wavelength ratio of 0.74, without signal distortion and transmission bandwidth of 90 GHz, representing 25.4% fractional bandwidth at 355 GHz. The broadband waveguide interconnect enables an aggregate data transfer rate of 327 Gbps by sending the complex modulated data over multiple carriers. This work augments the development of THz photonic integrated circuit (TPIC) for the future generations of on-chip high data-rate interconnect and wireless communication, ranging from the sixth to X generation (6G to XG)
Replication Data for: A Toroidal Metamaterial Switch
No full textToroidal dipole is a localized electromagnetic excitation that plays an important role in determining the fundamental properties of matter due to its unique potential to excite nearly non-radiating charge-current configuration. Toroidal dipoles were recently discovered in metamaterial systems where it has been shown that these dipoles manifest as poloidal currents on the surface of a torus and are distinctly different from the traditional electric and magnetic dipoles. Here, we demonstrate an active toroidal metamaterial switch in which the toroidal dipole could be dynamically switched to the fundamental electric dipole or magnetic dipole, through selective inclusion of active elements in a hybrid metamolecule design. Active switching of non-radiating toroidal configuration into highly radiating electric and magnetic dipoles can have significant impact in controlling the electromagnetic excitations in free space and matter that could have potential applications in designing efficient lasers, sensors, filters, and modulators
Replication Data for: Electrically Tunable Topological Notch Filter for THz Integrated Photonics
No full textElectromagnetic filtering is essential for emerging integrated photonic technologies and widely adaptable processing of high-bandwidth signals. Conventional electro-optic modulator-based photonic approach for signal filtering at microwave frequencies could not be implemented at terahertz (THz) frequencies due to the unavailability of the THz signal-driven optical modulator. Here, we demonstrate an electrically tunable on-chip THz photonic notch filter based on the topologically protected valley hall waveguide-cavity platform. Our device shows a significantly large notch suppression depth of more than 20 dB with a return loss of 13 dB at in the entire tuning range of notch frequency. The feedback control circuit enabled precise control of the notch frequency shift with a minimum step size of 7 MHz. Our work extends the application of topological photonic crystals in developing THz integrated photonic devices for transformative technologies, including sixth generation (6G) communication and high-resolution spectral sensing
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