arXiv subjects

Ran Duan

Publications and source records attributed to Ran Duan.

At least 37 records · Page 2Linked to original sources

arXiv2021

Maintaining Exact Distances under Multiple Edge Failures

We present the first compact distance oracle that tolerates multiple failures and maintains exact distances. Given an undirected weighted graph $G = (V, E)$ and an arbitrarily large constant $d$, we construct an oracle that given vertices $u, v \in V$ and a set of $d$ edge failures $D$, outputs the exact distance between $u$ and $v$ in $G - D$ (that is, $G$ with edges in $D$ removed). Our oracle has space complexity $O(d n^4)$ and query time $d^{O(d)}$. Previously, there were compact approximate distance oracles under multiple failures [Chechik, Cohen, Fiat, and Kaplan, SODA'17; Duan, Gu, and Ren, SODA'21], but the best exact distance oracles under $d$ failures require essentially $Ω(n^d)$ space [Duan and Pettie, SODA'09]. Our distance oracle seems to require $n^{Ω(d)}$ time to preprocess; we leave it as an open question to improve this preprocessing time.

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arXiv2021

CRAFTS for Fast Radio Bursts Extending the dispersion-fluence relation with new FRBs detected by FAST

We report three new FRBs discovered by the Five-hundred-meter Aperture Spherical radio Telescope (FAST), namely FRB 181017.J0036+11, FRB 181118 and FRB 181130, through the Commensal Radio Astronomy FAST Survey (CRAFTS). Together with FRB 181123 that was reported earlier, all four FAST-discovered FRBs share the same characteristics of low fluence ($\leq$0.2 Jy ms) and high dispersion measure (DM, $>1000$ \dmu), consistent with the anti-correlation between DM and fluence of the entire FRB population. FRB 181118 and FRB 181130 exhibit band-limited features. FRB 181130 is prominently scattered ($τ_s\simeq8$ ms) at 1.25 GHz. FRB 181017.J0036+11 has full-bandwidth emission with a fluence of 0.042 Jy ms, which is one of the faintest FRB sources detected so far. CRAFTS starts to built a new sample of FRBs that fills the region for more distant and fainter FRBs in the fluence-$\rm DM_E$ diagram, previously out of reach of other surveys. The implied all sky event rate of FRBs is $1.24^{+1.94}_{-0.90} \times 10^5$ sky$^{-1}$ day$^{-1}$ at the $95\%$ confidence interval above 0.0146 Jy ms. We also demonstrate here that the probability density function of CRAFTS FRB detections is sensitive to the assumed intrinsic FRB luminosity function and cosmological evolution, which may be further constrained with more discoveries.

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arXiv2020

Approximate Distance Oracles Subject to Multiple Vertex Failures

Given an undirected graph $G=(V,E)$ of $n$ vertices and $m$ edges with weights in $[1,W]$, we construct vertex sensitive distance oracles (VSDO), which are data structures that preprocess the graph, and answer the following kind of queries: Given a source vertex $u$, a target vertex $v$, and a batch of $d$ failed vertices $D$, output (an approximation of) the distance between $u$ and $v$ in $G-D$ (that is, the graph $G$ with vertices in $D$ removed). An oracle has stretch $α$ if it always holds that $δ_{G-D}(u,v)\le\tildeδ(u,v)\leα\cdotδ_{G-D}(u,v)$, where $δ_{G-D}(u,v)$ is the actual distance between $u$ and $v$ in $G-D$, and $\tildeδ(u,v)$ is the distance reported by the oracle. In this paper we construct efficient VSDOs for any number $d$ of failures. For any constant $c\geq 1$, we propose two oracles: $\bullet$ The first oracle has size $n^{2+1/c}(\log n/ε)^{O(d)}\cdot \log W$, answers a query in ${\rm poly}(\log n,d^c,\log\log W,ε^{-1})$ time, and has stretch $1+ε$, for any constant $ε>0$. $\bullet$ The second oracle has size $n^{2+1/c}{\rm poly}(\log (nW),d)$, answers a query in ${\rm poly}(\log n,d^c,\log\log W)$ time, and has stretch ${\rm poly}(\log n,d)$. Both of these oracles can be preprocessed in time polynomial in their space complexity. These results are the first approximate distance oracles of poly-logarithmic query time for any constant number of vertex failures in general undirected graphs. Previously there are $(1+ε)$-approximate $d$-edge sensitive distance oracles [Chechik et al. 2017] answering distance queries when $d$ edges fail, which have size $O(n^2(\log n/ε)^d\cdot d\log W)$ and query time ${\rm poly}(\log n, d, \log\log W)$.

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arXiv2020

Readout for Kinetic-Inductance-Detector-Based Submillimeter Radio Astronomy

A substantial amount of important scientific information is contained within astronomical data at the submillimeter and far-infrared (FIR) wavelengths, including information regarding dusty galaxies, galaxy clusters, and star-forming regions; however, these wavelengths are among the least-explored fields in astronomy because of the technological difficulties involved in such research. Over the past 20 years, considerable efforts have been devoted to developing submillimeter- and millimeter-wavelength astronomical instruments and telescopes. The number of detectors is an important property of such instruments and is the subject of the current study. Future telescopes will require as many as hundreds of thousands of detectors to meet the necessary requirements in terms of the field of view, scan speed, and resolution. A large pixel count is one benefit of the development of multiplexable detectors that use kinetic inductance detector (KID) technology. This paper presents the development of all aspects of the readout electronics for a KID-based instrument, which enabled one of the largest detector counts achieved to date in submillimeter-/millimeter-wavelength imaging arrays: a total of 2304 detectors. The work presented in this paper had been implemented in the MUltiwavelength Submillimeter Inductance Camera (MUSIC), a instrument for the Caltech Submillimeter Observatory (CSO) between 2013 and 2015.

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arXiv2020

Near-linear Time Algorithm for Approximate Minimum Degree Spanning Trees

Given a graph $G = (V, E)$, we wish to compute a spanning tree whose maximum vertex degree, i.e. tree degree, is as small as possible. Computing the exact optimal solution is known to be NP-hard, since it generalizes the Hamiltonian path problem. For the approximation version of this problem, a $\tilde{O}(mn)$ time algorithm that computes a spanning tree of degree at most $Δ^* +1$ is previously known [Fürer \& Raghavachari 1994]; here $Δ^*$ denotes the minimum tree degree of all the spanning trees. In this paper we give the first near-linear time approximation algorithm for this problem. Specifically speaking, we propose an $\tilde{O}(\frac{1}{ε^7}m)$ time algorithm that computes a spanning tree with tree degree $(1+ε)Δ^* + O(\frac{1}{ε^2}\log n)$ for any constant $ε\in (0,\frac{1}{6})$. Thus, when $Δ^*=ω(\log n)$, we can achieve approximate solutions with constant approximate ratio arbitrarily close to 1 in near-linear time.

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arXiv2020

Roundtrip Spanners with $(2k-1)$ Stretch

A roundtrip spanner of a directed graph $G$ is a subgraph of $G$ preserving roundtrip distances approximately for all pairs of vertices. Despite extensive research, there is still a small stretch gap between roundtrip spanners in directed graphs and undirected graphs. For a directed graph with real edge weights in $[1,W]$, we first propose a new deterministic algorithm that constructs a roundtrip spanner with $(2k-1)$ stretch and $O(k n^{1+1/k}\log (nW))$ edges for every integer $k> 1$, then remove the dependence of size on $W$ to give a roundtrip spanner with $(2k-1)$ stretch and $O(k n^{1+1/k}\log n)$ edges. While keeping the edge size small, our result improves the previous $2k+ε$ stretch roundtrip spanners in directed graphs [Roditty, Thorup, Zwick'02; Zhu, Lam'18], and almost matches the undirected $(2k-1)$-spanner with $O(n^{1+1/k})$ edges [Althöfer et al. '93] when $k$ is a constant, which is optimal under Erdös conjecture.

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arXiv2020

A Fast Radio Burst discovered in FAST drift scan survey

We report the discovery of a highly dispersed fast radio burst, FRB~181123, from an analysis of $\sim$1500~hr of drift-scan survey data taken using the Five-hundred-meter Aperture Spherical radio Telescope (FAST). The pulse has three distinct emission components, which vary with frequency across our 1.0--1.5~GHz observing band. We measure the peak flux density to be $>0.065$~Jy and the corresponding fluence $>0.2$~Jy~ms. Based on the observed dispersion measure of 1812~cm$^{-3}$~pc, we infer a redshift of $\sim 1.9$. From this, we estimate the peak luminosity and isotropic energy to be $\lesssim 2\times10^{43}$~erg~s$^{-1}$ and $\lesssim 2\times10^{40}$~erg, respectively. With only one FRB from the survey detected so far, our constraints on the event rate are limited. We derive a 95\% confidence lower limit for the event rate of 900 FRBs per day for FRBs with fluences $>0.025$~Jy~ms. We performed follow-up observations of the source with FAST for four hours and have not found a repeated burst. We discuss the implications of this discovery for our understanding of the physical mechanisms of FRBs.

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arXiv2020

First SETI Observations with China's Five-hundred-meter Aperture Spherical radio Telescope (FAST)

The Search for Extraterrestrial Intelligence (SETI) attempts to address the possibility of the presence of technological civilizations beyond the Earth. Benefiting from high sensitivity, large sky coverage, an innovative feed cabin for China's Five-hundred-meter Aperture Spherical radio Telescope (FAST), we performed the SETI first observations with FAST's newly commisioned 19-beam receiver; we report preliminary results in this paper. Using the data stream produced by the SERENDIP VI realtime multibeam SETI spectrometer installed at FAST, as well as its off-line data processing pipelines, we identify and remove four kinds of radio frequency interference(RFI): zone, broadband, multi-beam, and drifting, utilizing the Nebula SETI software pipeline combined with machine learning algorithms. After RFI mitigation, the Nebula pipeline identifies and ranks interesting narrow band candidate ET signals, scoring candidates by the number of times candidate signals have been seen at roughly the same sky position and same frequency, signal strength, proximity to a nearby star or object of interest, along with several other scoring criteria. We show four example candidates groups that demonstrate these RFI mitigation and candidate selection. This preliminary testing on FAST data helps to validate our SETI instrumentation techniques as well as our data processing pipeline.

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arXiv2020

A Scaling Algorithm for Weighted $f$-Factors in General Graphs

We study the maximum weight perfect $f$-factor problem on any general simple graph $G=(V,E,w)$ with positive integral edge weights $w$, and $n=|V|$, $m=|E|$. When we have a function $f:V\rightarrow \mathbb{N}_+$ on vertices, a perfect $f$-factor is a generalized matching so that every vertex $u$ is matched to $f(u)$ different edges. The previous best algorithms on this problem have running time $O(m f(V))$ [Gabow 2018] or $\tilde{O}(W(f(V))^{2.373}))$ [Gabow and Sankowski 2013], where $W$ is the maximum edge weight, and $f(V)=\sum_{u\in V}f(u)$. In this paper, we present a scaling algorithm for this problem with running time $\tilde{O}(mn^{2/3}\log W)$. Previously this bound is only known for bipartite graphs [Gabow and Tarjan 1989]. The running time of our algorithm is independent of $f(V)$, and consequently it first breaks the $Ω(mn)$ barrier for large $f(V)$ even for the unweighted $f$-factor problem in general graphs.

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arXiv2019

The design of China Reconfigurable Analog-digital backEnd for FAST

The Five-hundred-meter Aperture Spherical radio Telescope(FAST) was launched on September 25,2016.From early 2017,we began to use the FAST wideband receiver,which was designed,constructed and installed on the FAST in Guizhou,China.The front end of the receiver is composed an uncooled Quad Ridge Flared Horn feed(QRFH) with the frequency range of 270 to 1620 MHz,and a cryostat operating at 10 K.Stephen et al. 2016We have coop-erated with the Institute of Automation of the Chinese Academy of Sciences to developed the China Reconfigurable ANalog-digital backEnd.The system covers the 3 GHz operating band of FAST.The hardware part of the backend includes an Analog Front-end Board,a wideband high precision Analog Digital Converter,and a FAST Digital Back-end.Analog circuit boards, field programmable gate arrays, and control computers form a set of hardware, software, and firmware platforms to achieve flexible bandwidth requirements through parameter changes. It is also suitable for the versatility of different astronomical observations, and can meet specific requirements. This paper briefly introduces the hardware and software of CRANE, as well as some observations of the system.

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arXiv2019

Boundary Effect-Aware Visual Tracking for UAV with Online Enhanced Background Learning and Multi-Frame Consensus Verification

Due to implicitly introduced periodic shifting of limited searching area, visual object tracking using correlation filters often has to confront undesired boundary effect. As boundary effect severely degrade the quality of object model, it has made it a challenging task for unmanned aerial vehicles (UAV) to perform robust and accurate object following. Traditional hand-crafted features are also not precise and robust enough to describe the object in the viewing point of UAV. In this work, a novel tracker with online enhanced background learning is specifically proposed to tackle boundary effects. Real background samples are densely extracted to learn as well as update correlation filters. Spatial penalization is introduced to offset the noise introduced by exceedingly more background information so that a more accurate appearance model can be established. Meanwhile, convolutional features are extracted to provide a more comprehensive representation of the object. In order to mitigate changes of objects' appearances, multi-frame technique is applied to learn an ideal response map and verify the generated one in each frame. Exhaustive experiments were conducted on 100 challenging UAV image sequences and the proposed tracker has achieved state-of-the-art performance.

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arXiv2019

Purely Combinatorial Algorithms for Approximate Directed Minimum Degree Spanning Trees

Given a directed graph $G$ on $n$ vertices with a special vertex $s$, the directed minimum degree spanning tree problem requires computing a incoming spanning tree rooted at $s$ whose maximum tree in-degree is the smallest among all such trees. The problem is known to be NP-hard, since it generalizes the Hamiltonian path problem. The best LP-based polynomial time algorithm can achieve an approximation of $Δ^*+2$ [Bansal et al, 2009], where $Δ^*$ denotes the optimal maximum tree in-degree. As for purely combinatorial algorithms (algorithms that do not use LP), the best approximation is $O(Δ^*+\log n)$ [Krishnan and Raghavachari, 2001] but the running time is quasi-polynomial. In this paper, we focus on purely combinatorial algorithms and try to bridge the gap between LP-based approaches and purely combinatorial approaches. As a result, we propose a purely combinatorial polynomial time algorithm that also achieves an $O(Δ^* + \log n)$ approximation. Then we improve this algorithm to obtain a $(1+ε)Δ^* + O(\frac{\log n}{\log\log n})$ for any constant $0<ε<1$ approximation in polynomial time.

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arXiv2019

Faster Algorithms for All Pairs Non-decreasing Paths Problem

In this paper, we present an improved algorithm for the All Pairs Non-decreasing Paths (APNP) problem on weighted simple digraphs, which has running time $\tilde{O}(n^{\frac{3 + ω}{2}}) = \tilde{O}(n^{2.686})$. Here $n$ is the number of vertices, and $ω< 2.373$ is the exponent of time complexity of fast matrix multiplication [Williams 2012, Le Gall 2014]. This matches the current best upper bound for $(\max, \min)$-matrix product [Duan, Pettie 2009] which is reducible to APNP. Thus, further improvement for APNP will imply a faster algorithm for $(\max, \min)$-matrix product. The previous best upper bound for APNP on weighted digraphs was $\tilde{O}(n^{\frac{1}{2}(3 + \frac{3 - ω}{ω+ 1} + ω)}) = \tilde{O}(n^{2.78})$ [Duan, Gu, Zhang 2018]. We also show an $\tilde{O}(n^2)$ time algorithm for APNP in undirected graphs which also reaches optimal within logarithmic factors.

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arXiv2018

Single-Source Bottleneck Path Algorithm Faster than Sorting for Sparse Graphs

In a directed graph $G=(V,E)$ with a capacity on every edge, a \emph{bottleneck path} (or \emph{widest path}) between two vertices is a path maximizing the minimum capacity of edges in the path. For the single-source all-destination version of this problem in directed graphs, the previous best algorithm runs in $O(m+n\log n)$ ($m=|E|$ and $n=|V|$) time, by Dijkstra search with Fibonacci heap [Fredman and Tarjan 1987]. We improve this time bound to $O(m\sqrt{\log n})$, thus it is the first algorithm which breaks the time bound of classic Fibonacci heap when $m=o(n\sqrt{\log n})$. It is a Las-Vegas randomized approach. By contrast, the s-t bottleneck path has an algorithm with running time $O(mβ(m,n))$ [Chechik et al. 2016], where $β(m,n)=\min\{k\geq 1: \log^{(k)}n\leq\frac{m}{n}\}$.

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arXiv2018

An Improved Algorithm for Incremental DFS Tree in Undirected Graphs

Depth first search (DFS) tree is one of the most well-known data structures for designing efficient graph algorithms. Given an undirected graph $G=(V,E)$ with $n$ vertices and $m$ edges, the textbook algorithm takes $O(n+m)$ time to construct a DFS tree. In this paper, we study the problem of maintaining a DFS tree when the graph is undergoing incremental updates. Formally, we show: Given an arbitrary online sequence of edge or vertex insertions, there is an algorithm that reports a DFS tree in $O(n)$ worst case time per operation, and requires $O\left(\min\{m \log n, n^2\}\right)$ preprocessing time. Our result improves the previous $O(n \log^3 n)$ worst case update time algorithm by Baswana et al. and the $O(n \log n)$ time by Nakamura and Sadakane, and matches the trivial $Ω(n)$ lower bound when it is required to explicitly output a DFS tree. Our result builds on the framework introduced in the breakthrough work by Baswana et al., together with a novel use of a tree-partition lemma by Duan and Zhan, and the celebrated fractional cascading technique by Chazelle and Guibas.

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arXiv2017

Scaling Algorithms for Weighted Matching in General Graphs

We present a new scaling algorithm for maximum (or minimum) weight perfect matching on general, edge weighted graphs. Our algorithm runs in $O(m\sqrt{n}\log(nN))$ time, $O(m\sqrt{n})$ per scale, which matches the running time of the best cardinality matching algorithms on sparse graphs. Here $m,n,$ and $N$ bound the number of edges, vertices, and magnitude of any edge weight. Our result improves on a 25-year old algorithm of Gabow and Tarjan, which runs in $O(m\sqrt{n\log nα(m,n)} \log(nN))$ time.

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arXiv2017

Connectivity Oracles for Graphs Subject to Vertex Failures

We introduce new data structures for answering connectivity queries in graphs subject to batched vertex failures. A deterministic structure processes a batch of $d\leq d_{\star}$ failed vertices in $\tilde{O}(d^3)$ time and thereafter answers connectivity queries in $O(d)$ time. It occupies space $O(d_{\star} m\log n)$. We develop a randomized Monte Carlo version of our data structure with update time $\tilde{O}(d^2)$, query time $O(d)$, and space $\tilde{O}(m)$ for any failure bound $d\le n$. This is the first connectivity oracle for general graphs that can efficiently deal with an unbounded number of vertex failures. We also develop a more efficient Monte Carlo edge-failure connectivity oracle. Using space $O(n\log^2 n)$, $d$ edge failures are processed in $O(d\log d\log\log n)$ time and thereafter, connectivity queries are answered in $O(\log\log n)$ time, which are correct w.h.p. Our data structures are based on a new decomposition theorem for an undirected graph $G=(V,E)$, which is of independent interest. It states that for any terminal set $U\subseteq V$ we can remove a set $B$ of $|U|/(s-2)$ vertices such that the remaining graph contains a Steiner forest for $U-B$ with maximum degree $s$.

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arXiv2017

Faster Randomized Worst-Case Update Time for Dynamic Subgraph Connectivity

Real-world networks are prone to breakdowns. Typically in the underlying graph $G$, besides the insertion or deletion of edges, the set of active vertices changes overtime. A vertex might work actively, or it might fail, and gets isolated temporarily. The active vertices are grouped as a set $S$. $S$ is subjected to updates, i.e., a failed vertex restarts, or an active vertex fails, and gets deleted from $S$. Dynamic subgraph connectivity answers the queries on connectivity between any two active vertices in the subgraph of $G$ induced by $S$. The problem is solved by a dynamic data structure, which supports the updates and answers the connectivity queries. In the general undirected graph, the best results for it include $\widetilde{O}(m^{2/3})$ deterministic amortized update time, $\widetilde{O}(m^{4/5})$ and $\widetilde{O}(\sqrt{mn})$ deterministic worst-case update time. In the paper, we propose a randomized data structure, which has $\widetilde{O}(m^{3/4})$ worst-case update time.

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