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 $\Omega(n)$ 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

Classical Algorithms from Quantum and Arthur-Merlin Communication Protocols

In recent years, the polynomial method from circuit complexity has been applied to several fundamental problems and obtains the state-of-the-art running times (e.g., R. Williams\u27s n^3 / 2^{Omega(sqrt{log n})} time algorithm for APSP). As observed in [Alman and Williams, STOC 2017], almost all applications of the polynomial method in algorithm design ultimately rely on certain (probabilistic) low-rank decompositions of the computation matrices corresponding to key subroutines. They suggest that making use of low-rank decompositions directly could lead to more powerful algorithms, as the polynomial method is just one way to derive such a decomposition. Inspired by their observation, in this paper, we study another way of systematically constructing low-rank decompositions of matrices which could be used by algorithms - communication protocols. Since their introduction, it is known that various types of communication protocols lead to certain low-rank decompositions (e.g., P protocols/rank, BQP protocols/approximate rank). These are usually interpreted as approaches for proving communication lower bounds, while in this work we explore the other direction. We have the following two generic algorithmic applications of communication protocols: - Quantum Communication Protocols and Deterministic Approximate Counting. Our first connection is that a fast BQP communication protocol for a function f implies a fast deterministic additive approximate counting algorithm for a related pair counting problem. Applying known BQP communication protocols, we get fast deterministic additive approximate counting algorithms for Count-OV (#OV), Sparse Count-OV and Formula of SYM circuits. In particular, our approximate counting algorithm for #OV runs in near-linear time for all dimensions d = o(log^2 n). Previously, even no truly-subquadratic time algorithm was known for d = omega(log n). - Arthur-Merlin Communication Protocols and Faster Satisfying-Pair Algorithms. Our second connection is that a fast AM^{cc} protocol for a function f implies a faster-than-bruteforce algorithm for f-Satisfying-Pair. Using the classical Goldwasser-Sisper AM protocols for approximating set size, we obtain a new algorithm for approximate Max-IP_{n,c log n} in time n^{2 - 1/O(log c)}, matching the state-of-the-art algorithms in [Chen, CCC 2018]. We also apply our second connection to shed some light on long-standing open problems in communication complexity. We show that if the Longest Common Subsequence (LCS) problem admits a fast (computationally efficient) AM^{cc} protocol (polylog(n) complexity), then polynomial-size Formula-SAT admits a 2^{n - n^{1-delta}} time algorithm for any constant delta > 0, which is conjectured to be unlikely by a recent work [Abboud and Bringmann, ICALP 2018]. The same holds even for a fast (computationally efficient) PH^{cc} protocol

Reinforcement Learning for Robot Navigation with Adaptive Forward Simulation Time (AFST) in a Semi-Markov Model

Deep reinforcement learning (DRL) algorithms have proven effective in robot navigation, especially in unknown environments, by directly mapping perception inputs into robot control commands. However, most existing methods ignore the local minimum problem in navigation and thereby cannot handle complex unknown environments. In this paper, we propose the first DRL-based navigation method modeled by a semi-Markov decision process (SMDP) with continuous action space, named Adaptive Forward Simulation Time (AFST), to overcome this problem. Specifically, we reduce the dimensions of the action space and improve the distributed proximal policy optimization (DPPO) algorithm for the specified SMDP problem by modifying its GAE to better estimate the policy gradient in SMDPs. Experiments in various unknown environments demonstrate the effectiveness of AFST

Influence of Alkyl Trimethyl Ammonium Bromides on Hydrothermal Formation of α-CaSO4·0.5H2O Whiskers with High Aspect Ratios

In this paper, the influence of alkyl trimethyl ammonium bromides (CnH2n+1(CH3)3NBr, n = 10, 12, 14, 16, 18, abbreviated as ATAB) on the formation of alpha calcium sulfate hemihydrate (α-CaSO4·0.5H2O) whiskers under a hydrothermal condition (135 °C, 3.0 h) was analyzed. Specifically, it focuses on cetyl trimethyl ammonium bromide (C16H33(CH3)3NBr, abbreviated as CTAB). The rising CTAB concentration from 0 to 9.2 × 10−4 mol·L−1 led to the increase of the average aspect ratio of α-CaSO4·0.5H2O whiskers from 80 to 430, since the selective adsorption of CTAB on the negatively-charged side facets of the whiskers inhibited the growth of the whiskers along the direction normal to the lateral facets. The further increase of CTAB concentration above the critical micelle concentration (abbreviated as CMC) showed little effect on the morphology of α-CaSO4·0.5H2O whiskers, considering that CTAB tended to form micelles instead of being adsorbed on the whisker surfaces. Similar phenomena were observed in other ATABs (n = 10, 12, 14, 18)

Support-Free Hollowing for 3+2-Axis Additive Manufacturing

Additive manufacturing (AM), also known as 3d printing, has become a hot topic in academia and industry in the past decades. For a typical layer-based additive manufacturing where the object is printed in a layer-by-layer fashion, the battle to reduce or even eradicate the support structure is always faced by researchers and industrial practitioners. The newly emerging multi-axis printing platform inspired by the five-axis machine tool opens new directions, such as surface quality improvement, support-free printing, etc. In this paper, we have presented a framework for the support-free hollowing of 3+2-axis printing. A suite of algorithms including curved skeleton extraction, print sequence optimization, hollowing generation, and print path planning is introduced. It is expected that the print efficiency will increase while the residue artifacts caused by the support structure on the contact surface can be ultimately eradicated.Mechanical Engineerin

High-Performance Low-Pass Filter Using Stepped Impedance Resonator and Defected Ground Structure

A microstrip low-pass filter (LPF) using reformative stepped impedance resonator (SIR) and defected ground structure (DGS) is proposed in this paper. The proposed filter not only possesses the advantage of high frequency selectivity of SIR hairpin LPF with internal coupling, but also possesses the large stop-band (SB) bandwidth by adjusting the number and area of DGS units. The LPF proposed in this paper possesses the properties of miniaturization, wide SB, high selectivity, and low pass-band ripple (PBR) simultaneously. The characteristic parameters of the proposed LPF is that: the pass-band (PB) is 0~2 GHz, the PBR is 0.5 dB, the SB range is from 2.4 GHz to 9 GHz when the attenuation is under 20 dB, and the maximal attenuation could reach 45 dB in the SB. The size of this proposed LPF is 0.13 λ × 0.09 λ ; λ is the corresponding wavelength of the upper PB edge frequency of 2 GHz

Bounded Rationality of Restricted Turing Machines

Bounded rationality aims to understand the effects of how limited rationality affects decision-making. The traditional models in game theory and multiagent system research, such as finite automata or unrestricted Turing machine, fall short of capturing how intelligent agents make decision in realistic applications. To address this problem, we model bounded rational agents as restricted Turing machines: restrictions on running time and on storage space. We study our model under the context of two-person repeated games. In the case where the running time of Turing machines is restricted, we show that computing the best response of a given strategy is much harder than the strategy itself. In the case where the storage space of the Turing machines is restricted, we show the best response of a space restricted strategy can not be implemented by machines within the same size (up to a constant factor). Finally, we study how these restrictions affect the set of Nash equilibria in infinitely repeated games.We show restricting the agent’s computational resources will give rise to new Nash equilibria

Influence of Alkyl Trimethyl Ammonium Bromides on Hydrothermal Formation of α-CaSO4·0.5H2O Whiskers with High Aspect Ratios

In this paper, the influence of alkyl trimethyl ammonium bromides (CnH2n+1(CH3)3NBr, n = 10, 12, 14, 16, 18, abbreviated as ATAB) on the formation of alpha calcium sulfate hemihydrate (α-CaSO4·0.5H2O) whiskers under a hydrothermal condition (135 °C, 3.0 h) was analyzed. Specifically, it focuses on cetyl trimethyl ammonium bromide (C16H33(CH3)3NBr, abbreviated as CTAB). The rising CTAB concentration from 0 to 9.2 × 10−4 mol·L−1 led to the increase of the average aspect ratio of α-CaSO4·0.5H2O whiskers from 80 to 430, since the selective adsorption of CTAB on the negatively-charged side facets of the whiskers inhibited the growth of the whiskers along the direction normal to the lateral facets. The further increase of CTAB concentration above the critical micelle concentration (abbreviated as CMC) showed little effect on the morphology of α-CaSO4·0.5H2O whiskers, considering that CTAB tended to form micelles instead of being adsorbed on the whisker surfaces. Similar phenomena were observed in other ATABs (n = 10, 12, 14, 18)

Removal of SO42− from Li2CO3 by Recrystallization in Na2CO3 Solution

Li2CO3 with high purity is an important raw material for the fabrication of lithium rechargeable batteries. This paper reports a facile recrystallization way to produce Li2CO3 with high purity from commercial Li2CO3 containing 0.8 wt % of SO42− by the treatment of the commercial Li2CO3 in Na2CO3 solution. The increase of temperature from 30 °C to 90 °C favored the recrystallization of Li2CO3 in Na2CO3 solution and promoted the removal of SO42− adsorbed or doped on/in the commercial Li2CO3. The content of SO42− in Li2CO3 decreased to 0.08 wt % after the treatment of the commercial Li2CO3 in 1.0 mol·L−1 Na2CO3 solution at 90 °C for 10.0 h