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A tree search algorithm called successive cancellation ordered search (SCOS) is proposed for $\boldsymbol{G}_N$-coset codes that implements maximum-likelihood (ML) decoding with adaptive complexity for transmission over binary-input AWGN channels. Unlike bit-flip decoders, no outer code is needed to terminate decoding; therefore, SCOS also applies to $\boldsymbol{G}_N$-coset codes modified with dynamic frozen bits. The average complexity is close to that of successive cancellation (SC) decoding at practical frame error rates (FERs) for codes with wide ranges of rate and lengths up to $512$ bits, which perform within $0.25$ dB or less from the random coding union bound and outperform Reed--Muller codes under ML decoding by up to $0.5$ dB. Simulations illustrate simultaneous gains for SCOS over SC-Fano, SC stack (SCS) and SC list (SCL) decoding in FER and the average complexity at various SNR regimes. SCOS is further extended by forcing it to look for candidates satisfying a threshold, thereby outperforming basic SCOS under complexity constraints. The modified SCOS enables strong error-detection capability without the need for an outer code. In particular, the $(128, 64)$ polarization-adjusted convolutional code under modified SCOS provides gains in overall and undetected FER compared to CRC-aided polar codes under SCL/dynamic SC flip decoding at high SNR.

Erd\H{o}s and West (Discrete Mathematics'85) considered the class of $n$ vertex intersection graphs which have a {\em $d$-dimensional} {\em $t$-representation}, that is, each vertex of a graph in the class has an associated set consisting of at most $t$ $d$-dimensional axis-parallel boxes. In particular, for a graph $G$ and for each $d \geq 1$, they consider $i_d(G)$ to be the minimum $t$ for which $G$ has such a representation. For fixed $t$ and $d$, they consider the class of $n$ vertex labeled graphs for which $i_d(G) \leq t$, and prove an upper bound of $(2nt+\frac{1}{2})d \log n - (n - \frac{1}{2})d \log(4\pi t)$ on the logarithm of size of the class. In this work, for fixed $t$ and $d$ we consider the class of $n$ vertex unlabeled graphs which have a {\em $d$-dimensional $t$-representation}, denoted by $\mathcal{G}_{t,d}$. We address the problem of designing a succinct data structure for the class $\mathcal{G}_{t,d}$ in an attempt to generalize the relatively recent results on succinct data structures for interval graphs (Algorithmica'21). To this end, for each $n$ such that $td^2$ is in $o(n / \log n)$, we first prove a lower bound of $(2dt-1)n \log n - O(ndt \log \log n)$-bits on the size of any data structure for encoding an arbitrary graph that belongs to $\mathcal{G}_{t,d}$. We then present a $((2dt-1)n \log n + dt\log t + o(ndt \log n))$-bit data structure for $\mathcal{G}_{t,d}$ that supports navigational queries efficiently. Contrasting this data structure with our lower bound argument, we show that for each fixed $t$ and $d$, and for all $n \geq 0$ when $td^2$ is in $o(n/\log n)$ our data structure for $\mathcal{G}_{t,d}$ is succinct. As a byproduct, we also obtain succinct data structures for graphs of bounded boxicity (denoted by $d$ and $t = 1$) and graphs of bounded interval number (denoted by $t$ and $d=1$) when $td^2$ is in $o(n/\log n)$.

The Maximum s-Bundle Problem (MBP) addresses the task of identifying a maximum s-bundle in a given graph. A graph G=(V, E) is called an s-bundle if its vertex connectivity is at least |V|-s, where the vertex connectivity equals the minimum number of vertices whose deletion yields a disconnected or trivial graph. MBP is NP-hard and holds relevance in numerous realworld scenarios emphasizing the vertex connectivity. Exact algorithms for MBP mainly follow the branch-and-bound (BnB) framework, whose performance heavily depends on the quality of the upper bound on the cardinality of a maximum s-bundle and the initial lower bound with graph reduction. In this work, we introduce a novel Partition-based Upper Bound (PUB) that leverages the graph partitioning technique to achieve a tighter upper bound compared to existing ones. To increase the lower bound, we propose to do short random walks on a clique to generate larger initial solutions. Then, we propose a new BnB algorithm that uses the initial lower bound and PUB in preprocessing for graph reduction, and uses PUB in the BnB search process for branch pruning. Extensive experiments with diverse s values demonstrate the significant progress of our algorithm over state-of-the-art BnB MBP algorithms. Moreover, our initial lower bound can also be generalized to other relaxation clique problems.

This paper presents the first sub-10$\mu$W, sub-0.1% total harmonic distortion (THD) sinusoidal current generator (CG) integrated circuit (IC) that is capable of 20kHz output for the bio-impedance (Bio-Z) sensing applications. To benefit from the ultra-low-power nature of near-threshold operation, a 9b pseudo-sine lookup table (LUT) is 3b $\Delta\Sigma$ modulated in the digital domain, thus linearity burden of the digital-to-analog converter (DAC) is avoided and only a 1.29$\mu$W of logic power is consumed, from a 0.5V supply and a 2.56MHz clock frequency. A half-period (HP) reset is introduced in the capacitive DAC, leading to around 30dB reduction of in-band noise by avoiding the sampling of data-dependent glitches and attenuating the kT/C noise and the non-idealities of reset switches (SW).

The Freeze-Tag Problem, introduced in Arkin et al. (SODA'02) consists of waking up a swarm of $n$ robots, starting from a single active robot. In the basic geometric version, every robot is given coordinates in the plane. As soon as a robot is awakened, it can move towards inactive robots to wake them up. The goal is to minimize the wake-up time of the last robot, the makespan. Despite significant progress on the computational complexity of this problem and on approximation algorithms, the characterization of exact bounds on the makespan remains one of the main open questions. In this paper, we settle this question for the $\ell_1$-norm, showing that a makespan of at most $5r$ can always be achieved, where $r$ is the maximum distance between the initial active robot and any sleeping robot. Moreover, a schedule achieving a makespan of at most $5r$ can be computed in optimal time $O(n)$. Both bounds, the time and the makespan are optimal. This implies a new upper bound of $5\sqrt{2}r \approx 7.07r$ on the makespan in the $\ell_2$-norm, improving the best known bound so far $(5+2\sqrt{2}+\sqrt{5})r \approx 10.06r$.

We introduce a novel sufficient dimension-reduction (SDR) method which is robust against outliers using $\alpha$-distance covariance (dCov) in dimension-reduction problems. Under very mild conditions on the predictors, the central subspace is effectively estimated and model-free advantage without estimating link function based on the projection on the Stiefel manifold. We establish the convergence property of the proposed estimation under some regularity conditions. We compare the performance of our method with existing SDR methods by simulation and real data analysis and show that our algorithm improves the computational efficiency and effectiveness.

We consider a $\sf K$ user interference network with general connectivity, described by a matrix $\mat{N}$, and general message flows, described by a matrix $\mat{M}$. Previous studies have demonstrated that the standard interference scheme (IA) might not be optimal for networks with sparse connectivity. In this paper, we formalize a general IA coding scheme and an intuitive number-filling puzzle for given $\mat{M}$ and $\mat{N}$ in a way that the score of the solution to the puzzle determines the optimum sum degrees that can be achieved by the IA scheme. A solution to the puzzle is proposed for a general class of symmetric channels, and it is shown that this solution leads to significantly higher $\SDoF$ than the standard IA scheme.

For a fixed integer $r \geq 1$, a distance-$r$ dominating set (D$r$DS) of a graph $G = (V, E)$ is a vertex subset $D \subseteq V$ such that every vertex in $V$ is within distance $r$ from some member of $D$. Given two D$r$DSs $D_s, D_t$ of $G$, the Distance-$r$ Dominating Set Reconfiguration (D$r$DSR) problem asks if there is a sequence of D$r$DSs that transforms $D_s$ into $D_t$ (or vice versa) such that each intermediate member is obtained from its predecessor by applying a given reconfiguration rule exactly once. The problem for $r = 1$ has been well-studied in the literature. We consider D$r$DSR for $r \geq 2$ under two well-known reconfiguration rules: Token Jumping ($\mathsf{TJ}$, which involves replacing a member of the current D$r$DS by a non-member) and Token Sliding ($\mathsf{TS}$, which involves replacing a member of the current D$r$DS by an adjacent non-member). It is known that under any of $\mathsf{TS}$ and $\mathsf{TJ}$, the problem on split graphs is $\mathtt{PSPACE}$-complete for $r = 1$. We show that for $r \geq 2$, the problem is in $\mathtt{P}$, resulting in an interesting complexity dichotomy. Along the way, we prove some non-trivial bounds on the length of a shortest reconfiguration sequence on split graphs when $r = 2$ which may be of independent interest. Additionally, we design a linear-time algorithm under $\mathsf{TJ}$ on trees. On the negative side, we show that D$r$DSR for $r \geq 1$ on planar graphs of maximum degree three and bounded bandwidth is $\mathtt{PSPACE}$-complete, improving the degree bound of previously known results. We also show that the known $\mathtt{PSPACE}$-completeness results under $\mathsf{TS}$ and $\mathsf{TJ}$ for $r = 1$ on bipartite graphs and chordal graphs can be extended for $r \geq 2$.

We give an alternative derivation of $(N,N)$-isogenies between fastKummer surfaces which complements existing works based on the theory oftheta functions. We use this framework to produce explicit formulae for thecase of $N = 3$, and show that the resulting algorithms are more efficient thanall prior $(3, 3)$-isogeny algorithms.

Maximizing a non-negative, monontone, submodular function $f$ over $n$ elements under a cardinality constraint $k$ (SMCC) is a well-studied NP-hard problem. It has important applications in, e.g., machine learning and influence maximization. Though the theoretical problem admits polynomial-time approximation algorithms, solving it in practice often involves frequently querying submodular functions that are expensive to compute. This has motivated significant research into designing parallel approximation algorithms in the adaptive complexity model; adaptive complexity (adaptivity) measures the number of sequential rounds of $\text{poly}(n)$ function queries an algorithm requires. The state-of-the-art algorithms can achieve $(1-\frac{1}{e}-\varepsilon)$-approximate solutions with $O(\frac{1}{\varepsilon^2}\log n)$ adaptivity, which approaches the known adaptivity lower-bounds. However, the $O(\frac{1}{\varepsilon^2} \log n)$ adaptivity only applies to maximizing worst-case functions that are unlikely to appear in practice. Thus, in this paper, we consider the special class of $p$-superseparable submodular functions, which places a reasonable constraint on $f$, based on the parameter $p$, and is more amenable to maximization, while also having real-world applicability. Our main contribution is the algorithm LS+GS, a finer-grained version of the existing LS+PGB algorithm, designed for instances of SMCC when $f$ is $p$-superseparable; it achieves an expected $(1-\frac{1}{e}-\varepsilon)$-approximate solution with $O(\frac{1}{\varepsilon^2}\log(p k))$ adaptivity independent of $n$. Additionally, unrelated to $p$-superseparability, our LS+GS algorithm uses only $O(\frac{n}{\varepsilon} + \frac{\log n}{\varepsilon^2})$ oracle queries, which has an improved dependence on $\varepsilon^{-1}$ over the state-of-the-art LS+PGB; this is achieved through the design of a novel thresholding subroutine.