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This paper investigates the energy complexity of distributed graph problems in multi-hop radio networks, where the energy cost of an algorithm is measured by the maximum number of awake rounds of a vertex. Recent works revealed that some problems, such as broadcast, breadth-first search, and maximal matching, can be solved with energy-efficient algorithms that consume only $\text{poly} \log n$ energy. However, there exist some problems, such as computing the diameter of the graph, that require $\Omega(n)$ energy to solve. To improve energy efficiency for these problems, we focus on a special graph class: bounded-genus graphs. We present algorithms for computing the exact diameter, the exact global minimum cut size, and a $(1 \pm\epsilon)$-approximate $s$-$t$ minimum cut size with $\tilde{O}(\sqrt{n})$ energy for bounded-genus graphs. Our approach is based on a generic framework that divides the vertex set into high-degree and low-degree parts and leverages the structural properties of bounded-genus graphs to control the number of certain connected components in the subgraph induced by the low-degree part.

Given that reliable cloud quantum computers are becoming closer to reality, the concept of delegation of quantum computations and its verifiability is of central interest. Many models have been proposed, each with specific strengths and weaknesses. Here, we put forth a new model where the client trusts only its classical processing, makes no computational assumptions, and interacts with a quantum server in a single round. In addition, during a set-up phase, the client specifies the size $n$ of the computation and receives an untrusted, off-the-shelf (OTS) quantum device that is used to report the outcome of a single constant-sized measurement from a predetermined logarithmic-sized input. In the OTS model, we thus picture that a single quantum server does the bulk of the computations, while the OTS device is used as an untrusted and generic verification device, all in a single round. We show how to delegate polynomial-time quantum computations in the OTS model. Scaling up the technique also yields an interactive proof system for all of QMA, which, furthermore, we show can be accomplished in statistical zero-knowledge. This yields the first relativistic (one-round), two-prover zero-knowledge proof system for QMA. As a proof approach, we provide a new self-test for $n$-EPR pairs using only constant-sized Pauli measurements, and show how it provides a new avenue for the use of simulatable codes for local Hamiltonian verification. Along the way, we also provide an enhanced version of a well-known stability result due to Gowers and Hatami and show how it completes a common argument used in self-testing.

In formal languages and automata theory, the magic number problem can be formulated as follows: for a given integer n, is it possible to find a number d in the range [n,2n] such that there is no minimal deterministic finite automaton with d states that can be simulated by an optimal nondeterministic finite automaton with exactly n states? If such a number d exists, it is called magic. In this paper, we consider the magic number problem in the framework of deterministic automata with output, which are known to characterize automatic sequences. More precisely, we investigate magic numbers for periodic sequences viewed as either automatic, regular, or constant-recursive.

Data movement between the CPU and main memory is a first-order obstacle against improving performance, scalability, and energy efficiency in modern systems. Computer systems employ a range of techniques to reduce overheads tied to data movement, spanning from traditional mechanisms (e.g., deep multi-level cache hierarchies, aggressive hardware prefetchers) to emerging techniques such as Near-Data Processing (NDP), where some computation is moved close to memory. Our goal is to methodically identify potential sources of data movement over a broad set of applications and to comprehensively compare traditional compute-centric data movement mitigation techniques to more memory-centric techniques, thereby developing a rigorous understanding of the best techniques to mitigate each source of data movement. With this goal in mind, we perform the first large-scale characterization of a wide variety of applications, across a wide range of application domains, to identify fundamental program properties that lead to data movement to/from main memory. We develop the first systematic methodology to classify applications based on the sources contributing to data movement bottlenecks. From our large-scale characterization of 77K functions across 345 applications, we select 144 functions to form the first open-source benchmark suite (DAMOV) for main memory data movement studies. We select a diverse range of functions that (1) represent different types of data movement bottlenecks, and (2) come from a wide range of application domains. Using NDP as a case study, we identify new insights about the different data movement bottlenecks and use these insights to determine the most suitable data movement mitigation mechanism for a particular application. We open-source DAMOV and the complete source code for our new characterization methodology at //github.com/CMU-SAFARI/DAMOV.

In this paper, a new fast algorithm for path planning and a collision prediction framework for two dimensional dynamically changing environments are introduced. The method is called Time Distance (TD) and benefits from the space-time space idea. First, the TD concept is defined as the time interval that must be spent in order for an object to reach another object or a location. Next, TD functions are derived as a function of location, velocity and geometry of objects. To construct the configuration-time space, TD functions in conjunction with another function named "Z-Infinity" are exploited. Finally, an explicit formula for creating the length optimal collision free path is presented. Length optimization in this formula is achieved using a function named "Route Function" which minimizes a cost function. Performance of the path planning algorithm is evaluated in simulations. Comparisons indicate that the algorithm is fast enough and capable to generate length optimal paths as the most effective methods do. Finally, as another usage of the TD functions, a collision prediction framework is presented. This framework consists of an explicit function which is a function of TD functions and calculates the TD of the vehicle with respect to all objects of the environment.

Consensus is one of the most fundamental problems in distributed computing. This paper studies the consensus problem in a synchronous dynamic directed network, in which communication is controlled by an oblivious message adversary. The question when consensus is possible in this model has already been studied thoroughly in the literature from a combinatorial perspective, and is known to be challenging. This paper presents a topological perspective on consensus solvability under oblivious message adversaries, which provides interesting new insights. Our main contribution is a topological characterization of consensus solvability, which also leads to explicit decision procedures. Our approach is based on the novel notion of a communication pseudosphere, which can be seen as the message-passing analog of the well-known standard chromatic subdivision for wait-free shared memory systems. We further push the elegance and expressiveness of the "geometric" reasoning enabled by the topological approach by dealing with uninterpreted complexes, which considerably reduce the size of the protocol complex, and by labeling facets with information flow arrows, which give an intuitive meaning to the implicit epistemic status of the faces in a protocol complex.

We study error exponents for the problem of low-rate communication over a directed graph, where each edge in the graph represents a noisy communication channel, and there is a single source and destination. We derive maxflow-based achievability and converse bounds on the error exponent that match when there are two messages and all channels satisfy a symmetry condition called pairwise reversibility. More generally, we show that the upper and lower bounds match to within a factor of 4. We also show that with three messages there are cases where the maxflow-based error exponent is strictly suboptimal, thus showing that our tightness result cannot be extended beyond two messages without further assumptions.

This study presents insights from interviews with nineteen Knowledge Graph (KG) practitioners who work in both enterprise and academic settings on a wide variety of use cases. Through this study, we identify critical challenges experienced by KG practitioners when creating, exploring, and analyzing KGs that could be alleviated through visualization design. Our findings reveal three major personas among KG practitioners - KG Builders, Analysts, and Consumers - each of whom have their own distinct expertise and needs. We discover that KG Builders would benefit from schema enforcers, while KG Analysts need customizable query builders that provide interim query results. For KG Consumers, we identify a lack of efficacy for node-link diagrams, and the need for tailored domain-specific visualizations to promote KG adoption and comprehension. Lastly, we find that implementing KGs effectively in practice requires both technical and social solutions that are not addressed with current tools, technologies, and collaborative workflows. From the analysis of our interviews, we distill several visualization research directions to improve KG usability, including knowledge cards that balance digestibility and discoverability, timeline views to track temporal changes, interfaces that support organic discovery, and semantic explanations for AI and machine learning predictions.

Massive access has been challenging for the fifth generation (5G) and beyond since the abundance of devices causes communication overload to skyrocket. In an uplink massive access scenario, device traffic is sporadic in any given coherence time. Thus, channels across the antennas of each device exhibit correlation, which can be characterized by the row sparse channel matrix structure. In this work, we develop a bilinear generalized approximate message passing (BiGAMP) algorithm based on the row sparse channel matrix structure. This algorithm can jointly detect device activities, estimate channels, and detect signals in massive multiple-input multiple-output (MIMO) systems by alternating updates between channel matrices and signal matrices. The signal observation provides additional information for performance improvement compared to the existing algorithms. We further analyze state evolution (SE) to measure the performance of the proposed algorithm and characterize the convergence condition for SE. Moreover, we perform theoretical analysis on the error probability of device activity detection, the mean square error of channel estimation, and the symbol error rate of signal detection. The numerical results demonstrate the superiority of the proposed algorithm over the state-of-the-art methods in DADCE-SD, and the numerical results are relatively close to the theoretical analysis results.

Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use as a layer in neural networks trained by backpropagation. To address this issue, we propose to smooth the max operator in the dynamic programming recursion, using a strongly convex regularizer. This allows to relax both the optimal value and solution of the original combinatorial problem, and turns a broad class of DP algorithms into differentiable operators. Theoretically, we provide a new probabilistic perspective on backpropagating through these DP operators, and relate them to inference in graphical models. We derive two particular instantiations of our framework, a smoothed Viterbi algorithm for sequence prediction and a smoothed DTW algorithm for time-series alignment. We showcase these instantiations on two structured prediction tasks and on structured and sparse attention for neural machine translation.