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We study the inference of network archaeology in growing random geometric graphs. We consider the root finding problem for a random nearest neighbor tree in dimension $d \in \mathbb{N}$, generated by sequentially embedding vertices uniformly at random in the $d$-dimensional torus and connecting each new vertex to the nearest existing vertex. More precisely, given an error parameter $\varepsilon > 0$ and the unlabeled tree, we want to efficiently find a small set of candidate vertices, such that the root is included in this set with probability at least $1 - \varepsilon$. We call such a candidate set a $\textit{confidence set}$. We define several variations of the root finding problem in geometric settings -- embedded, metric, and graph root finding -- which differ based on the nature of the type of metric information provided in addition to the graph structure (torus embedding, edge lengths, or no additional information, respectively). We show that there exist efficient root finding algorithms for embedded and metric root finding. For embedded root finding, we derive upper and lower bounds (uniformly bounded in $n$) on the size of the confidence set: the upper bound is subpolyno

We study the quantum query algorithms for simplex finding, a generalization of triangle finding to hypergraphs. This problem satisfies a rank-reduction property: a quantum query algorithm for finding simplices in rank-$r$ hypergraphs can be turned into a faster algorithm for finding simplices in rank-$(r-1)$ hypergraphs. We then show that every nested Johnson graph quantum walk (with any constant number of nested levels) can be converted into an adaptive learning graph. Then, we introduce the concept of $α$-symmetric learning graphs, which is a useful framework for designing and analyzing complex quantum search algorithms. Inspired by the work of Le Gall, Nishimura, and Tani (2016) on $3$-simplex finding, we use our new technique to obtain an algorithm for $4$-simplex finding in rank-$4$ hypergraphs with $O(n^{2.46})$ quantum query cost, improving the trivial $O(n^{2.5})$ algorithm.

In this paper, we propose an approach to finding sets of similar-performing models (in terms of loss/accuracy measurements) with highly different context-aware characteristics. Through experiments on the METABRIC dataset, we show that the proposed method finds multiple models with highly different gene expressions than those found by the control methodology without performance penalties. We argue that the proposed methodology is important whenever one aims to analyze any global characteristic of a model to extract insight into the underlying phenomenon being studied.

We present a conceptually simple method for finding quasinormal modes (QNMs) in a Schwarzschild black hole. QNMs are defined by their boundary conditions at infinity and at the horizon. These include the intuitively satisfying assertion that the QNM should be purely outgoing at infinity, with no incoming wave coming from infinity and scattering off the black hole. One applies this condition at past null infinity by demanding that the incoming wave there vanish, despite the infinite outgoing wave at the same point in spacetime. We search for QNMs by minimizing the incoming wave, but we are forced to work at a finite distance rather than past null infinity, to avoid the infinite outgoing wave. This technique lets us find the fundamental QNM, but we do not succeed in finding the overtones since the incoming waves always vanish due to damping. The technique is inherently approximate due to the boundary condition at a finite distance.

A tournament is a complete directed graph. A king in a tournament is a vertex v such that every other vertex is reachable from v via a path of length at most 2. It is well known that every tournament has at least one king, one of which is a maximum out-degree vertex. The tasks of finding a king, a maximum out-degree vertex and a source in a tournament has been relatively well studied in the context of query complexity. We study the communication complexity of these tasks, where the edges are partitioned between two players. The following are our main results for n-vertex tournaments: 1) The deterministic communication complexity of finding whether a source exists is tilde{Theta}(log^2 n). 2) The deterministic and randomized communication complexities of finding a king are Theta(n). The quantum communication complexity is tilde{Theta}(sqrt{n}). 3) The deterministic, randomized and quantum communication complexities of finding a maximum out-degree vertex are Theta(n log n), tilde{Theta}(n) and tilde{Theta}(sqrt{n}), respectively. Our upper bounds hold for all partitions of edges, and the lower bounds for a specific partition of the edges. To show the first bullet above, we show, perh

A \emph{saddlepoint} of an $n \times n$ matrix is an entry that is the maximum of its row and the minimum of its column. Saddlepoints give the \emph{value} of a two-player zero-sum game, corresponding to its pure-strategy Nash equilibria; efficiently finding a saddlepoint is thus a natural and fundamental algorithmic task. For finding a \emph{strict saddlepoint} (an entry that is the strict maximum of its row and the strict minimum of its column) we recently gave an $O({n\log^*{n}})$-time algorithm, improving the $O({n\log{n}})$ bounds from 1991 of Bienstock, Chung, Fredman, Schäffer, Shor, Suri and of Byrne and Vaserstein. In this paper we present an optimal $O({n})$-time algorithm for finding a strict saddlepoint based on random sampling. Our algorithm, like earlier approaches, accesses matrix entries only via unit-cost binary comparisons. For finding a (non-strict) saddlepoint, we extend an existing lower bound to randomized algorithms, showing that the trivial $O(n^2)$ runtime cannot be improved even with the use of randomness.

Finding a Hadamard matrix (H-matrix) among the set of all binary matrices of corresponding order is a hard problem, which potentially can be solved by quantum computing. We propose a method to formulate the Hamiltonian of finding H-matrix problem and address its implementation limitation on existing quantum annealing machine (QAM) that allows up to quadratic terms, whereas the problem naturally introduces higher order ones. For an M-order H-matrix, such a limitation increases the number of variables from M^2 to (M^3 +M^2-M)/2, which makes the formulation of the Hamiltonian too exhaustive to do by hand. We use symbolic computing techniques to manage this problem. Three related cases are discussed: (1) finding N < M orthogonal binary vectors, (2) finding M-orthogonal binary vectors, which is equivalent to finding a H-matrix, and (3) finding N-deleted vectors of an M-order H-matrix. Solutions of the problems by a 2-body simulated annealing software and by an actual quantum annealing hardware are also discussed.

Given a belief network with evidence, the task of finding the I most probable explanations (MPE) in the belief network is that of identifying and ordering the I most probable instantiations of the non-evidence nodes of the belief network. Although many approaches have been proposed for solving this problem, most work only for restricted topologies (i.e., singly connected belief networks). In this paper, we will present a new approach for finding I MPEs in an arbitrary belief network. First, we will present an algorithm for finding the MPE in a belief network. Then, we will present a linear time algorithm for finding the next MPE after finding the first MPE. And finally, we will discuss the problem of finding the MPE for a subset of variables of a belief network, and show that the problem can be efficiently solved by this approach.

The edge list model is arguably the simplest input model for graphs, where the graph is specified by a list of its edges. In this model, we study the quantum query complexity of three variants of the triangle finding problem. The first asks whether there exists a triangle containing a target edge and raises general questions about the hiding of a problem's input among irrelevant data. The second asks whether there exists a triangle containing a target vertex and raises general questions about the shuffling of a problem's input. The third asks whether there exists a triangle; this problem bridges the $3$-distinctness and $3$-sum problems, which have been extensively studied by both cryptographers and complexity theorists. We provide tight or nearly tight results for these problems as well as some first answers to the general questions they raise. Furthermore, given any graph with low maximum degree, such as a typical random sparse graph, we prove that the quantum query complexity of finding a length-$k$ cycle in its length-$m$ edge list is $m^{3/4-1/(2^{k+2}-4)\pm o(1)}$, which matches the best-known upper bound for the quantum query complexity of $k$-distinctness on length-$m$ inpu

Offline reinforcement learning (offline RL) is an emerging field that has recently begun gaining attention across various application domains due to its ability to learn strategies from earlier collected datasets. Offline RL proved very successful, paving a path to solving previously intractable real-world problems, and we aim to generalize this paradigm to a multiplayer-game setting. To this end, we introduce a problem of offline equilibrium finding (OEF) and construct multiple types of datasets across a wide range of games using several established methods. To solve the OEF problem, we design a model-based framework that can directly apply any online equilibrium finding algorithm to the OEF setting while making minimal changes. The three most prominent contemporary online equilibrium finding algorithms are adapted to the context of OEF, creating three model-based variants: OEF-PSRO and OEF-CFR, which generalize the widely-used algorithms PSRO and Deep CFR to compute Nash equilibria (NEs), and OEF-JPSRO, which generalizes the JPSRO to calculate (Coarse) Correlated equilibria ((C)CEs). We also combine the behavior cloning policy with the model-based policy to further improve the pe

In this experience paper, we report on a large-scale empirical study of Static Application Security Testing (SAST) in Open-Source Embedded Software (EMBOSS) repositories. We collected a corpus of 258 of the most popular EMBOSS projects, and then measured their use of SAST tools via program analysis and a survey (N=25) of their developers. Advanced SAST tools are rarely used -- only 3% of projects go beyond trivial compiler analyses. Developers cited the perception of ineffectiveness and false positives as reasons for limited adoption. Motivated by this deficit, we applied the state-of-the-art (SOTA) CodeQL SAST tool and measured its ease of use and actual effectiveness. Across the 258 projects, CodeQL reported 709 true defects with a false positive rate of 34%. There were 535 (75%) likely security vulnerabilities, including in major projects maintained by Microsoft, Amazon, and the Apache Foundation. EMBOSS engineers have confirmed 376 (53%) of these defects, mainly by accepting our pull requests. Two CVEs were issued. Based on these results, we proposed pull requests to include our workflows as part of EMBOSS Continuous Integration (CI) pipelines, 37 (71% of active repositories) o

Path finding algorithm addresses problem of finding shortest path from source to destination avoiding obstacles. There exist various search algorithms namely A*, Dijkstra's and ant colony optimization. Unlike most path finding algorithms which require destination co-ordinates to compute path, the proposed algorithm comprises of a new method which finds path using backtracking without requiring destination co-ordinates. Moreover, in existing path finding algorithm, the number of iterations required to find path is large. Hence, to overcome this, an algorithm is proposed which reduces number of iterations required to traverse the path. The proposed algorithm is hybrid of backtracking and a new technique(modified 8- neighbor approach). The proposed algorithm can become essential part in location based, network, gaming applications. grid traversal, navigation, gaming applications, mobile robot and Artificial Intelligence.

Recently, Ambainis gave an O(N^(2/3))-query quantum walk algorithm for element distinctness, and more generally, an O(N^(L/(L+1)))-query algorithm for finding L equal numbers. We point out that this algorithm actually solves a much more general problem, the problem of finding a subset of size L that satisfies any given property. We review the algorithm and give a considerably simplified analysis of its query complexity. We present several applications, including two algorithms for the problem of finding an L-clique in an N-vertex graph. One of these algorithms uses O(N^(2L/(L+1))) edge queries, and the other uses \tilde{O}(N^((5L-2)/(2L+4))), which is an improvement for L <= 5. The latter algorithm generalizes a recent result of Magniez, Santha, and Szegedy, who considered the case L=3 (finding a triangle). We also pose two open problems regarding continuous time quantum walk and lower bounds.

Given a directed acyclic graph with labeled vertices, we consider the problem of finding the most common label sequences ("traces") among all paths in the graph (of some maximum length m). Since the number of paths can be huge, we propose novel algorithms whose time complexity depends only on the size of the graph, and on the frequency epsilon of the most frequent traces. In addition, we apply techniques from streaming algorithms to achieve space usage that depends only on epsilon, and not on the number of distinct traces. The abstract problem considered models a variety of tasks concerning finding frequent patterns in event sequences. Our motivation comes from working with a data set of 2 million RFID readings from baggage trolleys at Copenhagen Airport. The question of finding frequent passenger movement patterns is mapped to the above problem. We report on experimental findings for this data set.

Given points $p_1, \dots, p_n$ in $\mathbb{R}^d$, how do we find a point $x$ which maximizes $\frac{1}{n} \sum_{i=1}^n e^{-\|p_i - x\|^2}$? In other words, how do we find the maximizing point, or mode of a Gaussian kernel density estimation (KDE) centered at $p_1, \dots, p_n$? Given the power of KDEs in representing probability distributions and other continuous functions, the basic mode finding problem is widely applicable. However, it is poorly understood algorithmically. Few provable algorithms are known, so practitioners rely on heuristics like the "mean-shift" algorithm, which are not guaranteed to find a global optimum. We address this challenge by providing fast and provably accurate approximation algorithms for mode finding in both the low and high dimensional settings. For low dimension $d$, our main contribution is to reduce the mode finding problem to a solving a small number of systems of polynomial inequalities. For high dimension $d$, we prove the first dimensionality reduction result for KDE mode finding, which allows for reduction to the low dimensional case. Our result leverages Johnson-Lindenstrauss random projection, Kirszbraun's classic extension theorem, and pe

Finding a hidden partition in a random environment is a general and important problem, which contains as subproblems many famous questions, such as finding a hidden clique, finding a hidden coloring, finding a hidden bipartition etc. In this paper, we provide a simple SVD algorithm for this purpose, answering a question of McSherry. This algorithm is very easy to implement and works for sparse graphs with optimal density.

We use differentiable programming and gradient descent to find unitary matrices that can be used in the period finding algorithm to extract period information from the state of a quantum computer post application of the oracle. The standard procedure is to use the inverse quantum Fourier transform. Our findings suggest that that this is not the only unitary matrix appropriate for the period finding algorithm, There exist several unitary matrices that can affect out the same transformation and they are significantly different from each other as well. These unitary matrices can be learned by an algorithm. Neural networks can be applied to differentiate such unitary matrices from randomly generated ones indicating that these unitaries do have characteristic features that cannot otherwise be discerned easily.