Related papers: Optimizing alphabet reduction pairs of arrays
The peak power problem in multicarrier waveforms is well-known and imposes substantial limitations on wireless communications. As the quest for investigation of enabling technologies for the next generation of wireless communication systems…
In this work, we study two types of constraints on two-dimensional binary arrays. In particular, given $p,\epsilon>0$, we study (i) The $p$-bounded constraint: a binary vector of size $m$ is said to be $p$-bounded if its weight is at most…
The heap is a basic data structure used in a wide variety of applications, including shortest path and minimum spanning tree algorithms. In this paper we explore the design space of comparison-based, amortized-efficient heap…
We compare pushdown automata (PDAs for short) against other representations. First, we show that there is a family of PDAs over a unary alphabet with $n$ states and $p \geq 2n + 4$ stack symbols that accepts one single long word for which…
Qualitative reasoning involves expressing and deriving knowledge based on qualitative terms such as natural language expressions, rather than strict mathematical quantities. Well over 40 qualitative calculi have been proposed so far, mostly…
Ensemble methods combine the predictions of multiple models to improve performance, but they require significantly higher computation costs at inference time. To avoid these costs, multiple neural networks can be combined into one by…
Orthogonal arrays are a type of combinatorial design that were developed in the 1940s in the design of statistical experiments. In 1947, Rao proved a lower bound on the size of any orthogonal array, and raised the problem of constructing…
The Quadratic Assignment Problem (QAP) is a well-known NP-hard combinatorial optimization problem that is at the core of many real-world optimization problems. We prove that QAP can be written as the sum of three elementary landscapes when…
Key Point Analysis (KPA), the summarization of multiple arguments into a concise collection of key points, continues to be a significant and unresolved issue within the field of argument mining. Existing models adapt a two-stage pipeline of…
The area of parameterized approximation seeks to combine approximation and parameterized algorithms to obtain, e.g., (1+eps)-approximations in f(k,eps)n^{O(1)} time where k is some parameter of the input. We obtain the following results on…
Quadratically constrained quadratic programs (QCQPs) are an expressive family of optimization problems that occur naturally in many applications. It is often of interest to seek out sparse solutions, where many of the entries of the…
A common form of MapReduce application involves discovering relationships between certain pairs of inputs. Similarity joins serve as a good example of this type of problem, which we call a "some-pairs" problem. In the framework of Afrati et…
We introduce a relax-and-round approach embedding the quantum approximate optimization algorithm (QAOA) with $p\geq 1$ layers. We show for many problems, including Sherrington-Kirkpatrick spin glasses, that at $p=1$, it is as accurate as…
The detection of sequential patterns in data is a basic functionality of modern data processing systems for complex event processing (CEP), OLAP, and retrieval-augmented generation (RAG). In practice, pattern matching is challenging, since…
Locating arrays (LAs) can be used to detect and identify interaction faults among factors in a component-based system. The optimality and constructions of LAs with a single fault have been investigated extensively under the assumption that…
Conflict-avoiding codes (CACs) have been used in multiple-access collision channel without feedback. The size of a CAC is the number of potential users that can be supported in the system. A code with maximum size is called optimal. The use…
Range minimum queries (RMQs) are fundamental operations with widespread applications in database management, text indexing and computational biology. While many space-efficient data structures have been designed for RMQs on arrays with…
Errors are inevitable during all kinds quantum informational tasks and quantum error-correcting codes (QECCs) are powerful tools to fight various quantum noises. For standard QECCs physical systems have the same number of energy levels.…
Proximity gaps and correlated agreement have become central tools in the analysis of interactive oracle proofs of proximity (IOPPs) and code-based SNARKs. Informally, a proximity-gap statement says that for a structured set of words -- such…
A number of engineering and scientific problems require representing and manipulating probability distributions over large alphabets, which we may think of as long vectors of reals summing to $1$. In some cases it is required to represent…