Related papers: Combinatorial RNA Design: Designability and Struct…
Minimal multicast networks are fascinating and efficient combinatorial objects, where the removal of a single link makes it impossible for all receivers to obtain all messages. We study the structure of such networks, and prove some…
Optimal block designs in small blocks are explored when the treatments have a natural ordering and interest lies in comparing consecutive pairs of treatments. We first develop an approximate theory which leads to a convenient multiplicative…
We present a spectral approach to design approximation algorithms for network design problems. We observe that the underlying mathematical questions are the spectral rounding problems, which were studied in spectral sparsification and in…
This paper studies the problem of, given the structure of a linear-time invariant system and a set of possible inputs, finding the smallest subset of input vectors that ensures system's structural controllability. We refer to this problem…
Graphs are extremely versatile and ubiquitous mathematical structures with potential to model a wide range of domains. For this reason, graph problems have been of interest since the early days of computer science. Some of these problems…
We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…
In [1], we introduced a family of combinatorial designs, which we call "alphabet reduction pairs of arrays", ARPAs for short. These designs depend on three integer parameters $q, p \leq q, k\leq p$: $q$ is the size of the symbol set $\{0, 1…
This paper focuses on pattern matching in the DNA sequence. It was inspired by a previously reported method that proposes encoding both pattern and sequence using prime numbers. Although fast, the method is limited to rather small pattern…
The problem of identifying sparse solutions for the link structure and dynamics of an unknown linear, time-invariant network is posed as finding sparse solutions x to Ax=b. If the sensing matrix A satisfies a rank condition, this problem…
This paper investigates the connections between combinatorial design theory and the creation of new forms of poetry through a specific combinatorial structure called Steiner triple systems. We introduce five original poems constructed using…
Evolutionary neural architecture search (ENAS) employs evolutionary algorithms to find high-performing neural architectures automatically, and has achieved great success. However, compared to the empirical success, its rigorous theoretical…
Solving linear programs is often a challenging task in distributed settings. While there are good algorithms for solving packing and covering linear programs in a distributed manner (Kuhn et al.~2006), this is essentially the only class of…
We propose a new random sketching approach for embedding high-dimensional Hilbert-Schmidt operators, using random input-output pairs. Such operator can then be approximated in a low-dimensional subspace of operators by solving a small…
Our goal in this paper is to automatically extract a set of decision rules (rule set) that best explains a classification data set. First, a large set of decision rules is extracted from a set of decision trees trained on the data set. The…
Nucleic acid sequence design via codon optimization is a fundamental task with applications across synthetic biology, mRNA therapeutics, and vaccine design. Given a target protein, it is a major open challenge to navigate the…
In the Minimum Common String Partition Problem (MCSP), we are given two strings on input, and we want to partition both into the same collection of substrings, minimizing the number of the substrings in the partition. This combinatorial…
In distributed storage systems built using commodity hardware, it is necessary to have data redundancy in order to ensure system reliability. In such systems, it is also often desirable to be able to quickly repair storage nodes that fail.…
Low-bit width neural networks have been extensively explored for deployment on edge devices to reduce computational resources. Existing approaches have focused on gradient-based optimization in a two-stage train-and-compress setting or as a…
Modern experimental methods enable the creation of self-assembly building blocks with tunable interactions, but optimally exploiting this tunability for the self-assembly of desired structures remains an important challenge. Many studies of…
Automated design of neural network architectures tailored for a specific task is an extremely promising, albeit inherently difficult, avenue to explore. While most results in this domain have been achieved on image classification and…