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One of the most important problems in the field of distributed optimization is the problem of minimizing a sum of local convex objective functions over a networked system. Most of the existing work in this area focus on developing…
We currently see a steady rise in the usage and size of multiprocessor systems, and so the community is evermore interested in developing fast parallel processing algorithms. However, most algorithms require a synchronization mechanism,…
Codes are widely used in many engineering applications to offer robustness against noise. In large-scale systems there are several types of noise that can affect the performance of distributed machine learning algorithms -- straggler nodes,…
We study the scalability of consensus-based distributed optimization algorithms by considering two questions: How many processors should we use for a given problem, and how often should they communicate when communication is not free?…
In the recent decade companies started collecting of large amount of data. Without a proper analyse, the data are usually useless. The field of analysing the data is called data mining. Unfortunately, the amount of data is quite large: the…
Recent advancements in large language models (LLMs) have significantly improved their reasoning abilities, particularly through techniques involving search and backtracking. Backtracking naturally scales test-time compute by enabling…
Finding hidden/lost targets in a broad region costs strenuous effort and takes a long time. From a practical view, it is convenient to analyze the available data to exclude some parts of the search region. This paper discusses the…
We study the classic problem of dividing a collection of indivisible resources in a fair and efficient manner among a set of agents having varied preferences. Pareto optimality is a standard notion of economic efficiency, which states that…
Balanced partitioning is often a crucial first step in solving large-scale graph optimization problems, e.g., in some cases, a big graph can be chopped into pieces that fit on one machine to be processed independently before stitching the…
The problem of constrained clustering has attracted significant attention in the past decades. In this paper, we study the balanced $k$-center, $k$-median, and $k$-means clustering problems where the size of each cluster is constrained by…
Sorting has a natural generalization where the input consists of: (1) a ground set $X$ of size $n$, (2) a partial oracle $O_P$ specifying some fixed partial order $P$ on $X$ and (3) a linear oracle $O_L$ specifying a linear order $L$ that…
Low delay is an explicit requirement for applications such as cloud gaming and video conferencing. Delay-based congestion control can achieve the same throughput but significantly smaller delay than loss-based one and is thus ideal for…
An inherently parallel algorithm is proposed that efficiently performs selection: finding the K-th largest member of a set of N members. Selection is a common component of many more complex algorithms and therefore is a widely studied…
Distributed stochastic non-convex optimization problems have recently received attention due to the growing interest of signal processing, computer vision, and natural language processing communities in applications deployed over…
Mixed packing and covering problems are problems that can be formulated as linear programs using only non-negative coefficients. Examples include multicommodity network flow, the Held-Karp lower bound on TSP, fractional relaxations of set…
Tree of Thoughts (ToT) enhances Large Language Model (LLM) reasoning by structuring problem-solving as a spanning tree. However, recent methods focus on search accuracy while overlooking computational efficiency. The challenges of…
Cryptographic primitives have been used for various non-cryptographic objectives, such as eliminating or reducing randomness and interaction. We show how to use cryptography to improve the time complexity of solving computational problems.…
The need for scalable numerical solutions has motivated the development of asynchronous parallel algorithms, where a set of nodes run in parallel with little or no synchronization, thus computing with delayed information. This paper studies…
Given a text $T$ and a pattern $P$, the order-preserving matching problem is to find all substrings in $T$ which have the same relative orders as $P$. Order-preserving matching has been an active research area since it was introduced by…
Scalable real-time assortment optimization has become essential in e-commerce operations due to the need for personalization and the availability of a large variety of items. While this can be done when there are simplistic assortment…