Large Language Models (LLMs) have demonstrated remarkable capabilities across various
applications, but their performance on long-context tasks is often limited by the …

We give the first almost-linear time algorithms for several problems in incremental graphs
including cycle detection, strongly connected component maintenance, st shortest path …

We study connections between the problem of fully dynamic (1-ϵ)-approximate maximum
bipartite matching, and the dual (1+ϵ)-approximate vertex cover problem, with the online …

We give the first almost-linear total time algorithm for deciding if a flow of cost at most F still
exists in a directed graph, with edge costs and capacities, undergoing decremental updates …

We study dynamic (1− є)-approximate rounding of fractional matchings—a key ingredient in
numerous breakthroughs in the dynamic graph algorithms literature. Our first contribution is …

We provide an algorithm which, with high probability, maintains a (1—ɛ)-approximate
maximum flow on an undirected graph undergoing m-edge additions in amortized mo (1) ɛ …

In this paper we provide an algorithm for maintaining a (1− є)-approximate maximum flow in
a dynamic, capacitated graph undergoing edge insertions. Over a sequence of m insertions …

We provide an algorithm that maintains, against an adaptive adversary, a (1—ε)-
approximate maximum matching in n-node m-edge general (not necessarily bipartite) …

We study the problem of chasing positive bodies in 1: given a sequence of bodies
K_t=\left{x^t∈R_+^n∣C^tx^t≧1,P^tx^t≦1\right\} revealed online, where C^t and P^t are …

We study the problem of solving semidefinite programs (SDP) in the streaming model.
Specifically, $ m $ constraint matrices and a target matrix $ C $, all of size $ n\times n …