The Steiner tree problem is the canonical generalization of minimum spanning tree (MST). When connectivity is required only among a fixed subset of vertices (terminals), the goal is to maintain a minimum-cost tree connecting these terminals as the graph undergoes edge updates. While dynamic MST has been studied since t...
Jeff Giliberti, M. Hajiaghayi, Mohammad Mahdavi et al.· 0 citations
We give a deterministic $n^{O(\log n)}$-time algorithm for graph isomorphism. To our knowledge, this is the first proof of such a worst-case bound for general graphs. The algorithm uses the local-certificate and color-refinement steps of Babai's quasipolynomial algorithm, but retains the decomposition of each recursive...
We prove that every connected $n$-vertex graph admits a probabilistic embedding into its spanning trees with expected distance stretch $O(\log n)$. This settles the logarithmic stretch conjecture of Alon, Karp, Peleg, and West, whose spanning-tree game appeared at the 1991 DIMACS Workshop on On-Line Algorithms and in S...
We study the problem of submodular maximization under a matroid constraint. In this problem, there is a monotone submodular function $f: 2^{N} \rightarrow \mathbb{R}^+$ and a matroid $M(N, I)$, accessible via value and independence oracles and the goal is to find the independent set $S \in I$ maximizing the objective f...
Kiarash Banihashem, Samira Goudarzi, M. Hajiaghayi et al.· 0 citations
This work develops a residual-based dynamic algorithm that selectively propagates local errors via push operations, maintaining an approximation to the evolving fixed point without full recomputation, and proves that the method achieves amortized $O(1/\epsilon)$ update time per graph change under a degree-normalized er...
Kiarash Banihashem, M. Hajiaghayi, Mahdi JafariRaviz et al.· 0 citations
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