Zobrazeno 1 - 10
of 91
pro vyhledávání: '"BODWIN, GREG"'
Autor:
Bodwin, Greg, Le, Tuong
A reachability preserver is a basic kind of graph sparsifier, which preserves the reachability relation of an $n$-node directed input graph $G$ among a set of given demand pairs $P$ of size $|P|=p$. We give constructions of sparse reachability preser
Externí odkaz:
http://arxiv.org/abs/2410.20471
Autor:
Bodwin, Greg, Flics, Jeremy
A recent upper bound by Le and Solomon [STOC '23] has established that every $n$-node graph has a $(1+\varepsilon)(2k-1)$-spanner with lightness $O(\varepsilon^{-1} n^{1/k})$. This bound is optimal up to its dependence on $\varepsilon$; the remaining
Externí odkaz:
http://arxiv.org/abs/2406.04459
We construct $n$-node graphs on which any $O(n)$-size spanner has additive error at least $+\Omega(n^{3/17})$, improving on the previous best lower bound of $\Omega(n^{1/7})$ [Bodwin-Hoppenworth FOCS '22]. Our construction completes the first two ste
Externí odkaz:
http://arxiv.org/abs/2404.18337
The hereditary discrepancy of a set system is a certain quantitative measure of the pseudorandom properties of the system. Roughly, hereditary discrepancy measures how well one can $2$-color the elements of the system so that each set contains approx
Externí odkaz:
http://arxiv.org/abs/2401.15781
Autor:
Bodwin, Greg, Wang, Lily
The restoration lemma is a classic result by Afek, Bremler-Barr, Kaplan, Cohen, and Merritt [PODC '01], which relates the structure of shortest paths in a graph $G$ before and after some edges in the graph fail. Their work shows that, after one edge
Externí odkaz:
http://arxiv.org/abs/2309.07964
We study a new and stronger notion of fault-tolerant graph structures whose size bounds depend on the degree of the failing edge set, rather than the total number of faults. For a subset of faulty edges $F \subseteq G$, the faulty-degree $\deg(F)$ is
Externí odkaz:
http://arxiv.org/abs/2309.06696
Autor:
Bodwin, Greg, Fleischmann, Henry
Suppose we are given an $n$-node, $m$-edge input graph $G$, and the goal is to compute a spanning subgraph $H$ on $O(n)$ edges. This can be achieved in linear $O(m + n)$ time via breadth-first search. But can we hope for \emph{sublinear} runtime in s
Externí odkaz:
http://arxiv.org/abs/2308.13890
The aspect ratio of a (positively) weighted graph $G$ is the ratio of its maximum edge weight to its minimum edge weight. Aspect ratio commonly arises as a complexity measure in graph algorithms, especially related to the computation of shortest path
Externí odkaz:
http://arxiv.org/abs/2308.13054
Autor:
Bodwin, Greg
In 2016, a breakthrough result of Chechik and Wulff-Nilsen [SODA '16] established that every $n$-node graph $G$ has a $(1+\varepsilon)(2k-1)$-spanner of lightness $O_{\varepsilon}(n^{1/k})$, and recent followup work by Le and Solomon [STOC '23] gener
Externí odkaz:
http://arxiv.org/abs/2305.18647
Autor:
Bodwin, Greg, Hoppenworth, Gary
For a graph $G$, a $D$-diameter-reducing exact hopset is a small set of additional edges $H$ that, when added to $G$, maintains its graph metric but guarantees that all node pairs have a shortest path in $G \cup H$ using at most $D$ edges. A shortcut
Externí odkaz:
http://arxiv.org/abs/2304.02193