ملخص
This research was supported in part by a Walter and Abstract. A k-spanner of a connected (undirected unweighted) graph G = (V, E) is a subgraph G' consisting of all the vertices of V and a subset of the edges, with the additional property that the distance between any two vertices in G' is larger than that distance in G by no more than a factor of k. This paper is concerned with approximating the problem of finding a 2-spanner in a given graph, with minimum maximum degree. We first show that the problem is at least as hard to approximate as set cover. Then a randomized approximation algorithm is provided for this problem, with approximation ratio of Õ(Δ1/4). We then present a probabilistic algorithm that is more efficient for sparse graphs. Our algorithms are converted into deterministic ones using derandomization.
اللغة الأصلية | الإنجليزيّة |
---|---|
الصفحات (من إلى) | 1438-1456 |
عدد الصفحات | 19 |
دورية | SIAM Journal on Computing |
مستوى الصوت | 27 |
رقم الإصدار | 5 |
المعرِّفات الرقمية للأشياء | |
حالة النشر | نُشِر - 1998 |