Random hashing is a standard method to balance loads among nodes in Peer‐to‐Peer networks. However, hashing destroys locality properties of object keys, the critical properties to many applications, more specifically, those that require range searching. To preserve a key order while keeping loads balanced, Ganesan, Bawa, and Garcia‐Molina proposed a load‐balancing algorithm that supports both object's key insertion and deletion with a guaranteed max–min load ratio, the imbalance ratio, of 4.237 using constant amortized costs. Nonetheless, the algorithm is not straightforward to implement in real networks because of its recursiveness. The algorithm mostly uses local operations with global max–min load information. In this work, we present a simple nonrecursive algorithm using essentially the same primitive operations as in Ganesan et al.'s work. For insertions and deletions, our algorithm guarantees a proven constant imbalance ratio of 7.464 with constant amortized costs. © 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 66(3), 235–249 2015

We consider the problem of finding semi-matching in bipartite graphs, which is also extensively studied under various names in the scheduling literature. We give faster algorithms for both weighted and unweighted cases. For the weighted case, we give an O ( nm log n )-time algorithm, where n is the number of vertices and m is the number of edges, by exploiting the geometric structure of the problem. This improves the classical O ( n 3 )-time algorithms by Horn [1973] and Bruno et al. [1974b]. For the unweighted case, the bound can be improved even further. We give a simple divide-and-conquer algorithm that runs in O (√ nm log n ) time, improving two previous O ( nm )-time algorithms by Abraham [2003] and Harvey et al. [2003, 2006]. We also extend this algorithm to solve the Balanced Edge Cover problem in O (√ nm log n ) time, improving the previous O ( nm )-time algorithm by Harada et al. [2008].

We present an $O(\log^2{k})$-approximation algorithm for the problem of finding a $k$-vertex connected spanning subgraph of minimum cost, where $n$ is the number of vertices in an input graph, and $k$ is a connectivity requirement. Our algorithm is the first that achieves a polylogarithmic approximation ratio for all values of $k$ and $n$, and it works for both directed and undirected graphs. As in previous works, we use the Frank--Tardos algorithm for finding $k$-outconnected subgraphs as a subroutine. However, with our structural lemmas, we are able to show that we need only partial solutions returned by the Frank--Tardos algorithm; thus, we can avoid paying the whole cost of an optimal solution every time the algorithm is applied.

We present an O(log n• log k)-approximation algorithm for the problem of finding k-vertex connected spanning subgraph of minimum cost, where n is the number of vertices in the input graph, and k is the connectivity requirement. Our algorithm works for both directed and undirected graphs. The best known approximation guarantees for these problems are O(ln k• min{√k,n/n-k ln k}) by Kortsarz and Nutov, and O(ln{k}) in the case of undirected graphs where n≥ 6k2 by Cheriyan, Vempala, and Vetta. Our algorithm is the first that has a polylogarithmic guarantee for all values of k. Combining our algorithm with the algorithm of Kortsarz and Nutov in case of small k, e.g., k

We consider the k -traveling repairmen problem, also known as the minimum latency problem, to multiple repairmen. We give a polynomial-time 8.497α-approximation algorithm for this generalization, where α denotes the best achievable approximation factor for the problem of finding the least-cost rooted tree spanning i vertices of a metric. For the latter problem, a (2 + ε)-approximation is known. Our results can be compared with the best-known approximation algorithm using similar techniques for the case k = 1, which is 3.59α. Moreover, recent work of Chaudry et al. [2003] shows how to remove the factor of α, thus improving all of these results by that factor. We are aware of no previous work on the approximability of the present problem. In addition, we give a simple proof of the 3.59α-approximation result that can be more easily extended to the case of multiple repairmen, and may be of independent interest.

In this paper, we show that any n point metric space can be embedded into a distribution over dominating tree metrics such that the expected stretch of any edge is O(log n). This improves upon the result of Bartal who gave a bound of O(log n log log n). Moreover, our result is existentially tight; there exist metric spaces where any tree embedding must have distortion Ω(log n)-distortion. This problem lies at the heart of numerous approximation and online algorithms including ones for group Steiner tree, metric labeling, buy-at-bulk network design and metrical task system. Our result improves the performance guarantees for all of these problems.

The authors present an O(n log/sup 3/ n) time algorithm for finding shortest paths in a planar graph with real weights. This can be compared to the best previous strongly polynomial time algorithm developed by R. Lipton et al., (1978 )which ran in O(n/sup 3/2/) time, and the best polynomial algorithm developed by M. Henzinger et al. (1994) which ran in O/spl tilde/(n/sup 4/3/) time. We also present significantly improved algorithms for query and dynamic versions of the shortest path problems.