We present improved deterministic algorithms for approximating shortest paths in the Congested Clique model of distributed computing. obtain poly(log log n )-round following problems unweighted undirected -vertex graphs: ( 1 + ϵ )-approximation multi-source (MSSP) from O (√ ) sources. (2 all pairs (APSP). (1 , β)-approximation APSP where β = (log / . These bounds improve exponentially over stat...

With the growth in global trade and its environmental footprint, sustainable modes of freight movement are increasingly important today’s globalized world. This study focuses on on-dock rail, where rail terminal is located within marine container terminal. On-dock has recent years become an essential mode transportation to move containers out congested terminals. contributes literature by prese...

This article is concerned with the analysis of one-dimensional compressible Euler equations a singular pressure law, so-called hard sphere equation state. The result twofold. First, we establish existence bounded weak solutions by means viscous regularization and refined compensated compactness arguments. Second, investigate smooth setting providing detailed description impact on breakdown solu...

This paper proposes a new simple method for network measurement. It extracts 6-bit control flags of TCP (Transmission Control Protocol) packets. The idea is based on the unique feature of flag ratios which is discovered by our exhaustive search for the new indexes of network traffic. By the use of flag ratios, one can tell if the network is really congested. It is much simpler than the conventi...

Article history: Received 21 July 2012 Received in revised form 21 March 2013 Accepted 21 March 2013

In this paper, we propose a network efficiency measure for congested networks, that captures demands, costs, flows, and behavior. The network efficiency/performance measure can identify which network components, that is, nodes and links, have the greatest impact in terms of their removal, due to, for example, natural disasters, structural failures, terrorist attacks, etc., and, hence, are impor...

Graph problems are troublesome when it comes to MapReduce. Typically, to be able to design algorithms that make use of the advantages of MapReduce, assumptions beyond what the model imposes, such as the density of the input graph, are required. In a recent shift, a simple and robust model of MapReduce for graph problems, where the space per machine is set to be O(|V |) has attracted considerabl...

Interval Routing Schemes (IRS for short) have been extensively investigated in the past years with special regard to shortest paths. Besides their theoretical interest , IRS have practical applications, as they have been implemented with wormhole routing in the last generation of INMOS Transputer Router Chips. In this paper we consider IRS that are optimal with respect to the congestion of the ...

Congested traffic problems on very dense networks lead, at the limit, to minimization problems posed on measures on curves as shown in [2]. Here, we go one step further by showing that these problems can be reformulated in terms of the minimization of an integral functional over a set of vector fields with prescribed divergence. We prove a Sobolev regularity result for their minimizers despite ...