Improved Distributed Algorithms for Exact Shortest Paths

Computing shortest paths is one of the central problems in the theory of distributed computing. For the last few years, substantial progress has been made on the approximate single source shortest paths problem, culminating in an algorithm of Becker et al. [DISC'17] which deterministically computes $(1+o(1))$-approximate shortest paths in $\tilde O(D+\sqrt n)$ time, where $D$ is the hop-diameter of the graph. Up to logarithmic factors, this time complexity is optimal, matching the lower bound of Elkin [STOC'04]. The question of exact shortest paths however saw no algorithmic progress for decades, until the recent breakthrough of Elkin [STOC'17], which established a sublinear-time algorithm for exact single source shortest paths on undirected graphs. Shortly after, Huang et al. [FOCS'17] provided improved algorithms for exact all pairs shortest paths problem on directed graphs. In this paper, we present a new single-source shortest path algorithm with complexity $\tilde O(n^{3/4}D^{1/4})$. For polylogarithmic $D$, this improves on Elkin's $\tilde{O}(n^{5/6})$ bound and gets closer to the $\tilde{\Omega}(n^{1/2})$ lower bound of Elkin [STOC'04]. For larger values of $D$, we present an improved variant of our algorithm which achieves complexity $\tilde{O}\left( n^{3/4+o(1)}+ \min\{ n^{3/4}D^{1/6},n^{6/7}\}+D\right)$, and thus compares favorably with Elkin's bound of $\tilde{O}(n^{5/6} + n^{2/3}D^{1/3} + D )$ in essentially the entire range of parameters. This algorithm provides also a qualitative improvement, because it works for the more challenging case of directed graphs (i.e., graphs where the two directions of an edge can have different weights), constituting the first sublinear-time algorithm for directed graphs. Our algorithm also extends to the case of exact $\kappa$-source shortest paths...Comment: 26 page

Strategi Pemilihan Layanan Pelabuhan Berbasis Kondisi Pasar: Studi Kasus Terminal Curah Kering Tanjung Priok

Pemerintah terus berupaya mendorong pertumbuhan di bidang maritim dengan cara mengerluarkan peraturan, salah satunya melalui PM. No 15 Tahun 2015 mengenai izin konsesi dan bentuk kerjasama dalam penyelenggaraan kepelabuhanan. Konsensi ini membuka peluang sebesar-besarnya untuk instansi non-BUMN melakukan kegiatan penyediaan atau pelayasanan jasa kepelabuhanan. Tujuan yang ingin dicapai yakni membentuk iklim persaingan yang lebih sehat dalam penyelanggeraan jasa kepelabuhanan. Di lain sisi tentu kebijakan ini memiliki dampak yang dapat menimbulkan kerugian untuk pihak lain. PT Pelabuhan Tanjung Priok atau sering disebut PT PTP merupakan operator terminal multipurpose yang menangani muatan curah kering, general cargo, curah cair, dan petikemas dimana dalam beberapa tahun terakhir terjadi penurunan kargo muatan khususnya curah kering dengan rata-rata sebesar 5% pertahun. Hal ini diakibatkan oleh kehadiran Pelabuhan Marunda yang memiliki core bisnis yang sama yakni menangani muatan curah dan general cargo. Salah satu yang membuat pengguna jasa beralih ke Pelabuhan Marunda yakni tarif yang ditawarkan jauh dibawah Pelabuhan Tanjung Priok. PT PTP memerlukan strategi bisnis apakah tetap menangani muatan curah kering ataukah mengganti dengan muatan lain yang dalam jangka panjang lebih menjanjikan bagi perusahaan. Metode pendekatan yang digunakan yakni membandingkan nilai net present value (NPV) dari masing-masing skenario yang telah dibuat. ========================================================= The government continues to encourage growth in the maritime sector by passing regulations, one of which is through PM. No 15 of 2015 concerning concession licenses and forms of cooperation in port management. This concession opens up as many opportunities as possible for non-SOE agencies to conduct port provisioning services or foundation activities. The goal to be achieved is to form a healthier competition climate in the provision of port services. On the other hand of course this policy has an impact that can cause harm to other parties. PT Pelabuhan Tanjung Priok or often referred to as PT PTP is a multipurpose terminal operator that handles dry bulk cargo, general cargo, liquid bulk, and containers where in recent years cargo cargo has decreased especially dry bulk with an average of 5% per year. This is caused by the presence of the Port of Marunda which has the same core business that is handling bulk cargo and general cargo. One of the reasons why service users switch to Marunda Port is that the tariff offered is far below Tanjung Priok Port. PT PTP requires a business strategy whether to handle dry bulk loads or replace with other loads that are more promising for the company in the long run. The method used is to compare the present value of each scenario that has been made

Backlund transformations for many-body systems related to KdV

We present Backlund transformations (BTs) with parameter for certain classical integrable n-body systems, namely the many-body generalised Henon-Heiles, Garnier and Neumann systems. Our construction makes use of the fact that all these systems may be obtained as particular reductions (stationary or restricted flows) of the KdV hierarchy; alternatively they may be considered as examples of the reduced sl(2) Gaudin magnet. The BTs provide exact time-discretizations of the original (continuous) systems, preserving the Lax matrix and hence all integrals of motion, and satisfy the spectrality property with respect to the Backlund parameter.Comment: LaTeX2e, 8 page