A simple local-control approximation algorithm for multicommodity flow

Low local recurrence rate without postmastectomy radiation in node-negative breast cancer patients with tumors 5 cm and larger

This paper presents an algorithm for solving the Lower and Upper Bounded delay Minimal Spanning Tree (LUBMST) problem. The proposed heuristic method is based on the classical Kruskal MST construction. For any given value of parameters /spl epsiv//sub 1/ and /spl epsiv//sub 2/, the algorithm constructs a routing tree with the shortest interconnection path length at least /spl epsiv//sub 1//spl middot/R and the longest interconnection path length at most (1+/spl epsiv//sub 2/)/spl middot/R, where R is the length of the direct path from the source to the farthest sink. Extension of these techniques to the Elmore delay model is presented as well. Empirical results demonstrate the effectiveness of these algorithms on a large benchmark set.

Background: To investigate the efficacy, toxicity and prognosis of image-guided intensity-modulated radiotherapy (IG-IMRT) in patients with FIGO IIIC1 cervical cancer.Methods: We retrospectively reviewed clinical records of patients with FIGO IIIC1 cervical cancer treated with definitive IG-IMRT in our institute from January 2008 to December 2017. A dose of 50.4Gy in 28 fractions was prescribed to at least 95% of PCTV, the positive pelvic lymph nodes received a dose of 56-61.6Gy in 28 fractions with simultaneous integrated boost (SIB). Weekly cone beam compute tomography (CBCT) and daily megavoltage CT (MVCT) was performed before treatment. Both 2D brachytherapy and 3D brachytherapy were allowed in our study. Weekly Cisplatin (30-40mg/m2) was the first line regimen for concurrent chemotherapy. Overall survival (OS), disease free survival (DFS), local control (LC) and local regional control (LRC) was calculated with Kaplan-Meier method. Cox proportional hazard model was used to perform univariate and multivariate analyses.Results: A total of 502 patients were enrolled in this study. The median follow-up duration was 42.1 months (range: 2.3-137.3 months). The 3-year and 5-year estimated OS, DFS, LC, LRC were 81.7% and 75.5%, 71.4% and 68.6%, 89.9% and 89.9%, 86.1% and 84.3%, respectively. The incidences of chronic grade 3 or greater gastrointestinal and genitourinary toxicities were 2.7 % and 0.8%, respectively. Pelvic lymph nodes recurrence occurred in 21 patients (4.2%). Advanced T stage was identified as adverse factor for OS and LC. More positive lymph nodes (≥2) were associated with worse OS, DFS and LRC. The cycles of concurrent chemotherapy significantly affected OS, DFS and LRC.Conclusion: For patients with FIGO IIIC1 cervical cancer, IG-IMRT was well tolerated with excellent survivals. T stage and number of positive lymph nodes significantly influenced the survivals indicating the heterogeneity of stage IIIC1 cervical cancer patients. Adequate cycles of chemotherapy (≥4 cycles) was of great value for this group of patients.

The routing of vehicles or personnel in complex logistics systems is a task that needs to be solved in numerous applications, e.g., detailed models of transport networks or order picking areas. The number of relevant nodes in such networks can easily exceed 10,000 nodes. Often, a basic task is finding the shortest path from one node (start) to another (destination). Within the last years various simulation tools have been extended by respective algorithms. However, the execution time of the simulation model may significantly depend on the number of nodes in the network. We present algorithms from the literature and a comparison of three simulation tools with respect to execution time and model size for different scenarios. We further present an approach to work with so called sub-networks, i.e., the network is separated into areas, where finding the shortest path includes the task of starting at a node in one sub-network with a destination in another one.

This paper proposes a parallel shortest path-searching algorithm and implements it on a newly structured parallel reconfigurable processor, DAPDNA-2 (IPFlex Inc). Routing determines the shortest paths from the source to the ultimate destination through intermediate nodes. In open shortest path first (OSPF), Dijkstra's shortest path algorithm, which is the conventional one, finds the shortest paths from the source on a program counter-based processor. The calculation time for Dijkstra's algorithm is O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) when the number of nodes is N. When the network scale is large, calculation time required by Dijkstra's algorithm increases rapidly. It's very difficult to compute Dijkstra's algorithm in parallel because of the need for previous calculation results, so Dijkstra's algorithm is unsuitable for parallel processors. Our proposed scheme finds the shortest paths using a simultaneous multi-path search method. In contrast with Dijkstra's algorithm, several nodes can be determined at one time. Moreover, we partition the network into different groups (network groups) and find the all-node pair's shortest path in each group using a pipeline operation. Networks can be abstracted, and the shortest paths in very large networks can be found easily. The proposed scheme can decrease calculation time from O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) to O(N) using a pipeline operation on DAPDNA-2. Our simulations show that the proposed algorithm uses 99.6% less calculation time than Dijkstra's algorithm. The proposed algorithm can be applied to the very large Internet network designs of the future.

We introduce a simple erasure recovery algorithm for codes derived from cascades of sparse bipartite graphs and analyze the algorithm by analyzing a corresponding discrete-time random process. As a result, we obtain a simple criterion involving the fractions of nodes of different degrees on both sides of the graph which is necessary and sufficient for the decoding process to finish successfully with high probability. By carefully designing these graphs we can construct for any given rate R and any given real number /spl epsiv/ a family of linear codes of rate R which can be encoded in time proportional to ln(1//spl epsiv/) times their block length n. Furthermore, a codeword can be recovered with high probability from a portion of its entries of length (1+/spl epsiv/)Rn or more. The recovery algorithm also runs in time proportional to n ln(1//spl epsiv/). Our algorithms have been implemented and work well in practice; various implementation issues are discussed.

In various applications where the problem domain can be modeled into graphs, the shortest path computation in the graph is an indispensable challenge. In applications like online social networks and shortest route computation problems, the size of the graph is so large; the number of nodes have become close to hundreds of billions. Shortest path graph algorithms like SSSP (Single Source Shortest Path) and APSP (All Pairs Shortest Path) have low arithmetic intensity and irregular memory access patterns. The GPU implementation of many arithmetic and logical problems exceed the performance of the CPU system implementations. There is an increasing need for faster computation of shortest path in graphs for various applications. The objective of the work is to demonstrate that GPUs can efficiently perform shortest path computations on undirected weighted graphs considering space efficiency. For the implementation, GPUs supporting CUDA (Compute Unified Device Architecture) programming have been used. Additionally a space efficient approach called Triangular Matrix Method has been used.

Joint probabilistic data association (JPDA) is a powerful tool for solving data association problems. However, the exact computation of association probabilities {/spl beta//sub jk/} in JPDA is NP-hard, where /spl beta//sub jk/ is the probability that j-th observation is from k-th track. Hence, we cannot expect to compute association probabilities in JPDA exactly in polynomial time unless P = NP. In this paper, we present a simple Markov chain Monte Carlo data association (MCMCDA) algorithm that finds an approximate solution to JPDA in polynomial time. For /spl epsiv/ > 0 and 0 < /spl eta/ < .5, we prove that the algorithm finds good estimates of /spl beta//sub jk/ with probability at least 1 - /spl eta/ in time complexity O(/spl epsiv//sup -2/ log /spl eta//sup -1/N(N log N + log /spl epsiv//sup -1/))), where N is the number of observations.

In this paper, the problem of finding a shortest path tree rooted at a given source node on a directed graph (SPT) is considered. A new efficient algorithm based on a primal-dual approach is presented, which improves both the convergence and the complexity of the best known auction-like algorithm. It uses the virtual source (VS) concept based on the following consideration: when a node i is visited for the first time by any algorithm which preserves verified the dual admissibility conditions, then the shortest path (SP) from the source node to i is found. Therefore, the SP from the source to the remaining nodes may be computed by considering i as a “virtual source”. We propose a very efficient implementation of an auction-like algorithm that uses this concept and enables us to obtain a computational cost of O(n2), where n is the number of nodes. Numerical experiments are reported showing that the new method outdoes previously proposed auction-like algorithms and is highly competitive with other state-of-art SP approaches.

We present a quite simple, fast and practical algorithm to find a short cyclic tour that visits a set of points distributed on the plane. The algorithm runs in O(n log n) time with O(n) space, and is simple enough to easily implement on resource restricted machines. It constructs a tour essentially by axis-sorts of the points and takes a kind of the 'fixed dissection strategy,' though it neither tries to find best tours in subregions nor optimizes the order among subregions. As well as the worst-case approximation ratio of produced tours, we show that the algorithm is a 'probabilistic' constant-ratio approximation algorithm for uniform random distributions. We made computational comparisons of our algorithm, Karp's partitioning algorithm, Lin-Kernighan local search, Arora's randomized PTAS, etc. The results indicate that in running time our algorithm overwhelms existing ones, and the average approximation ratio is better or competitive.

The Steiner tree problem is one of the fundamental optimization problems in distributed graph algorithms. Recently Saikia and Karmakar [27] proposed a deterministic distributed algorithm for the Steiner tree problem that constructs a Steiner tree in \(O(S + \sqrt{n} \log ^* n)\) rounds whose cost is optimal upto a factor of \(2(1 - 1/\ell )\), where n and S are the number of nodes and shortest path diameter [17] respectively of the given input graph and \(\ell \) is the number of terminal leaf nodes in the optimal Steiner tree. The message complexity of the algorithm is \(O(\varDelta (n - t) S + n^{3/2})\), which is equivalent to \(O(mS + n^{3/2})\), where \(\varDelta \) is the maximum degree of a vertex in the graph, t is the number of terminal nodes (we assume that \(t < n\)), and m is the number of edges in the given input graph. This algorithm has a better round complexity than the previous best algorithm for Steiner tree construction due to Lenzen and Patt-Shamir [21]. In this paper we present a deterministic distributed algorithm which constructs a Steiner tree in \(\tilde{O}(S + \sqrt{n})\) rounds and \(\tilde{O}(mS)\) messages and still achieves an approximation factor of \(2(1 - 1/\ell )\). Note here that \(\tilde{O}(\cdot )\) notation hides polylogarithmic factors in n. This algorithm improves the message complexity of Saikia and Karmakar’s algorithm by dropping the additive term of \(O(n^{3/2})\) at the expense of a logarithmic multiplicative factor in the round complexity. Furthermore, we show that for sufficiently small values of the shortest path diameter \((S=O(\log n))\), a \(2(1 - 1/\ell )\)-approximate Steiner tree can be computed in \(\tilde{O}(\sqrt{n})\) rounds and \(\tilde{O}(m)\) messages and these complexities almost coincide with the results of some of the singularly-optimal minimum spanning tree (MST) algorithms proposed in [9, 12, 23].

This study aims to optimize the number of nodes and arcs in a constructed network employing a given criteria. For this, we subject the constructed network using the methods like Shortest Path (SP), Critical Path (CP) and Max-Flow (MF) between any pair of nodes. A set of iterative algorithms have been generated using matrix operations to meet the above requirement, which is named as Pandit’s algorithm. The equivalent algorithms for SP, CP and MF are hereby represented as Pandit’s Mini-additive, Maxi-additive and Max-min algorithms respectively. The generated algorithms take less number of iterations when compared to the established methods. The proposed new algorithms are shown with suitable numerical examples and discuss their merits over the established methods. These new algorithms take less computational time and hence suggested for solving the bulk networks such as transportation GIS, telecommunication networks, information systems, project scheduling etc.

This paper presents a new strongly polynomial cut canceling algorithm for minimum cost submodular flow. The algorithm is a generalization of our similar cut canceling algorithm for ordinary min-cost flow. The algorithm scales a relaxed optimality parameter and creates a second, inner relaxation that is a kind of submodular max flow problem. The outer relaxation uses a novel technique for relaxing the submodular constraints that allows our previous proof techniques to work. The algorithm uses the min cuts from the max flow subproblem as the relaxed most positive cuts it chooses to cancel. We show that this algorithm needs to cancel only ${\mathrm O}(n^3)$ cuts per scaling phase, where n is the number of nodes. Furthermore, we show how to slightly modify this algorithm to get a strongly polynomial running time. Finally, we briefly show how to extend this algorithm to the separable convex cost case and that the same technique can be used to construct a polynomial time maximum mean cut canceling algorithm for submodular flow.

Chapter 1 Applications of network optimization

We study problems in multiobjective optimization, in which solutions to a combinatorial optimization problem are evaluated with respect to several cost criteria, and we are interested in the trade-off between these objectives (the so-called Pareto curve). We point out that, under very general conditions, there is a polynomially succinct curve that /spl epsiv/-approximates the Pareto curve, for any /spl epsiv/>0. We give a necessary and sufficient condition under which this approximate Pareto curve can be constructed in time polynomial in the size of the instance and 1//spl epsiv/. In the case of multiple linear objectives, we distinguish between two cases: when the underlying feasible region is convex, then we show that approximating the multi-objective problem is equivalent to approximating the single-objective problem. If however the feasible region is discrete, then we point out that the question reduces to an old and recurrent one: how does the complexity of a combinatorial optimization problem change when its feasible region is intersected with a hyperplane with small coefficients; we report some interesting new findings in this domain. Finally, we apply these concepts and techniques to formulate and solve approximately a cost-time-quality trade-off for optimizing access to the World-Wide Web, in a model first studied by Etzioni et al. (1996) (which was actually the original motivation for this work).