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\u4e5d\u5dde\u5927\u5b66 (Kyushu University, Department of Computer Science and Communication Engineering)
\n\u30bf\u30a4\u30c8\u30eb\uff1a \u5727\u7e2e\u30c7\u30fc\u30bf\u69cb\u9020\u3068\u305d\u306e\u6700\u65b0\u52d5\u5411
\nThe Latest Trend of Compressed Data Structures
\n\u6982\u8981\uff1a\u5927\u91cf\u306e\u30c7\u30fc\u30bf\u3092\u6271\u3046\u5834\u5408\u306e\u554f\u984c\u70b9\u3068\u3057\u3066\u8a18\u61b6\u9818\u57df\u306e\u5927\u304d\u3055\u304c\u3042\u308b\uff0e\u305d\u306e\u89e3\u6c7a\u306e\u305f\u3081\u306b\u8fd1\u5e74\u5727\u7e2e\u30c7\u30fc\u30bf\u69cb\u9020\u304c\u76db\u3093\u306b\u7814\u7a76\u3055\u308c\u3066\u3044\u308b\uff0e\u3053\u308c\u306f\u5f93\u6765\u306e\u30c7\u30fc\u30bf\u69cb\u9020\u306e\u30b5\u30a4\u30ba\u3092\u5727\u7e2e\u3057\uff0c\u304b\u3064\u554f\u5408\u305b\u306e\u8a08\u7b97\u91cf\u3082\u5897\u3048\u306a\u3044\u3068\u3044\u3046\u3082\u306e\u3067\u3042\u308b\uff0e\u3053\u308c\u3089\u306e\u30c7\u30fc\u30bf\u69cb\u9020\u306e\u57fa\u672c\u3068\uff0c\u6700\u8fd1\u306e\u7d50\u679c\u306b\u3064\u3044\u3066\u89e3\u8aac\u3059\u308b\uff0e<\/p>\n
\u5c0f\u6a3d\u5546\u79d1\u5927\u5b66 (Otaru University of Commerce, Department of Information and Management Science)
\n\u30bf\u30a4\u30c8\u30eb\uff1a\u9023\u7d50\u5ea6\u8981\u6c42\u3092\u6301\u3064\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u69cb\u6210\u554f\u984c
\nNetwork Design Problem with Connectivity Requirements
\n\u6982\u8981\uff1a\u30b0\u30e9\u30d5\u7406\u8ad6\u306b\u304a\u3051\u308b\u9023\u7d50\u5ea6\u306e\u6982\u5ff5\u306f, \u7a2e\u3005\u306e\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306e\u5236\u5fa1\u30fb\u8a2d\u8a08\u306b\u304a\u3044\u3066\uff0c\u8010\u6545\u969c\u6027\u306b\u95a2\u3059\u308b\u57fa\u672c\u7684\u306a\u8a55\u4fa1\u5c3a\u5ea6\u3068\u3057\u3066\u7528\u3044\u3089\u308c\u308b. \u6240\u671b\u306e\u9023\u7d50\u5ea6\u3092\u4fdd\u8a3c\u3059\u308b\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u3092\u6700\u9069\u69cb\u6210\u3059\u308b\u554f\u984c\u3068\u3057\u3066\uff0c\u9023\u7d50\u5ea6\u5897\u5927\u554f\u984c\u3068\u4f9b\u7d66\u70b9\u914d\u7f6e\u554f\u984c\u3092\u53d6\u308a\u4e0a\u3052\u308b\uff0e\u8fd1\u5e74\uff0c\u3053\u308c\u3089\u306e\u554f\u984c\u306b\u5bfe\u3057\uff0c\u52b9\u7387\u7684\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u7814\u7a76\u304c\u76db\u3093\u306b\u884c\u308f\u308c\u3066\u304a\u308a\uff0c\u307e\u305f\u52a3\u30e2\u30b8\u30e5\u30e9\u95a2\u6570\u3092\u7528\u3044\u3066\u4e00\u822c\u5316\u3055\u308c\u305f\u96e2\u6563\u6700\u9069\u5316\u554f\u984c\u306e\u7814\u7a76\u3082\u3055\u308c\u3066\u304d\u3066\u3044\u308b\uff0e\u672c\u767a\u8868\u3067\u306f\uff0c\u3053\u308c\u3089\u306e\u554f\u984c\u306b\u5bfe\u3059\u308b\u6700\u8fd1\u306e\u7814\u7a76\u7d50\u679c\u3092\u7d39\u4ecb\u3059\u308b\uff0e<\/p>\n
\u4eac\u90fd\u5927\u5b66\u6570\u7406\u89e3\u6790\u7814\u7a76\u6240 (Research Institute for Mathematical Sciences, Kyoto University)
\n\u30bf\u30a4\u30c8\u30eb\uff1a\u52a3\u30e2\u30b8\u30e5\u30e9\u6700\u9069\u5316\u306e\u6700\u8fd1\u306e\u9032\u5c55
\nRecent Progress in Submodular Optimization
\n\u6982\u8981\uff1a\u52a3\u30e2\u30b8\u30e5\u30e9\u95a2\u6570\u306f\uff0c\u884c\u5217\u306e\u968e\u6570\uff0c\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306e\u30ab\u30c3\u30c8\u5bb9\u91cf\uff0c\u591a\u5143\u60c5\u5831\u6e90\u306e\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u95a2\u6570\u306a\u3069\uff0c\u5fdc\u7528\u6570\u5b66\u306e\u5e83\u7bc4\u306a\u5206\u91ce\u3067\u73fe\u308c\u308b\u96c6\u5408\u95a2\u6570\u3067\u3042\u308a\uff0c\u51f8\u95a2\u6570\u306e\u96e2\u6563\u7248\u3068\u3057\u3066\u8a8d\u8b58\u3055\u308c\u3066\u3044\u308b\uff0e\u6570\u7406\u8a08\u753b\u6cd5\u306b\u304a\u3044\u3066\u306f, 1970\u5e74\u306b J. Edmonds \u306b\u3088\u3063\u3066\u91cd\u8981\u6027\u304c\u6307\u6458\u3055\u308c\u3066\u4ee5\u6765\uff0c\u52b9\u7387\u7684\u306b\u89e3\u304f\u3053\u3068\u306e\u3067\u304d\u308b\u96e2\u6563\u6700\u9069\u5316\u554f\u984c\u306b\u5171\u901a\u306e\u69cb\u9020\u3068\u3057\u3066\u6ce8\u76ee\u3055\u308c\u3066\u304d\u305f\uff0e\u672c\u8b1b\u6f14\u3067\u306f\uff0c\u52a3\u30e2\u30b8\u30e5\u30e9\u95a2\u6570\u306e\u6700\u5c0f\u5316\u3092\u4e2d\u5fc3\u306b\uff0c\u52a3\u30e2\u30b8\u30e5\u30e9\u6700\u9069\u5316\u306e\u6700\u8fd1\u306e\u9032\u5c55\u3092\u7d39\u4ecb\u3059\u308b\uff0e<\/p>\n
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\u30bf\u30a4\u30c8\u30eb\uff1a The split delivery vehicle routing problem
\n\u6982\u8981\uff1aIn the vehicle routing problem (VRP) the objective is to construct a minimum cost set of routes serving all customers where the demand of each customer is less than or equal to the vehicle capacity and where each customer is visited once. In the split delivery vehicle routing problem (SDVRP) the restriction that each customer is visited once is removed. Moreover, the demand of each customer can be greater than the capacity of the vehicles. The SDVRP is NP-hard, even under restricted conditions on the costs, when all vehicles have a capacity greater than two, while it is solvable in polynomial time when the vehicles have a maximum capacity of two.<\/p>\n
We show that the cost savings that can be reached by allowing split deliveries is at most 50%. The variant of the VRP in which the demand of a customer may be larger than the vehicle capacity, but where each customer has to be visited a minimum number of times, is also considered. We show that the cost savings that can be reached by allowing more than the minimum number of required visits is again at most 50%. Furthermore, we analyze the performance of simple heuristics that handle customers with demands larger than the vehicle capacity by employing full load out-and-back trips to these customers until the demands become less than or equal to the vehicle capacity. Computational results are also shown to estimate the average savings that can be obtained with split deliveries.<\/p>\n
A simple and effective tabu search algorithm is compared with a sophisticated heuristic that, starting from the solution obtained by the tabu search algorithm and using the information collected during the tabu search, builds promising routes and solves MILP models to decide which routes to use and how to serve the customers through those routes. Computational experiments are reported for a set of benchmark problems.<\/p>\n
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\u30bf\u30a4\u30c8\u30eb\uff1a\u6642\u9593\u5236\u7d04\u4ed8\u304d\u6df7\u8f09\u8f38\u9001\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u8a2d\u8a08\u554f\u984c
\n\u6982\u8981\uff1a\u5168\u56fd\u898f\u6a21\u306e\u7269\u6d41\u30b5\u30fc\u30d3\u30b9\u3092\u5b9f\u73fe\u3059\u308b\u8f38\u9001\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306e\u8a2d\u8a08\u554f\u984c\u3092\u53d6\u308a\u4e0a\u3052\u308b\u3002\u3053\u306e\u554f\u984c\u3067\u306f\u3001\u5168\u56fd\u306b\u914d\u7f6e\u3055\u308c\u305f\u62e0\u70b9\u306b\u8377\u7269\u3092\u96c6\u7d04\u3057\u3001\u76ee\u7684\u62e0\u70b9\u306e\u7570\u306a\u308b\u8377\u7269\u3092\u6df7\u8f09\u3059\u308b\u3053\u3068\u3067\u8f38\u9001\u52b9\u7387\u3092\u9ad8\u3081\u308b\u7269\u6d41\u5f62\u614b\u3092\u6271\u3046\u3002\u3059\u3079\u3066\u306e\u51fa\u767a\u62e0\u70b9\u3068\u76ee\u7684\u62e0\u70b9\u306e\u30da\u30a2\u3054\u3068\u306b\u6700\u5927\u5230\u9054\u6642\u9593\u304c\u898f\u5b9a\u3055\u308c\u3066\u304a\u308a\u3001\u305d\u306e\u6642\u9593\u5236\u7d04\u306e\u7bc4\u56f2\u3067\u8377\u7269\u306e\u8f38\u9001\u7d4c\u8def\u3068\u30ad\u30e3\u30ea\u30a2\u306e\u904b\u884c\u30b9\u30b1\u30b8\u30e5\u30fc\u30eb\u3092\u6c7a\u5b9a\u3059\u308b\u3002\u3053\u306e\u554f\u984c\u306b\u5bfe\u3057\u3001\u8377\u7269\u306e\u30eb\u30fc\u30c6\u30a3\u30f3\u30b0\u3068\u30ad\u30e3\u30ea\u30a2\u5272\u5f53\u306e\u4e8c\u3064\u306e\u554f\u984c\u306b\u5206\u5272\u3059\u308b\u30a2\u30d7\u30ed\u30fc\u30c1\u3092\u63d0\u6848\u3057\u3001\u305d\u306e\u6709\u52b9\u6027\u3092\u8b70\u8ad6\u3059\u308b\u3002<\/p>\n
\u8a08\u7b97\u5e7e\u4f55\u5b66\u306f\u305d\u306e\u8a95\u751f\u304b\u308930\u5e74\u307b\u3069\u306e\u9593\u306b\u76ee\u899a\u3057\u3044\u767a\u5c55\u3092\u3068\u3052\u3001\u73fe\u5728\u3082\u6d3b\u767a\u306a\u7814\u7a76\u304c\u306a\u3055\u308c\u3066\u3044\u308b\u3002\u8a08\u7b97\u5e7e\u4f55\u5b66\u3068\u6700\u9069\u5316\u6280\u6cd5\u3068\u306f\u89aa\u5bc6\u306a\u95a2\u4fc2\u306b\u3042\u308a\u3001\u8a08\u7b97\u5e7e\u4f55\u5b66\u306e\u554f\u984c\u306b\u5bfe\u3057\u6700\u9069\u5316\u624b\u6cd5\u304c\u5fdc\u7528\u3055\u308c\u305f\u308a\u3001\u9006\u306b\u3001\u6700\u9069\u5316\u6280\u6cd5\u306e\u4e2d\u306b\u8a08\u7b97\u5e7e\u4f55\u5b66\u306e\u624b\u6cd5\u3092\u6301\u3061\u8fbc\u3080\u3053\u3068\u3067\u8a08\u7b97\u52b9\u7387\u3092\u5927\u304d\u304f\u6539\u5584\u3057\u305f\u308a\u3059\u308b\u3053\u3068\u304c\u3042\u308b\u3002\u672c\u30bb\u30c3\u30b7\u30e7\u30f3\u3067\u306f\u8a08\u7b97\u5e7e\u4f55\u5b66\u306e\u5206\u91ce\u3067\u6d3b\u8e8d\u3057\u3066\u304a\u3089\u308c\u308b4\u540d\u306e\u7814\u7a76\u8005\u306b\u3054\u8b1b\u6f14\u3044\u305f\u3060\u304f\u3002<\/p>\n
Yoshio Okamoto (Department of Information and Computer Sciences, Toyohashi University of Technology)
\n\u30bf\u30a4\u30c8\u30eb\uff1a \u51f8\u591a\u9762\u4f53\u30b0\u30e9\u30d5\u306e\u5411\u304d\u4ed8\u3051\uff1a\u6570\u7406\u3068\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0
\nPolytopal Digraphs: Mathematics and Algorithms
\n\u6982\u8981\uff1a\u7dda\u578b\u8a08\u753b\u554f\u984c\uff0c\u7dda\u578b\u76f8\u88dc\u6027\u554f\u984c\uff0c\u53cc\u884c\u5217\u30b2\u30fc\u30e0\u306a\u3069\u306b\u5bfe\u3057\u3066\uff0c\u30d4\u30dc\u30c3\u30c8\u64cd\u4f5c\u306b \u57fa\u3065\u304f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u53e4\u304f\u304b\u3089\u63d0\u6848\u3055\u308c\u3066\u3044\u308b\u304c\uff0c\u305d\u308c\u3089\u3092\u62bd\u8c61\u5316\u3059\u308b\u3053\u3068\u3067 \u51f8\u591a\u9762\u4f53\u30b0\u30e9\u30d5\u306e\u5411\u304d\u4ed8\u3051\u304c\u5f97\u3089\u308c\u308b\uff0e\u672c\u8b1b\u6f14\u3067\u306f\uff0c\u305d\u306e\u3088\u3046\u306a\u5411\u304d\u4ed8\u3051\u306b\u5bfe \u3057\u3066\u77e5\u3089\u308c\u3066\u3044\u308b\u3053\u3068\u3084\u8003\u3048\u3089\u308c\u3066\u3044\u308b\u554f\u984c\u3092\u7d39\u4ecb\u3059\u308b\uff0e<\/p>\n
Takeshi Tokuyama (Graduate School of Information Sciences, Tohoku University)
\n\u30bf\u30a4\u30c8\u30eb\uff1a\u98a8\u5909\u308f\u308a\u306a\u30dc\u30ed\u30ce\u30a4\u56f3\u3068\u8a08\u7b97\u53ef\u80fd\u6027
\nNon-standard variations of Voronoi diagrams and related computability problems
\n\u6982\u8981\uff1a\u30dc\u30ed\u30ce\u30a4\u56f3\u306f\u8a08\u7b97\u5e7e\u4f55\u5b66\u3067\u306f\u57fa\u672c\u7684\u306a\u30c6\u30fc\u30de\u3067\u3042\u308a\u3001\u5165\u529b\u70b9\u96c6\u5408\u306e\u5782\u76f4\u4e8c\u7b49\u5206\u7dda\u305f\u3061\u3092\u7528\u3044\u3066\u5e73\u9762\u3082\u3057\u304f\u306f\u7a7a\u9593\u3092\u52e2\u529b\u57df\u306b\u5206\u5272\u3059\u308b\u3002\u3055\u307e\u3056\u307e\u306a\u30d0\u30ea\u30a8\u30fc\u30b7\u30e7\u30f3\u304c\u77e5\u3089\u308c\u3066\u3044\u308b\u304c\u3001\u672c\u8b1b\u6f14\u3067\u306f\u3001\u70b9\u96c6\u5408\u304c\u6575\u5bfe\u95a2\u4fc2\u3068\u5354\u529b\u95a2\u4fc2\u3092\u6df7\u5408\u3057\u3066\u6301\u3061\u3001\u4e2d\u7acb\u5730\u5e2f\u3082\u6709\u3059\u308b\u5834\u5408\u306e\u65b0\u3057\u3044\u30e2\u30c7\u30eb\u3092\u4e0d\u52d5\u70b9\u5b9a\u7406\u3068\u95a2\u9023\u3057\u3066\u7d39\u4ecb\u3092\u884c\u3044\u3001\u7d44\u307f\u5408\u308f\u305b\u7684\u6027\u8cea\u3084\u8a08\u7b97\u53ef\u80fd\u6027\u306b\u3064\u3044\u3066\u306e\u8b70\u8ad6\u3092\u884c\u3046\u3002\u6d45\u91ce\u54f2\u592b\u6c0f\u3068J. Matousek\u6c0f\u3068\u306e\u5171\u540c\u7814\u7a76\u3092\u30d9\u30fc\u30b9\u306b\u3057\u305f\u3082\u306e\u3067\u3042\u308b\u3002<\/p>\n
Tetsuo Asano (School of Information Science, JAIST (Japan Advanced Institute of Science and Technology))
\n\u30bf\u30a4\u30c8\u30eb\uff1a\u6700\u5c0f\uff12\u4e57\u6cd5\u306e\u4e00\u822c\u5316
\nOn generalization of a least-squared fitting
\n\u6982\u8981\uff1a\u6700\u5c0f\uff12\u4e57\u6cd5\u3068\u3044\u3046\u3068\uff0c\u5b9f\u9a13\u30c7\u30fc\u30bf\u306e\u76f4\u7dda\u5f53\u3066\u306f\u3081\u304c\u601d\u3044\u6d6e\u304b\u3076\u304c\uff0c\u672c\u8b1b\u6f14\u3067\u306f\u305d\u306e\u4e00\u822c\u5316\u3068\uff0c\u540c\u69d8\u306e\u624b\u6cd5\u306e\u5225\u306e\u554f\u984c\u3078\u306e\u5fdc\u7528\u306b\u3064\u3044\u3066\u8ff0\u3079\u308b\uff0e \uff12\u6b21\u5143\u5e73\u9762\u4e0a\u306e\u70b9\u5217<\/p>\n
$(x_1, y_1), (x_2, y_2)< \\ldots, x_n, y_n)$<\/pre>\n\u3068\u3057\u3066\u6307\u5b9a\u3055\u308c\u308b\u5b9f\u9a13\u30c7\u30fc\u30bf\u3092\u6700\u3082\u826f\u304f\u8fd1\u4f3c\u3059\u308b\u76f4\u7dda$y=ax + b$\u306f\uff0c\u3053\u306e\u76f4\u7dda\u3068\u306e\u5782\u76f4\u65b9\u5411\u8ddd\u96e2\u306e\u5dee\u306e\uff12\u4e57\u548c$\\sum_{i=1}^n ax_i + b – y_i)^2$\u3092\u6700\u5c0f\u306b\u3059\u308b\u5b9a\u6570$a, b$\u306b\u3088\u3063\u3066\u5b9a\u307e\u308b\uff0e\u305d\u306e\u3088\u3046\u306a\uff12\u3064\u306e\u5b9a\u6570\u3092\u6c42\u3081\u308b\u306b\u306f\uff0c\uff12\u4e57\u548c\u306e\u5f0f\u3092$a$\u3068$b$\u3092\u5909\u6570\u3068\u898b\u306a\u3057\u3066\uff0c\u305d\u308c\u305e\u308c\u3067\u504f\u5fae\u5206\u3057\u3066$0$\u3068\u7f6e\u3044\u3066\u5f97\u3089\u308c\u308b\u9023\u7acb\u65b9\u7a0b\u5f0f\u3092\u89e3\u3051\u3070\u3088\u3044\uff0e\u3057\u304b\u3057\uff0c\u57fa\u6e96\u3092\u5782\u76f4\u65b9\u5411\u306e\u8ddd\u96e2\u306e\u5dee\uff08\u7d76\u5bfe\u5024\uff09\u306e\u548c\u306b\u5909\u66f4\u3059\u308b\u3068\uff0c\u4e00\u822c\u7684\u306a\u504f\u5fae\u5206\u304c\u53d6\u308c\u306a\u304f\u306a\u3063\u3066\u554f\u984c\u304c\u96e3\u3057\u304f\u306a\u308b\uff0e\u3057\u304b\u3057\uff0c\u8a08\u7b97\u91cf\u7684\u306b\u306f\u540c\u3058\u7dda\u5f62\u6642\u9593\u3067\u6700\u9069\u306a\u76f4\u7dda\u304c\u6c42\u307e\u308b\u3053\u3068\u304c\u65e2\u306b\u77e5\u3089\u308c\u3066\u3044\u308b\uff0e \u672c\u8b1b\u6f14\u3067\u306f\uff0c\u5225\u306e\u610f\u5473\u3067\u306e\u4e00\u822c\u5316\u3092\u8003\u3048\u308b\uff0e\u3059\u306a\u308f\u3061\uff0c\uff11\u672c\u306e\u76f4\u7dda\u3067\u8fd1\u4f3c\u3059\u308b\u306e\u3067\u306f\u306a\u304f\uff0c\u4efb\u610f\u306b\u4e0e\u3048\u3089\u308c\u305f\u6574\u6570$k$\u306b\u5bfe\u3057\u3066\uff0c\u6700\u9069\u306a$k$\u56de\u6298\u308c\u66f2\u304c\u308a\u306e\u7dda\u5206\u5217\u3092\u6c42\u3081\u308b\u306e\u3067\u3042\u308b\uff0e1\u56de\u6298\u308c\u66f2\u304c\u308a\u3060\u3051\u3067\u3042\u3063\u3066\u3082\u554f\u984c\u306f\u96e3\u3057\u3044\u304c\uff0c\u591a\u9805\u5f0f\u6642\u9593\u3067\u89e3\u3051\u308b\u3053\u3068\u3092\u793a\u3059\uff0e\u3057\u304b\u3082\uff0c\u5dee\u306e\uff12\u4e57\u548c\u3067\u3082\u5dee\u306e\u7d76\u5bfe\u5024\u548c\u3067\u3082\u540c\u69d8\u306b\u89e3\u3051\u308b\u3053\u3068\u3092\u793a\u3059\uff0e\u307e\u305f\uff0c\u4e00\u822c\u306e$k$\u306e\u5024\u306b\u5bfe\u3057\u3066\u306f\uff0c\u8fd1\u4f3c\u6bd4\u3092\u5e7e\u3089\u3067\u3082\u5c0f\u3055\u304f\u3067\u304d\u308b\u8fd1\u4f3c\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3082\u793a\u3059\uff0e \u76f4\u7dda\u5f53\u3066\u306f\u3081\u4ee5\u5916\u306e\u554f\u984c\u306b\u3082\u540c\u3058\u624b\u6cd5\u3092\u7528\u3044\u308b\u3053\u3068\u304c\u3067\u304d\u308b\uff0e\u305f\u3068\u3048\u3070\uff0c\u5e73\u9762\u4e0a\u306b\u591a\u6570\u306e\u70b9\u304c\u914d\u7f6e\u3055\u308c\u3066\u3044\u308b\u3068\u3057\u3066\uff0c\u305d\u308c\u305e\u308c\u306e\u70b9\u3078\u306e\u8ddd\u96e2\u3092\u6307\u5b9a\u3057\u3066\uff0c\u306a\u308b\u3079\u304f\u305d\u306e\u8ddd\u96e2\u306b\u306a\u308b\u3088\u3046\u306b\u65b0\u305f\u306a\u70b9\u3092\u633f\u5165\u3059\u308b\u3068\u3044\u3046\u554f\u984c\u3092\u8003\u3048\u308b\uff0e\u5b9f\u969b\u306b\u914d\u7f6e\u3057\u305f\u3068\u304d\u306e\u8ddd\u96e2\u3068\u6700\u521d\u306b\u4e0e\u3048\u3089\u308c\u3066\u3044\u305f\u8ddd\u96e2\u3068\u306e\u5dee\u306e\uff08\uff12\u4e57\uff0c\u7d76\u5bfe\u5024\uff09\u548c\u3092\u6700\u5c0f\u306b\u3059\u308b\u3068\u3044\u3046\u554f\u984c\u3092\u8003\u3048\u305f\u3068\u304d\uff0c\u8a08\u7b97\u5e7e\u4f55\u5b66\u306b\u304a\u3051\u308b\u30a2\u30ec\u30f3\u30b8\u30e1\u30f3\u30c8\u306e\u6982\u5ff5\u3068\u4f75\u7528\u3059\u308b\u3068\uff0c\u540c\u3058\u624b\u6cd5\u3067\u89e3\u3051\u308b\u3053\u3068\u3092\u793a\u3059\uff0e<\/p>\n
\u52a0\u85e4 \u76f4\u6a39 \uff08\u4eac\u90fd\u5927\u5b66\uff09<\/h5>\n
Naoki Katou (Kyoto University)
\n\u30bf\u30a4\u30c8\u30eb\uff1a\u4e09\u89d2\u5f62\u5206\u5272\u3068\u30e9\u30fc\u30de\u30f3\u30b0\u30e9\u30d5\uff1a\u5efa\u7bc9\u3078\u306e\u5fdc\u7528
\nTriangulation and Laman Graph: Application to Architecture
\n\u6982\u8981\uff1a\u90e8\u6750\u304c\u30b8\u30e7\u30a4\u30f3\u30c8\u3067\u3064\u306a\u304c\u3063\u3066\u3044\u308b\u30c8\u30e9\u30b9\u69cb\u9020\u7269\u306f\u30b0\u30e9\u30d5\u69cb\u9020\u3067\u8868\u73fe\u3055\u308c\u308b\u3002\u30c8\u30e9\u30b9\u69cb\u9020\u7269\u304c\u5b89\u5b9a\u3067\u3042\u308b\u305f\u3081\u306e\u5fc5\u8981\u6700\u4f4e\u9650\u306e\u90e8\u6750\u304b\u3089\u6210\u308b\u5834\u5408\u3001\u9759\u5b9a\u69cb\u9020\u7269\u3068\u547c\u3070\u308c\u3066\u3044\u308b\u3002\u9759\u5b9a\u69cb\u9020\u7269\u306b\u5bfe\u5fdc\u3059\u308b\u30b0\u30e9\u30d5\u306fminimally rigid graph\u3068\u3057\u3066\u77e5\u3089\u308c\u3066\u3044\u308b\u3002\u672c\u8ad6\u6587\u3067\u306f\u5e73\u9762\u4e0a\u306e\u30c8\u30e9\u30b9\u69cb\u9020\u7269\u3092\u5bfe\u8c61\u3068\u3057\u3066\u3001\u3042\u305f\u3048\u3089\u308c\u305f\u5e73\u9762\u4e0a\u306e\u70b9\u96c6\u5408\uff30\u306b\u5bfe\u3057\u3066\u3001\uff30\u3092\u9802\u70b9\u3068\u3057\u3001\u8fba\u304c\u4ea4\u5dee\u3057\u306a\u3044minimally rigid graph\u3092\u3059\u3079\u3066\u5217\u6319\u3059\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u3064\u3044\u3066\u8ff0\u3079\u308b\u3002minimally rigid graph\u306fLaman graph\u3068\u3082\u547c\u3070\u308c\u3001\u305d\u306e\u7d44\u5408\u305b\u7684\u6027\u8cea\u306b\u3064\u3044\u3066\u306f\u591a\u304f\u306e\u7814\u7a76\u8005\u306b\u3088\u3063\u3066\u7814\u7a76\u3055\u308c\u3066\u304a\u308a\u3001\u305d\u306e\u3088\u3046\u306a\u30b0\u30e9\u30d5\u5168\u4f53\u304c\u30de\u30c8\u30ed\u30a4\u30c9\u306e\u57fa\u3092\u4f5c\u308b\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u3044\u308b\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u9006\u63a2\u7d22\u6cd5\u306b\u3088\u308a\u3059\u3079\u3066\u306eLaman graph\u3092\u5217\u6319\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002 \u4e00\u65b9\u3001\u5e73\u9762\u4e0a\u306b\u57cb\u3081\u8fbc\u307e\u308c\u305f\u975e\u4ea4\u5deeLaman graph\u5168\u4f53\u306f\u30de\u30c8\u30ed\u30a4\u30c9\u3068\u306f\u306a\u3089\u306a\u3044\u3002\u6700\u8fd1\u3001\u975e\u4ea4\u5deeLaman graph\u306b\u5bfe\u3057\u3066\u3001\u30b0\u30e9\u30d5\u69cb\u9020\u3084\u5e7e\u4f55\u7684\u69cb\u9020\u3092\u660e\u3089\u304b\u306b\u3057\u3001\u975e\u4ea4\u5deeLaman graph\u540c\u58eb\u306b\u5bfe\u3057\u3066\u96a3\u63a5\u95a2\u4fc2\u3092\u4e0a\u624b\u306b\u5b9a\u3081\u308b\u3053\u3068\u306b\u3088\u308a\u9006\u63a2\u7d22\u6cd5\u306b\u3088\u3063\u3066\u3001\u975e\u4ea4\u5deeLaman graph\u3092\u3059\u3079\u3066\u5217\u6319\u3059\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u958b\u767a\u3057\u305f\u3002\u3042\u3089\u304b\u3058\u3081\u7528\u3044\u308b\u679d\u304c\u4e00\u90e8\u6307\u5b9a\u3055\u308c\u3066\u3044\u308b\u5834\u5408\u3082\u53d6\u308a\u6271\u3046\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u672c\u8b1b\u6f14\u3067\u306f\u305d\u306e\u6982\u8981\u3068\u69cb\u9020\u6700\u9069\u5316\u3078\u306e\u5fdc\u7528\u306b\u3064\u3044\u3066\u8ff0\u3079\u308b\u3002<\/p>\n\u30bb\u30c3\u30b7\u30e7\u30f3\uff14: \u9310\u6700\u9069\u5316\u306b\u304a\u3051\u308b\u7406\u8ad6\u3068\u5fdc\u7528 (Theory and Applications of Conic Optimization)<\/h4>\n
\u30aa\u30fc\u30ac\u30ca\u30a4\u30b6\u30fc\uff1a \u5409\u702c \u7ae0\u5b50 \uff08\u7b51\u6ce2\u5927\u5b66\uff09<\/h5>\n
\u534a\u6b63\u5b9a\u5024\u8a08\u753b\u554f\u984c\uff08SDP\uff09\u306f\u300c2000\u5e74\u306e\u7dda\u5f62\u8a08\u753b\u554f\u984c\uff08LP\uff09\u300d\u3068\u3082\u547c\u3070\u308c\uff0cLP\u306b\u304a\u3051\u308b\u975e\u8ca0\u5236\u7d04\u3092\uff0c\u5bfe\u79f0\u884c\u5217\u306e \u534a\u6b63\u5b9a\u5024\u5236\u7d04\u306b\u7f6e\u304d\u63db\u3048\u305f\u554f\u984c\u3067\u3042\u308b\uff0e\u5236\u5fa1\u7406\u8ad6\uff0c\u7d44\u5408\u305b\u7406\u8ad6\u306a\u3069\u306b\u591a\u304f\u306e\u5fdc\u7528\u4f8b\u304c\u3042\u308b\uff0e\u975e\u8ca0\u5236\u7d04\u3068\u534a\u6b63\u5b9a\u5024 \u5236\u7d04\u306f\u5168\u304f\u7570\u8cea\u306a\u5236\u7d04\u306b\u898b\u53d7\u3051\u3089\u308c\u308b\u304c\uff0c\u3068\u3082\u306b\u9589\u51f8\u9310\u3092\u4e0e\u3048\u308b\u3068\u3044\u3046\u5171\u901a\u70b9\u3092\u3082\u3064\uff0e1990\u5e74\u4ee3\u306b\u5185\u70b9\u6cd5\u306e\u89e3\u6cd5 \u3068\u3057\u3066\u306e\u6709\u52b9\u6027\u304c\u793a\u3055\u308c\u3066\u4ee5\u6765\uff0cSDP\u306fLP\u3092\u5305\u62ec\u3059\u308b\u65b0\u3057\u3044\u6700\u9069\u5316\u554f\u984c\u3068\u3057\u3066\u5b9a\u7740\u3057\u3064\u3064\u3042\u308b\uff0e\u8fd1\u5e74\u306f\u3055\u3089\u306b\u9589 \u51f8\u9310\u4e0a\u306e\u6700\u9069\u5316\u554f\u984c\uff08\u9310\u8a08\u753b\u554f\u984c\uff09\u306b\u5bfe\u8c61\u304c\u62e1\u5f35\u3055\u308c\uff0c\u6d3b\u767a\u306a\u7814\u7a76\u304c\u884c\u308f\u308c\u3066\u3044\u308b\uff0e\u672c\u30bb\u30c3\u30b7\u30e7\u30f3\u3067\u306f\u540c\u5206\u91ce\u3067 \u6d3b\u8e8d\u3055\u308c\u3066\u3044\u308b4\u540d\u306e\u7814\u7a76\u8005\u3092\u304a\u8fce\u3048\u3057\uff0c\u7406\u8ad6\u3068\u5fdc\u7528\u306b\u95a2\u3059\u308b\u6700\u65b0\u306e\u6210\u679c\u3092\u304a\u8a71\u3057\u9802\u304f\uff0e<\/p>\n
Etienne de Klerk (Tilburg University)<\/h5>\n
\u30bf\u30a4\u30c8\u30eb\uff1a The complexity of optimization over a simplex
\n\u6982\u8981\uff1aWe consider the problem of minimizing a continuous function over a simplex. This relatively simple optimization problem has several applications. If the function is quadratic, the applications already include portfolio optimization, population dynamics, genetics, finding maximum stable sets in graphs, and lower bounding the crossing number of certain classes of graphs. For more general functions, the applications include training neural networks and minimizing the expected shortfall of a portfolio.<\/p>\nWe will first review complexity results for minimizing polynomials over the standard simplex. In addition, we show that there exists a polynomial time approximation scheme (PTAS) for minimizing some classes of functions (including Lipschitz continuous functions) over the standard simplex.<\/p>\n
\u6797 \u4fca\u4ecb \uff08\u4eac\u90fd\u5927\u5b66\uff09<\/h5>\n
\u30bf\u30a4\u30c8\u30eb\uff1a\u4e8c\u6b21\u9310\u5236\u7d04\u3092\u3082\u3064\u534a\u7121\u9650\u8a08\u753b\u554f\u984c\u306b\u5bfe\u3059\u308b\u5207\u9664\u5e73\u9762\u30a2\u30d7\u30ed\u30fc\u30c1
\nA cutting plane approach for semi-infinite programming problems with second-order cone constraints
\n\u6982\u8981\uff1a\u534a\u7121\u9650\u8a08\u753b\u554f\u984c\u3068\u306f\uff0c\u6709\u9650\u6b21\u5143\u306e\u6c7a\u5b9a\u5909\u6570\u3068\u7121\u9650\u500b\u306e\u5236\u7d04\u5f0f\u3067\u7279\u5fb4\u4ed8\u3051\u3089\u308c\u308b\u6700\u9069\u5316\u554f\u984c\u3067\u3042\u308a\uff0c\u5e45\u5e83\u3044\u5206\u91ce\u306b \u5fdc\u7528\u304c\u53ef\u80fd\u306a\u3053\u3068\u304b\u3089\uff0c\u3053\u308c\u307e\u3067\u76db\u3093\u306b\u7814\u7a76\u304c\u306a\u3055\u308c\u3066\u304d\u305f\uff0e\u3057\u304b\u3057\uff0c\u65e2\u5b58\u306e\u7814\u7a76\u306e\u6b86\u3069\u306f\u7b49\u5f0f\u5236\u7d04\u304a\u3088\u3073\u4e0d\u7b49 \u5f0f\u5236\u7d04\u306e\u307f\u3067\u8868\u3055\u308c\u308b\u3088\u3046\u306a\u554f\u984c\u3092\u5bfe\u8c61\u3068\u3057\u3066\u304a\u308a\uff0c\u4e8c\u6b21\u9310\u5236\u7d04\u3092\u542b\u3080\u3088\u3046\u306a\u534a\u7121\u9650\u8a08\u753b\u554f\u984c\u306b\u5bfe\u3059\u308b\u7814\u7a76\u306f\u3053 \u308c\u307e\u3067\u6b86\u3069\u306a\u3055\u308c\u3066\u3044\u306a\u304b\u3063\u305f\uff0e\u305d\u3053\u3067\uff0c\u672c\u7814\u7a76\u3067\u306f\uff0cLai and Wu\u306e\u63d0\u6848\u3057\u305f\u5207\u9664\u5e73\u9762\u30a2\u30d7\u30ed\u30fc\u30c1\u3092\u4e8c\u6b21\u9310\u5236\u7d04 \u3092\u542b\u3080\u534a\u7121\u9650\u8a08\u753b\u554f\u984c\u306b\u62e1\u5f35\u3057\u305f\u624b\u6cd5\u3092\u63d0\u6848\u3059\u308b\uff0e\u307e\u305f\uff0c\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u304a\u3051\u308b\u90e8\u5206\u554f\u984c\u3068\u305d\u306e\u53cc\u5bfe\u554f\u984c\u306e\u89e3\u304c \u6e80\u305f\u3059\u3079\u304d\u4e8c\u6b21\u9310\u76f8\u88dc\u6027\u6761\u4ef6\u306b\u5bfe\u3057\u3066\uff0cJordan\u4ee3\u6570\u306b\u57fa\u3065\u3044\u305f\u89e3\u6790\u3092\u884c\u3046\u3053\u3068\u306b\u3088\u308a\uff0c\u63d0\u6848\u624b\u6cd5\u306e\u53ce\u675f\u6027\u3092\u793a\u3059\uff0e \u3055\u3089\u306b\uff0c\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u6027\u80fd\u3092\u8abf\u3079\u308b\u305f\u3081\u306b\u884c\u3063\u305f\u3044\u304f\u3064\u304b\u306e\u6570\u5024\u5b9f\u9a13\u306e\u7d50\u679c\u3082\u5408\u308f\u305b\u3066\u5831\u544a\u3059\u308b\uff0e<\/p>\nYu Xia (\u7d71\u8a08\u6570\u7406\u7814\u7a76\u6240)<\/h5>\n
\u30bf\u30a4\u30c8\u30eb\uff1aThe Maxdet problem – Algorithm and applications in machine learning
\n\u6982\u8981\uff1aWe give some applications of the Maxdet problem in machine learning. The Maxdet problem is an extension of the semidefinite program and the weighted analytic center problem. It concerns the maximization of a sum of linear function and some weighted logarithmic determinants over the intersection of an affine space and the cone of positive semidefinite matrices. This problem can be approximated by interior-point methods with polynomial complexity. This is a joint work with Takashi Tsuchiya.<\/p>\n\u5c71\u4e0b \u771f \uff08\u795e\u5948\u5ddd\u5927\u5b66\uff09<\/h5>\n
\u30bf\u30a4\u30c8\u30eb\uff1a\u91cf\u5b50\u5316\u5b66\u306b\u304a\u3051\u308b\u8d85\u5927\u898f\u6a21\u534a\u6b63\u5b9a\u5024\u8a08\u753b\u554f\u984c\u3068\u4e26\u5217\u8a08\u7b97\u306b\u3088\u308b\u9ad8\u901f\u6c42\u89e3
\nSemiDefinite Programming arising from\u3000Quantum Chemistry and Parallel Solver
\n\u6982\u8981\uff1a\u539f\u5b50\u304a\u3088\u3073\u5206\u5b50\u306e\u96fb\u5b50\u69cb\u9020\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u306f\u3001\u91cf\u5b50\u5316\u5b66\u306e\u57fa\u672c\u7684\u306a\u5bfe\u8c61\u3068\u3057\u3066\u4f4d\u7f6e\u3057\u3066\u3044\u308b\uff0e\u5206\u5b50\u306e\u57fa\u5e95\u72b6 \u614b\u306b\u304a\u3051\u308b\u96fb\u5b50\u69cb\u9020\u3092\u77e5\u308b\u306b\u306f\u3001\u96fb\u5b50\u9593\u306e\u76f8\u95a2\u3092\u8868\u3059\u884c\u5217\u304c\u6c42\u307e\u308c\u3070\u5341\u5206\u3067\u3042\u308b\uff0e\u3053\u306e\u884c\u5217\u306f\u7269\u7406\u7684\u5236\u7d04\u3067\u3042\u308b N-representability\u6761\u4ef6\u3092\u6e80\u305f\u3055\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u304c\u3001\u534a\u6b63\u5b9a\u5024\u7de9\u548c\u3092\u65bd\u3059\u3068\u534a\u6b63\u5b9a\u5024\u8a08\u753b\u554f\u984c\u306b\u5e30\u7740\u3067\u304d\u308b\uff0e \u3053\u308c\u3092\u89e3\u304f\u3053\u3068\u3067\uff0c\u5206\u5b50\u306e\u96fb\u5b50\u72b6\u614b\u3001\u30a8\u30cd\u30eb\u30ae\u30fc\u3092\u5909\u5206\u7684\u306b\u6c42\u3081\u3089\u308c\u308b\u3002\u3053\u306e\u4e8b\u5b9f\u306f 1960 \u5e74\u4ee3\u306b\u306f\u65e2\u306b\u77e5\u3089\u308c \u3066\u3044\u305f\u304c\uff0c1990\u5e74\u4ee3\u5f8c\u534a\u306e\u4e3b\u53cc\u5bfe\u5185\u70b9\u6cd5\u306e\u7814\u7a76\u306b\u3088\u308a\u6570\u5024\u7684\u306b\u8a08\u7b97\u3059\u308b\u3053\u3068\u304c\u53ef\u80fd\u3068\u306a\u3063\u305f\uff0e\u3055\u3089\u306b\uff0c2000\u5e74\u4ee5 \u964d\u306b\u306f, \u3088\u308a\u7cbe\u5bc6\u306a\u5316\u5b66\u6761\u4ef6\u3092\u53d6\u308a\u8fbc\u3093\u3060\u534a\u6b63\u5b9a\u5024\u8a08\u753b\u554f\u984c\u3078\u3068\u767a\u5c55\u3057\u3066\u3044\u308b\uff0e<\/p>\n\u3057\u304b\u3057\u306a\u304c\u3089\uff0c\u5e30\u7740\u3055\u308c\u305f\u534a\u6b63\u5b9a\u5024\u8a08\u753b\u554f\u984c\u306e\u898f\u6a21\u306f\u975e\u5e38\u306b\u5927\u304d\u304f\uff0c1\u53f0\u306e\u8a08\u7b97\u6a5f\u3067\u306f\u8a08\u7b97\u4e0d\u53ef\u80fd\u306a\u898f\u6a21\u306b\u306a\u308b \u50be\u5411\u306b\u3042\u308b\uff0e\u305d\u3053\u3067\u3001\u534a\u6b63\u5b9a\u5024\u8a08\u753b\u554f\u984c\u306b\u5bfe\u3059\u308b\u30bd\u30d5\u30c8\u30a6\u30a7\u30a2\u3067\u3042\u308bSDPA \u3092\u4e26\u5217\u5316\u3057\uff0cPC \u30af\u30e9\u30b9\u30bf\u4e0a\u306e\u8a08\u7b97\u30d1 \u30ef\u30fc\u3092\u7528\u3044\u3066\u3053\u306e\u3088\u3046\u306a\u8d85\u5927\u898f\u6a21\u534a\u6b63\u5b9a\u5024\u8a08\u753b\u554f\u984c\u306b\u53d6\u308a\u7d44\u3080\u7814\u7a76\u3092\u884c\u3063\u3066\u3044\u308b\uff0e<\/p>\n
\u672c\u767a\u8868\u3067\u306f\uff0c\u524d\u534a\u3092\u96fb\u5b50\u69cb\u9020\u304c\u534a\u6b63\u5b9a\u5024\u8a08\u753b\u554f\u984c\u306b\u5e30\u7740\u3055\u308c\u308b\u904e\u7a0b\u306e\u30c0\u30a4\u30b8\u30a7\u30b9\u30c8\u3068\u3057\uff0c\u5f8c\u534a\u3092 SDPA \u306e\u4e26 \u5217\u5316\uff0c\u304a\u3088\u3073 PC \u30af\u30e9\u30b9\u30bf\u4e0a\u306e\u6570\u5024\u7d50\u679c\u306e\u7d39\u4ecb\u3068\u3059\u308b\uff0e<\/p>\n","protected":false},"excerpt":{"rendered":"
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