Exact Algorithms for Minimum-Cost Network Embeddings

Exact Algorithms for the Minimum-Cost Embeddings of ReliaЫ e Virtual Private Networks into Telecommunication Networks Summary: vVhen estaЬlisl1ing а viitual piivate net\VOik (VPN), а telecommunication piovideI l1as to balance t\V0 conflicting goals. On the one hand, the customeI Iequiies Ieliabllity, on the otheI hand, the pmvideI has to keep costs at а minimum. This article presents two Ielated approaches fOI the optimal computational solution of the embedding of а VPN \vhich is crucial in modern network planning. 1. Introd uction In te]ecommнnications engineering, there is more to do tha.n acce]erating tra.nsmission or constrнcting safer encryption codes. Raising а large techno]ogical system typical1y shows an incieasing Iisk of failure due to unfOieseen influences, inheient inconsistencies, OI lack of control despite all effOits. Keeping their netwOiks stable and ореrаЫе are the primary goals of all telecommunication providers. Tl1eiefoie, safety measures aie being called fOI Ьу theiI customers. А typical example in this context is the routing of а virtual piivate net\vOik (VPN). А VPN, as the name indicates, is а network that appeais to Ье exclнsively contiolled and opeiated Ьу а customer company alone. In reality, it consists of а numbeI of permanent lines that aie leased fiom а carrieI. So control also lies upon the latte1· to а significant extent. And for this Ieason, the carrier has to piovide these lines sнbject to а Ieliabllity demand. Tl1is means that one failure in the carrier's net,vork may at most cause one failure on the VPN level, in the customer's net\VOik. Technically speaking, the different leased lines must Ье routed disjointly through the carrier's network. In ordeI to Ье competitive, the carrieI must also consideI the cost side of this demand. So natural1y, а reliaЫe embedding of minimum cost is Iequired. The pioЬlem of finding this optimum is the mathematical task ,ve treat in this paper. The basis fOI this paper \vas а joint R&D project bet\veen the group Comblnatoiial Optimization and Å ¹kƛ²Ü÷ö¼¾¿gÊÂǽò·Å²›Õ+¶¹Y·Tß T´ÂǼ¾½¾µ¹kµ›Ö+·Å²›´AÐö´·áÈcʸËÜÛ6Æf·Ç½¾Õ+½ "¹Y·Å½¾Êgµã¿¸ÊěÆܹk· 6´Äf·Å¶ÇÔº²›´6ß,´¼¾´ËgÊgÕ ÷ ·Å²Ž¹Y· ²Ž¹g¶ö·º¹kËk´#µƛ¼¾¹kÔ#´=âxÂÇÊgÕ kě¼ÃÞ z·Å²›Â¸Êě¿g² gěµ›´ fÚ ð ·öÈq¹k¶6½Ãµ›½Ã·Å½¾¹k·Å´Ö»Ùޕ´"¹kÂǼý¾´Âö½ÃµÙÀg´#¶¸·Ç½¾¿¹k·Å½ÃÊgµ›¶öÊkâ·Å²›´ 6´#Äd·Å¶ÇÔº²›´£ß,´#¼¾´ËkÊÕ ÷ [ÚqÛ6µ›´=Êk␷Ų›´=¹kÄf·Å²›ÊgÂǶö²Ž¹k¶JÈJÂǽ÷ǷǴ#µ²›½¾¶ A½¾Æ›¼¾ÊgÕܹ=·Å²›´¶Ç½¾¶ ,¹g»jÊgÄf··Å²›½¾¶àƛÂÇÊeûÇ´Ô· Ô#ÊgµÙ·º¹k½¾µf½¾µ›¿F¹k¼¾¼,ƛÂÇ´¶Ç´#µ·Å´#Öu¹g¶ÇÆj´Ô·Å¶Á½Ãµ3֛´·º¹k½¾¼[ÒC¹k¼¾Êgµ›¿+ÈJ½ò·Å²Õ+¹gµޕ´øf¹gÕƛ¼¾´¶2¹kµ›Ö ½¾ÕÆjʸ·Å¹gµ·A´Šød·Å´µ›¶Ç½¾Êgµ›¶#ÚÁ÷ Õ+ÊgÂÇ´3´¼×¹k»jÊÂŹY·Å´ÖuûÇÊgěÂǵŽ¹k¼AƎ¹kÆj´# 6½¾¶Ü½¾µ:ƛÂÇ´Ǝ¹gÂǹk·Å½ÃʵKÒqâx´"¹Y·ÅěÂǽõ›¿¦ÕÊgÂÇ´ÔʵfÔ#´#Æd·Å¶¹kµ›Ö:֛´·º¹k½¾¼¾¶ÜÊgâÁ·Ç²›½¾¶ ÂÇ´#¶Ç´#¹kÂÇԊ²CÚ   
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