Graphs

Shortest-path queries in static networks. We consider the point-to-point (approximate) shortest-path query problem, which is the following generalization of the classical single-source (SSSP) and all-pairs shortest-path (APSP) problems: we are first presented with a network (graph). A so-called preprocessing algorithm may compute certain information (a data structure or index) to prepare for the next phase. After this preprocessing step, applications may ask shortest-path or distance queries, which should be answered as fast as possible. Due to its many applications in areas such as transportation, networking, and social science, this problem has been considered by researchers from various communities (sometimes under different names): algorithm engineers construct fast route planning methods; database and information systems researchers investigate materialization tradeoffs, query processing on spatial networks, and reachability queries; and theoretical computer scientists analyze distance oracles and sparse spanners. Related problems are considered for compact routing and distance labeling schemes in networking and distributed computing and for metric embeddings in geometry as well. In this survey, we review selected approaches, algorithms, and results on shortest-path queries from these fields, with the main focus lying on the tradeoff between the index size and the query time. We survey methods for general graphs as well as specialized methods for restricted graph classes, in particular for those classes with arguable practical significance such as planar graphs and complex networks.


References in zbMATH (referenced in 109 articles , 1 standard article )

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  1. Bresler, Guy: Efficiently learning Ising models on arbitrary graphs (extended abstract) (2015)
  2. Canetti, Ran; Holmgren, Justin; Jain, Abhishek; Vaikuntanathan, Vinod: Succinct garbling and indistinguishability obfuscation for RAM programs (2015)
  3. Chan, Timothy M.; Lewenstein, Moshe: Clustered integer 3SUM via additive combinatorics (2015)
  4. Chawla, Shuchi; Makarychev, Konstantin; Schramm, Tselil; Yaroslavtsev, Grigory: Near optimal LP rounding algorithm for correlation clustering on complete and complete (k)-partite graphs (2015)
  5. Chechik, Shiri: Approximate distance oracles with improved bounds (2015)
  6. Chen, Xi; De, Anindya; Servedio, Rocco A.; Tan, Li-Yang: Boolean function monotonicity testing requires (almost) (n^1/2) non-adaptive queries (2015)
  7. Chen, Xi; Durfee, David; Orfanou, Anthi: On the complexity of Nash equilibria in anonymous games (2015)
  8. Chen, Zitan; Jaggi, Sidharth; Langberg, Michael: A characterization of the capacity of online (causal) binary channels (2015)
  9. Christiani, Tobias; Pagh, Rasmus; Thorup, Mikkel: From independence to expansion and back again (2015)
  10. Chuzhoy, Julia: Excluded grid theorem: improved and simplified (2015)
  11. Cohen, Michael B.; Elder, Sam; Musco, Cameron; Musco, Christopher; Persu, Madalina: Dimensionality reduction for (k)-means clustering and low rank approximation (2015)
  12. Cohen, Michael B.; Peng, Richard: (\ell_p) row sampling by Lewis weights (2015)
  13. Cole, Richard; Gkatzelis, Vasilis: Approximating the Nash social welfare with indivisible items (2015)
  14. Cousins, Benjamin; Vempala, Santosh: Bypassing KLS: Gaussian cooling and an (O^\ast(n^3)) volume algorithm (2015)
  15. Czumaj, Artur: Random permutations using switching networks (2015)
  16. Czumaj, Artur; Peng, Pan; Sohler, Christian: Testing cluster structure of graphs (2015)
  17. Daniely, Amit; Schapira, Michael; Shahaf, Gal: Inapproximability of truthful mechanisms via generalizations of the VC dimension (2015)
  18. Ding, Jian; Sly, Allan; Sun, Nike: Proof of the satisfiability conjecture for large (k) (2015)
  19. Dinur, Irit; Harsha, Prahladh; Kindler, Guy: Polynomially low error PCPs with (\operatornamepolyloglogn) queries via modular composition (2015)
  20. Dvir, Zeev; Gopi, Sivakanth: 2-server PIR with sub-polynomial communication (2015)