Computing with Advice: when Knowledge Helps

In several areas of computer science the possibility and efficiency of the solution is determined by information that is not accessible to the algorithm. Traditionally, a qualitative approach to the study of this information has been pursued, in which the impact of enhancing the algorithm with various specific types of information has been studied. Recently, a number of authors have proposed a quantitative approach, where the amount of the added information is studied in relation with the improvement of the quality or efficiency of the solution. We survey several recent examples of this approach from the area of distributed and online computing.

[1]  Daniel J. Rosenkrantz,et al.  An Analysis of Several Heuristics for the Traveling Salesman Problem , 1977, SIAM J. Comput..

[2]  Andrzej Pelc,et al.  Deterministic Rendezvous in Graphs , 2003, ESA.

[3]  Allan Borodin,et al.  Competitive Paging with Locality of Reference (Preliminary Version) , 1991, Symposium on the Theory of Computing.

[4]  Yuichi Asahiro,et al.  Weighted nearest neighbor algorithms for the graph exploration problem on cycles , 2010, Inf. Process. Lett..

[5]  Joseph Naor,et al.  A Polylogarithmic-Competitive Algorithm for the k-Server Problem , 2011, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science.

[6]  Sandy Irani,et al.  Strongly competitive algorithms for paging with locality of reference , 1992, SODA '92.

[7]  Robert E. Tarjan,et al.  Amortized efficiency of list update and paging rules , 1985, CACM.

[8]  Susanne Albers,et al.  On the Influence of Lookahead in Competitive Paging Algorithms , 1997, Algorithmica.

[9]  Ueli Maurer.  On the oracle complexity of factoring integers , 2005, computational complexity.

[10]  Nicola Santoro,et al.  Black hole search in common interconnection networks , 2006, Networks.

[11]  David Ilcinkas,et al.  Setting port numbers for fast graph exploration , 2006, Theor. Comput. Sci..

[12]  Bernard Mans,et al.  Sense of direction in distributed computing , 2003, Theor. Comput. Sci..

[13]  Bernard Mans,et al.  On the Impact of Sense of Direction on Message Complexity , 1997, Inf. Process. Lett..

[14]  Gerhard J. Woeginger,et al.  On the nearest neighbor rule for the traveling salesman problem , 2004, Oper. Res. Lett..

[15]  Sebastian Seibert,et al.  Advice Complexity of the Online Coloring Problem , 2013, CIAC.

[16]  Lali Barrière,et al.  Rendezvous and Election of Mobile Agents: Impact of Sense of Direction , 2007, Theory of Computing Systems.

[17]  David Peleg,et al.  Distributed Computing: A Locality-Sensitive Approach , 1987 .

[18]  Allan Borodin,et al.  Online computation and competitive analysis , 1998 .

[19]  Xiaohui Zhang,et al.  Fast periodic graph exploration with constant memory , 2007, J. Comput. Syst. Sci..

[20]  Pierre Fraigniaud.  Informative Labeling Schemes , 2010, ICALP.

[21]  Stefan Dobrev,et al.  Broadcasting on Anonymous Unoriented Tori , 1998, WG.

[22]  Pierre Fraigniaud,et al.  Local MST Computation with Short Advice , 2007, SPAA '07.

[23]  Andrzej Pelc,et al.  Drawing maps with advice , 2010, J. Parallel Distributed Comput..

[24]  Jérémie Chalopin,et al.  Rendezvous of Mobile Agents in Directed Graphs , 2010, DISC.

[25]  Michal Forisek,et al.  Advice Complexity of Online Coloring for Paths , 2012, LATA.

[26]  Reza Dorrigiv,et al.  On the Advice Complexity of Buffer Management , 2012, ISAAC.

[27]  Monika Steinová,et al.  On the Power of Local Orientations , 2008, SIROCCO.

[28]  Lothar Budach,et al.  Environments, Labyrinths and Automata , 1977, FCT.

[29]  David Peleg,et al.  Constructing Labeling Schemes Through Universal Matrices , 2006, ISAAC.

[30]  Nicolas Nisse,et al.  Graph searching with advice , 2009, Theor. Comput. Sci..

[31]  Andrzej Pelc,et al.  Distributed computing with advice: information sensitivity of graph coloring , 2007, Distributed Computing.

[32]  Susanne Albers,et al.  Exploring Unknown Environments , 2000, SIAM J. Comput..

[33]  Lothar Budach,et al.  On Universal Traps , 1979, J. Inf. Process. Cybern..

[34]  Dennis Komm,et al.  Advice Complexity and Barely Random Algorithms , 2011, RAIRO Theor. Informatics Appl..

[35]  Juraj Hromkovic,et al.  On the Advice Complexity of the Online L(2, 1)-Coloring Problem on Paths and Cycles , 2013, COCOON.

[36]  Euripides Markou,et al.  Online Graph Exploration with Advice , 2012, SIROCCO.

[37]  Kurt Mehlhorn,et al.  Online graph exploration: New results on old and new algorithms , 2012, Theor. Comput. Sci..

[38]  Dennis Komm,et al.  On the Advice Complexity of the Set Cover Problem , 2012, CSR.

[39]  Yasuo Okabe,et al.  The Online Graph Exploration Problem on Restricted Graphs , 2009, IEICE Trans. Inf. Syst..

[40]  David Peleg,et al.  A Near-Tight Lower Bound on the Time Complexity of Distributed Minimum-Weight Spanning Tree Construction , 2000, SIAM J. Comput..

[41]  Dennis Komm,et al.  On the Advice Complexity of Online Problems , 2009, ISAAC.

[42]  Rudolf Fleischer,et al.  Exploring an Unknown Graph Efficiently , 2005, ESA.

[43]  Nicola Santoro,et al.  Map construction of unknown graphs by multiple agents , 2007, Theor. Comput. Sci..

[44]  Neil Robertson,et al.  Graph Minors .XIII. The Disjoint Paths Problem , 1995, J. Comb. Theory B.

[45]  Andrzej Pelc,et al.  Graph exploration by a finite automaton , 2005, Theor. Comput. Sci..

[46]  Dennis Komm,et al.  The string guessing problem as a method to prove lower bounds on the advice complexity , 2013, Theor. Comput. Sci..

[47]  Stefan Dobrev,et al.  Independent Set with Advice: The Impact of Graph Knowledge - (Extended Abstract) , 2012, WAOA.

[48]  Amos Fiat,et al.  Competitive Paging Algorithms , 1991, J. Algorithms.

[49]  Andrzej Pelc,et al.  Impact of topographic information on graph exploration efficiency , 2000, Networks.

[50]  Andrzej Pelc,et al.  Exploring unknown undirected graphs , 1999, SODA '98.

[51]  Eli Upfal,et al.  Can entropy characterize performance of online algorithms? , 2001, SODA '01.

[52]  Alfredo Navarra,et al.  Graph Decomposition for Memoryless Periodic Exploration , 2011, Algorithmica.

[53]  Stefan Dobrev,et al.  Measuring the problem-relevant information in input , 2009, RAIRO Theor. Informatics Appl..

[54]  Andrzej Pelc,et al.  Trade-offs Between the Size of Advice and Broadcasting Time in Trees , 2008, SPAA '08.

[55]  Krzysztof Diks,et al.  Broadcasting in Unlabeled Hypercubes with a Linear Number of Messages , 1998, Inf. Process. Lett..

[56]  Yang Xiang,et al.  Additive Spanners and Distance and Routing Labeling Schemes for Hyperbolic Graphs , 2010, Algorithmica.

[57]  Kunihiko Sadakane,et al.  Finding Short Right-Hand-on-the-Wall Walks in Graphs , 2005, SIROCCO.

[58]  Shay Kutten,et al.  Proof labeling schemes , 2005, PODC '05.

[59]  Nicola Santoro,et al.  Searching for a black hole in arbitrary networks: optimal mobile agents protocols , 2006, Distributed Computing.

[60]  Xiaotie Deng,et al.  Exploring an unknown graph , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[61]  Andrzej Pelc,et al.  Fast radio broadcasting with advice , 2008, Theor. Comput. Sci..

[62]  Reuven Cohen,et al.  Labeling Schemes for Tree Representation , 2007, Algorithmica.

[63]  Lucia Keller,et al.  Online Coloring of Bipartite Graphs with and without Advice , 2012, Algorithmica.

[64]  Bala Kalyanasundaram,et al.  Constructing Competitive Tours from Local Information , 1993, Theor. Comput. Sci..

[65]  Reuven Cohen,et al.  Label-guided graph exploration by a finite automaton , 2005, TALG.

[66]  Jurek Czyzowicz,et al.  Black Hole Search in Directed Graphs , 2009, SIROCCO.

[67]  Dariusz R. Kowalski,et al.  How to meet in anonymous network , 2006, Theor. Comput. Sci..

[68]  Andrzej Pelc,et al.  Oracle size: a new measure of difficulty for communication tasks , 2006, PODC '06.

[69]  Andrzej Pelc,et al.  Tree exploration with advice , 2008, Inf. Comput..

[70]  Baruch Awerbuch,et al.  A trade-off between information and communication in broadcast protocols , 1990, JACM.

[71]  Juraj Hromkovic,et al.  On the advice complexity of the online L(2, 1)-coloring problem on paths and cycles , 2013, Theor. Comput. Sci..

[72]  G. Rosen.  Cybernetics. Circular Causal and Feedback Mechanisms in Biological and Social Systems , 1952 .

[73]  Magnús M. Halldórsson,et al.  Online independent sets , 2000, Theor. Comput. Sci..

[74]  Christian Schindelhauer,et al.  Why Robots Need Maps , 2007, SIROCCO.

[75]  Lothar Budach,et al.  On the Solution of the Labyrinth Problem for Finite Automata , 1975, J. Inf. Process. Cybern..

[76]  Amos Korman,et al.  Labeling schemes for vertex connectivity , 2007, TALG.

[77]  Paul D. Seymour,et al.  Graph Minors: XV. Giant Steps , 1996, J. Comb. Theory, Ser. B.

[78]  Dennis Komm,et al.  On the Advice Complexity of the Knapsack Problem , 2012, LATIN.

[79]  Pierre Fraigniaud,et al.  Online computation with advice , 2009, Theor. Comput. Sci..

[80]  Michael A. Bender,et al.  The power of team exploration: two robots can learn unlabeled directed graphs , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.