TY - GEN

T1 - Deterministic stateless centralized local algorithms for bounded degree graphs

AU - Even, Guy

AU - Medina, Moti

AU - Ron, Dana

PY - 2014/1/1

Y1 - 2014/1/1

N2 - We design centralized local algorithms for: maximal independent set, maximal matching, and graph coloring. The improvement is threefold: the algorithms are deterministic, stateless, and the number of probes is O(log* n), where n is the number of vertices of the input graph. Our algorithms for maximal independent set and maximal matching improves over previous randomized algorithms by Alon et al. (SODA 2012) and Mansour et al. (ICALP 2012). In these previous algorithms, the number of probes and the space required for storing the state between queries are poly(logn). We also design the first centralized local algorithm for graph coloring. Our graph coloring algorithms are deterministic and stateless. Let Δ denote the maximum degree of a graph over n vertices. Our algorithm for coloring the vertices by Δ+1 colors requires O(log* n) probes for constant degree graphs. Surprisingly, for the case where the number of colors is O(Δ2 logΔ), the number of probes of our algorithm is O(Δ· log* n+Δ2), that is, the number of probes is sublinear if Δ =o9√n), i.e., our algorithm applies for graphs with unbounded degrees.

AB - We design centralized local algorithms for: maximal independent set, maximal matching, and graph coloring. The improvement is threefold: the algorithms are deterministic, stateless, and the number of probes is O(log* n), where n is the number of vertices of the input graph. Our algorithms for maximal independent set and maximal matching improves over previous randomized algorithms by Alon et al. (SODA 2012) and Mansour et al. (ICALP 2012). In these previous algorithms, the number of probes and the space required for storing the state between queries are poly(logn). We also design the first centralized local algorithm for graph coloring. Our graph coloring algorithms are deterministic and stateless. Let Δ denote the maximum degree of a graph over n vertices. Our algorithm for coloring the vertices by Δ+1 colors requires O(log* n) probes for constant degree graphs. Surprisingly, for the case where the number of colors is O(Δ2 logΔ), the number of probes of our algorithm is O(Δ· log* n+Δ2), that is, the number of probes is sublinear if Δ =o9√n), i.e., our algorithm applies for graphs with unbounded degrees.

KW - Centralized Local Algorithms

KW - Graph Algorithms

KW - Sublinear Approximation Algorithms

UR - http://www.scopus.com/inward/record.url?scp=84958528133&partnerID=8YFLogxK

U2 - 10.1007/978-3-662-44777-2_33

DO - 10.1007/978-3-662-44777-2_33

M3 - Conference contribution

AN - SCOPUS:84958528133

SN - 9783662447765

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 394

EP - 405

BT - Algorithms, ESA 2014 - 22nd Annual European Symposium, Proceedings

PB - Springer Verlag

T2 - 22nd Annual European Symposium on Algorithms, ESA 2014

Y2 - 8 September 2014 through 10 September 2014

ER -