TY - GEN

T1 - Multiply balanced k∈-partitioning

AU - Amir, Amihood

AU - Ficler, Jessica

AU - Krauthgamer, Robert

AU - Roditty, Liam

AU - Sar Shalom, Oren

PY - 2014

Y1 - 2014

N2 - The problem of partitioning an edge-capacitated graph on n vertices into k balanced parts has been amply researched. Motivated by applications such as load balancing in distributed systems and market segmentation in social networks, we propose a new variant of the problem, called Multiply Balanced k Partitioning, where the vertex-partition must be balanced under d vertex-weight functions simultaneously. We design bicriteria approximation algorithms for this problem, i.e., they partition the vertices into up to k parts that are nearly balanced simultaneously for all weight functions, and their approximation factor for the capacity of cut edges matches the bounds known for a single weight function times d. For the case where d = 2, for vertexweights that are integers bounded by a polynomial in n and any fixed ∈ > 0, we obtain a (2+∈, O( √ log n log k))-bicriteria approximation, namely, we partition the graph into parts whose weight is at most 2+∈ times that of a perfectly balanced part (simultaneously for both weight functions), and whose cut capacity is O( √ log n log k) OPT. For unbounded (exponential) vertex weights, we achieve approximation (3, O(log n)). Our algorithm generalizes to d weight functions as follows: For vertex weights that are integers bounded by a polynomial in n and any fixed ∈ > 0, we obtain a (2d + ∈, O(√ log n log k))-bicriteria approximation. For unbounded (exponential) vertex weights, we achieve approximation (2d + 1, O(d log n)).

AB - The problem of partitioning an edge-capacitated graph on n vertices into k balanced parts has been amply researched. Motivated by applications such as load balancing in distributed systems and market segmentation in social networks, we propose a new variant of the problem, called Multiply Balanced k Partitioning, where the vertex-partition must be balanced under d vertex-weight functions simultaneously. We design bicriteria approximation algorithms for this problem, i.e., they partition the vertices into up to k parts that are nearly balanced simultaneously for all weight functions, and their approximation factor for the capacity of cut edges matches the bounds known for a single weight function times d. For the case where d = 2, for vertexweights that are integers bounded by a polynomial in n and any fixed ∈ > 0, we obtain a (2+∈, O( √ log n log k))-bicriteria approximation, namely, we partition the graph into parts whose weight is at most 2+∈ times that of a perfectly balanced part (simultaneously for both weight functions), and whose cut capacity is O( √ log n log k) OPT. For unbounded (exponential) vertex weights, we achieve approximation (3, O(log n)). Our algorithm generalizes to d weight functions as follows: For vertex weights that are integers bounded by a polynomial in n and any fixed ∈ > 0, we obtain a (2d + ∈, O(√ log n log k))-bicriteria approximation. For unbounded (exponential) vertex weights, we achieve approximation (2d + 1, O(d log n)).

UR - http://www.scopus.com/inward/record.url?scp=84899906740&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-54423-1_51

DO - 10.1007/978-3-642-54423-1_51

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AN - SCOPUS:84899906740

SN - 9783642544224

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

SP - 586

EP - 597

BT - LATIN 2014

PB - Springer Verlag

T2 - 11th Latin American Theoretical Informatics Symposium, LATIN 2014

Y2 - 31 March 2014 through 4 April 2014

ER -