We consider the problem of covering multiple submodular constraints. Given a finite ground set
 Home
 Search Results
 Page 1 of 1
Search for: All records

Total Resources1
 Resource Type

00010
 Availability

10
 Author / Contributor
 Filter by Author / Creator


Chekuri, Chandra (1)

Inamdar, Tanmay (1)

Quanrud, Kent (1)

Varadarajan, Kasturi (1)

Zhang, Zhao (1)

#Tyler Phillips, Kenneth E. (0)

#Willis, Ciara (0)

& AbreuRamos, E. D. (0)

& Abramson, C. I. (0)

& AbreuRamos, E. D. (0)

& Adams, S.G. (0)

& Ahmed, K. (0)

& Ahmed, Khadija. (0)

& Aina, D.K. Jr. (0)

& AkcilOkan, O. (0)

& Akuom, D. (0)

& Aleven, V. (0)

& AndrewsLarson, C. (0)

& Archibald, J. (0)

& Arnett, N. (0)

 Filter by Editor


& Spizer, S. M. (0)

& . Spizer, S. (0)

& Ahn, J. (0)

& Bateiha, S. (0)

& Bosch, N. (0)

& Brennan K. (0)

& Brennan, K. (0)

& Chen, B. (0)

& Chen, Bodong (0)

& Drown, S. (0)

& Ferretti, F. (0)

& Higgins, A. (0)

& J. Peters (0)

& Kali, Y. (0)

& RuizArias, P.M. (0)

& S. Spitzer (0)

& Sahin. I. (0)

& Spitzer, S. (0)

& Spitzer, S.M. (0)

(submitted  in Review for IEEE ICASSP2024) (0)


Have feedback or suggestions for a way to improve these results?
!
Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher.
Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?
Some links on this page may take you to nonfederal websites. Their policies may differ from this site.

Abstract N , a weight function ,$$w: N \rightarrow \mathbb {R}_+$$ $w:N\to {R}_{+}$r monotone submodular functions over$$f_1,f_2,\ldots ,f_r$$ ${f}_{1},{f}_{2},\dots ,{f}_{r}$N and requirements the goal is to find a minimum weight subset$$k_1,k_2,\ldots ,k_r$$ ${k}_{1},{k}_{2},\dots ,{k}_{r}$ such that$$S \subseteq N$$ $S\subseteq N$ for$$f_i(S) \ge k_i$$ ${f}_{i}\left(S\right)\ge {k}_{i}$ . We refer to this problem as$$1 \le i \le r$$ $1\le i\le r$MultiSubmodCover and it was recently considered by HarPeled and Jones (Few cuts meet many point sets. CoRR.arxiv:abs1808.03260 HarPeled and Jones 2018) who were motivated by an application in geometry. Even with$$r=1$$ $r=1$MultiSubmodCover generalizes the wellknown Submodular Set Cover problem (SubmodSC ), and it can also be easily reduced toSubmodSC . A simple greedy algorithm gives an approximation where$$O(\log (kr))$$ $O(log(kr\left)\right)$ and this ratio cannot be improved in the general case. In this paper, motivated by several concrete applications, we consider two ways to improve upon the approximation given by the greedy algorithm. First, we give a bicriteria approximation algorithm for$$k = \sum _i k_i$$ $k={\sum}_{i}{k}_{i}$MultiSubmodCover that covers each constraint to within a factor of while incurring an approximation of$$(11/e\varepsilon )$$ $(11/e\epsilon )$ in the cost. Second, we consider the special case when each$$O(\frac{1}{\epsilon }\log r)$$ $O(\frac{1}{\u03f5}logr)$ is a obtained from a truncated coverage function and obtain an algorithm that generalizes previous work on partial set cover ($$f_i$$ ${f}_{i}$PartialSC ), covering integer programs (CIPs ) and multiple vertex cover constraints Bera et al. (Theoret Comput Sci 555:2–8 Bera et al. 2014). Both these algorithms are based on mathematical programming relaxations that avoid the limitations of the greedy algorithm. We demonstrate the implications of our algorithms and related ideas to several applications ranging from geometric covering problems to clustering with outliers. Our work highlights the utility of the highlevel model and the lens of submodularity in addressing this class of covering problems.