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In a multiple-message broadcast, an arbitrary number of messages originate at arbitrary nodes in the network at arbitrary times. The problem is to disseminate all these messages to the whole network. This paper gives the first randomized distributed multiple-message broadcast algorithm with worst-case performance guarantee in wireless ad hoc networks employing the SINR interference model which takes interferences from all the nodes in the network into account. The network model used in this paper also considers the harsh characteristics of wireless ad hoc networks: there is no prior structure, and nodes cannot perform collision detection and have little knowledge of the network topology. Under all these restrictions, our proposed randomized distributed multiple-message broadcast protocol can deliver any message m to all nodes in the network in O ( D + k + log 2 ⁡ n ) timeslots with high probability, where D is the network diameter, k is the number of messages whose broadcasts overlap with m , and n is the number of nodes in the network. We also study the lower bound for randomized distributed multiple-message broadcast protocols. In particular, we prove that any uniform randomized algorithm needs Ω ( D + k + log 2 ⁡ n log ⁡ log ⁡ log ⁡ n ) timeslots to disseminate k messages initially stored at k nodes. [ABSTRACT FROM AUTHOR]

In multi-hop radio networks, such as wireless ad-hoc networks and wireless sensor networks, nodes employ a MAC (Medium Access Control) protocol such as TDMA to coordinate accesses to the shared medium and to avoid interference of close-by transmissions. These protocols can be implemented using standard node coloring. The ( Δ + 1 ) -coloring problem is to color all nodes in as few timeslots as possible using at most Δ + 1 colors such that any two nodes within distance R are assigned different colors, where R is a given parameter and Δ is the maximum degree of the modeled unit disk graph using R as a scaling factor. Being one of the most fundamental problems in distributed computing, this problem is well studied and there is a long chain of algorithms prescribed for it. However, all previous works are based on abstract models, such as message passing models and graph based interference models, which limit the utility of these algorithms in practice. In this paper, for the first time, we consider the distributed ( Δ + 1 ) -coloring problem under the more practical SINR interference model. In particular, without requiring any knowledge about the neighborhood, we propose a novel randomized ( Δ + 1 ) -coloring algorithm with time complexity O ( Δ log ⁡ n + log 2 ⁡ n ) . For the case where nodes cannot adjust their transmission power, we give an O ( Δ log 2 ⁡ n ) randomized algorithm, which only incurs a logarithmic multiplicative factor overhead. [ABSTRACT FROM AUTHOR]

Abstract: Acyclic coloring problem is a specialized problem that arises in the efficient computation of Hessians. A proper edge coloring of a graph is called acyclic if there is no -colored cycle in . The acyclic edge chromatic number of is the least number of colors in an acyclic edge coloring of . Alon et al. conjectured that . In this paper, we consider the sufficient conditions for the planar graphs satisfying and . [Copyright &y& Elsevier]

Abstract: Given a universe containing elements and a collection of multisets or sets over , the multiset multicover (MSMC) problem or the set multicover (SMC) problem is to cover all elements at least a number of times as specified in their coverage requirements with the minimum number of multisets or sets. In this paper, we give various exact algorithms for these two problems with or without constraints on the number of times a multiset or set may be chosen. First, we show that the MSMC without multiplicity constraints problem can be solved in time and polynomial space, where is the maximum coverage requirement and denotes the total number of given multisets over . (The notation suppresses a factor polynomial in .) To our knowledge, this is the first known exact algorithm for the MSMC without multiplicity constraints problem. Second, by combining dynamic programming and the inclusion–exclusion principle, we can exactly solve the SMC without multiplicity constraints problem in time. Compared with two recent results, in [Q.-S. Hua, Y. Wang, D. Yu, F.C.M. Lau, Set multi-covering via inclusion–exclusion, Theoretical Computer Science, 410 (38–40) (2009) 3882–3892] and [J. Nederlof, Inclusion exclusion for hard problems, Master Thesis, Utrecht University, The Netherlands, 2008], respectively, ours is the fastest exact algorithm for the SMC without multiplicity constraints problem. Finally, by directly using dynamic programming, we give the first known exact algorithm for the MSMC or the SMC with multiplicity constraints problem in time and space. This algorithm can also be easily adapted as a constructive algorithm for the MSMC without multiplicity constraints problem. [Copyright &y& Elsevier]

Abstract: Set multi-covering is a generalization of the set covering problem where each element may need to be covered more than once and thus some subset in the given family of subsets may be picked several times for minimizing the number of sets to satisfy the coverage requirement. In this paper, we propose a family of exact algorithms for the set multi-covering problem based on the inclusion–exclusion principle. The presented ESMC (Exact Set Multi-Covering) algorithm takes time and space where is the maximum value in the coverage requirement set (The notation omits a factor). We also propose the other three exact algorithms through different tradeoffs of the time and space complexities. To the best of our knowledge, this present paper is the first one to give exact algorithms for the set multi-covering problem with nontrivial time and space complexities. This paper can also be regarded as a generalization of the exact algorithm for the set covering problem given in [A. Björklund, T. Husfeldt, M. Koivisto, Set partitioning via inclusion–exclusion, SIAM Journal on Computing, in: FOCS 2006 (in press, special issue)]. [Copyright &y& Elsevier]

Given a seller with k types of items and n single-minded buyers, i.e., each buyer is only interested in a particular bundle of items, to maximize the revenue, the seller must assign some amount of bundles to each buyer with respect to the buyer's accepted price. Each buyer b i is associated with a value function v i (⋅) such that v i (x) is the accepted unit bundle price b i is willing to pay for x bundles. In this paper, we assume that bundles can be sold fractionally. The single-minded item selling problem is proved to be NP-hard. Moreover, we give an O (k) -approximation algorithm. For the online version, i.e., buyers come one by one and the decision must be made immediately on the arrival of each buyer, an O (k ⋅ (log ⁡ h + log ⁡ k)) -competitive algorithm is given, where h is the highest unit item price among all buyers. [ABSTRACT FROM AUTHOR]