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Atomic routing games on maximum congestion
 In Proceedings of the Second Internation Conference on Algorithmic Aspects of Information and Management
, 2006
"... We study atomic routing congestion games in which each player chooses a path in the network from its strategy set (a collection of paths) with the objective to minimize the maximum congestion along any edge on its selected path. The social cost is the global maximum congestion on any edge in the net ..."
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Cited by 12 (4 self)
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We study atomic routing congestion games in which each player chooses a path in the network from its strategy set (a collection of paths) with the objective to minimize the maximum congestion along any edge on its selected path. The social cost is the global maximum congestion on any edge in the network. We show that for arbitrary routing games, the price of stability is 1, and the price of anarchy, PoA, is bounded by κ − 1 ≤ PoA ≤ c(κ 2 + log 2 n), where κ is the length of the longest cycle in the network, n is the size of the network and c is a constant. Further, any best response dynamic converges to a Nash equilibrium. Our bounds show that for maximum congestion games, the topology of the network, in particular the length of cycles, plays an important role in determining the quality of the Nash equilibria. A fundamental issue in the management of large scale communication networks is to route the packet traffic so as to optimize the network performance. Our measure of network performance is the worst bottleneck (most used link) in the system. The model we use for network traffic is that of finite, unsplittable packets (atomic flow), and each packet’s path is controlled independently
Õ(Congestion + Dilation) hotpotato routing on leveled networks
 In Proceedings of the Fourteenth ACM Symposium on Parallel Algorithms and Architectures
, 2002
"... We study packet routing problems, in which we are given a set of N packets which will be sent on preselected paths with congestion C and dilation D. For storeandforward routing, in which nodes have buffers for packets in transit, there are routing algorithms with performance that matches the lower ..."
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Cited by 11 (8 self)
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We study packet routing problems, in which we are given a set of N packets which will be sent on preselected paths with congestion C and dilation D. For storeandforward routing, in which nodes have buffers for packets in transit, there are routing algorithms with performance that matches the lower bound Ω(C + D). Motivated from optical networks, we study hotpotato routing in which the nodes are bufferless. Due to the lack of buffers, in hotpotato routing the packets may be delayed more than in storeandforward routing. An interesting question is how much is the performance of routing algorithms affected from the absence of buffers. Here, we answer this question for the class of leveled networks, in which the nodes are partitioned into L + 1 distinct levels. We present a randomized hotpotato routing algorithm for leveled networks, which routes the packets in O((C +L) ln 9 (LN)) time with high probability. For routing problems with dilation Ω(L), and where N is a polynonial in L, this bound is within polylogarithmic factors of the lower bound Ω(C + L). Our algorithm demonstrates that for such routing problems the benefit from using buffers is no more than polylogarithmic; thus, hotpotato routing is an efficient way to route packets in leveled networks. In hotpotato routing, due to the lack of buffers, the packets may not be able to remain on their preselected paths during the course of routing (while in storeandforward routing the packets remain on their preselected paths). However, in our algorithm the actual path that each packet follows contains its original preselected path; thus the lower bound Ω(C + L) is also a lower bound for the new paths. Our algorithm is distributed, that is, routing decisions are taken locally at each node while packets are routed in the network. To our knowledge, this is the first hotpotato algorithm designed and analyzed, in terms of congestion and dilation, for leveled networks.
Direct routing: Algorithms and Complexity
 In Proceedings of the 12th Annual European Symposium on Algorithms (ESA
, 2004
"... Direct routing is the special case of bufferless routing where N packets, once injected into the network, must be delivered to their destinations without collisions. We give a general treatment of three facets of direct routing: (i) Algorithms. We present a polynomial time greedy direct algorithm wh ..."
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Cited by 6 (3 self)
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Direct routing is the special case of bufferless routing where N packets, once injected into the network, must be delivered to their destinations without collisions. We give a general treatment of three facets of direct routing: (i) Algorithms. We present a polynomial time greedy direct algorithm which is worstcase optimal. We improve the bound of the greedy algorithm for special cases, by applying variants of the this algorithm to commonly used network topologies. In particular, we obtain nearoptimal routing time for the tree, mesh, butterfly and hypercube. (ii) Complexity. By a reduction from Vertex Coloring, we show that optimal Direct Routing is inapproximable, unless P=NP. (iii) Lower Bounds for Buffering. We show that certain direct routing problems cannot be solved efficiently; in order to solve these problems, any routing algorithm needs buffers. We give nontrivial lower bounds on such buffering requirements for general routing algorithms.
Efficient Bufferless Packet Switching on Trees and Leveled Networks ∗
"... In bufferless networks the packets cannot be buffered while they are in transit; thus, once injected, the packets have to move constantly. Bufferless networks are interesting because they model optical networks. We consider the tree and leveled network topologies, which represent a wide class of net ..."
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Cited by 2 (0 self)
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In bufferless networks the packets cannot be buffered while they are in transit; thus, once injected, the packets have to move constantly. Bufferless networks are interesting because they model optical networks. We consider the tree and leveled network topologies, which represent a wide class of network configurations. On these networks, we study manytoone batch problems where each node is the source of at most one packet, and the destination of an arbitrary number of packets. Each packet is to follow a preselected path from the source to the destination. Let T ∗ be the optimal delivery time for the packets. We have the following results: • For trees, we present two bufferless algorithms: (i) a deterministic algorithm with delivery time O(δ · T ∗ · log n), and (ii) a randomized algorithm with delivery time O(T ∗ · log 2 n); where, δ is the maximum node degree, and n is the number of nodes. Both algorithms are distributed in the sense that packet forwarding decisions are made locally at the nodes. • For leveled networks, we present two algorithms: (i) a centralized algorithm with
UNIVERSAL BUFFERLESS PACKET SWITCHING ∗
"... Abstract. A packetswitching algorithm specifies the actions of the nodes in order to deliver packets in the network. A packetswitching algorithm is universal if it applies to any network topology and for any batch communication problem on the network. A long standing open problem has concerned the ..."
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Abstract. A packetswitching algorithm specifies the actions of the nodes in order to deliver packets in the network. A packetswitching algorithm is universal if it applies to any network topology and for any batch communication problem on the network. A long standing open problem has concerned the existence of a universal packetswitching algorithm with near optimal performance guarantees for the class of bufferless networks where the buffer size for packets in transit is zero. We give a positive answer to this question. In particular, we give a universal bufferless algorithm which is within a polylogarithmic factor from optimal for arbitrary batch problems: T = O ` T ∗ · log 3 (n + N) ´, where T is the packet delivery time of our algorithm, T ∗ is the optimal delivery time, n is the size of the network, and N is the number of packets. At the heart of our result is a new deterministic technique for constructing a universal bufferless algorithm by emulating a storeandforward algorithm on a transformation of the network. The main idea is to replace packet buffering in the transformed network with packet circulation in regions of the original network. The cost of the emulation on the packet delivery time is proportional to the buffer sizes used by the storeandforward algorithm. We obtain the advertised result by using a storeandforward algorithm with logarithmic sized buffers. The resulting bufferless algorithm is constructive and it can be implemented in a distributed way.
Quality of Routing Congestion Games in Wireless Sensor Networks (Invited Paper)
"... We consider congestion games in wireless sensor networks that offer quantitatively distinct classes of routing paths. Each routing class is characterized by a service cost. Within a routing class, the maximum link congestion is also an important metric for measuring the quality of the paths. Here, w ..."
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We consider congestion games in wireless sensor networks that offer quantitatively distinct classes of routing paths. Each routing class is characterized by a service cost. Within a routing class, the maximum link congestion is also an important metric for measuring the quality of the paths. Here, we study routing games where each player i selfishly selects a path with a respective routing class that simultaneously minimizes its maximum edge congestion Ci and service cost Si, in other words minimizes Ci+Si. We examine the quality of Nashequilibria and prove that the price of stability is 1. The price of anarchy is bounded above by min(C∗, S∗) ·m logn, where m is the number of routing classes, n is the size of the graph, and C ∗ and S ∗ are the optimal coordinated congestion and service costs. Thus, under certain circumstances, the player’s selfishness does not hurt the social welfare and actually the equilibria can give good approximations for the coordinated optimal social cost. Categories and Subject Descriptors C.2.2 [Computercommunication networks]: Network
VIRTUAL CHANNELS IN WORMHOLE ROUTERS
, 1999
"... This paper analyzes the impact of virtual channels on the performance of wormhole routing algorithms. We study wormhole routing on network in which each physical channel, i.e., communication link, can support up to B virtual channels. We show that it is possible to route any set of messages with L f ..."
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This paper analyzes the impact of virtual channels on the performance of wormhole routing algorithms. We study wormhole routing on network in which each physical channel, i.e., communication link, can support up to B virtual channels. We show that it is possible to route any set of messages with L flits each, whose paths have congestion C and dilation D in O((L+ D) C(D log D) 1 B B) flit steps, where a flit step is the time taken to transmit B flits, i.e., one flit per virtual channel, across a physical channel. We also prove a nearly matching lower bound; i.e., for any values of C, D, B, and L, where C, D B+1 and L=(1+0(1)) D, we show how to construct a network and a set of Lflit messages whose paths have congestion C and dilation D that require 0(LCD 1 B B) flit steps to route. These upper and lower bounds imply that increasing the buffering capacity and the bandwidth of each physical channel by a factor of B can speed up a wormhole routing algorithm by a superlinear factor, i.e., a factor significantly larger than B. We also present a simple randomized wormhole routing algorithm for the butterfly network. The algorithm routes any qrelation on the inputs and outputs